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Short course on principles and applications of beach nourishment, July 10, 1989

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Title:
Short course on principles and applications of beach nourishment, July 10, 1989
Series Title:
UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 89/018
Creator:
Campbell, Thomas
Dean, Robert G.
Mehta, Ashish J.
Wang, Hsiang
Affiliation:
Coastal and Oceanographic Program -- Department of Civil and Coastal Engineering
Publisher:
Coastal and Oceanographic Engineering Department

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Subjects / Keywords:
Beach nourisment

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Funding:
This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.

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University of Florida
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University of Florida
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All applicable rights reserved by the source institution and holding location.

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Full Text
SHORT COURSE ON
PRINCIPLES AND APPLICATIONS OF
BEACH NOURISHMENT

July 10,1989
Instructors Thomas Campbell Robert G. Dean Ashish J. Mehta Hsiang Wang
Organized by COASTAL AND OCEANOGRAPHIC ENGINEERING DEPARTMENT UNIVERSITY OF FLORIDA, GAINESVILLE, FLORIDA 32611

........ I .....I .M.n .... M ... ..... 8111, ................. ........ I. .. ..... n. ...... ...................... I ......... -.... ........ I ...... .... 1




SHORT COURSE
ON
PRINCIPLES AND APPLICATIONS OF
BEACH NOURISHMENT
July 10, 1989
... Instructors ...
Thomas Campbell Robert G. Dean Ashish J. Mehta
Hsiang Wang
... Organized by ...
Coastal and Oceanographic Engineering Department University of Florida
Gainesville, Florida 32611




TABLE OF CONTENTS

CHAPTER
I OVERVIEW
AIM OF BEACH NOURISHMENT
HISTORY AND OUTLOOK
MAJOR STEPS IN PROJECT PLANNING
REFERENCES
2 ENGINEERING DESIGN PRINCIPLES
PART I BOUNDARY CONDITIONS
HISTORICAL SHORELINE INFORMATION
A. Estimation of closure depth
B. Errors induced by survey inaccuracy
C. Seasonal variations
LONG-TERM AND EXTREME SEA CONDITIONS
A. Summary of Synoptic Meteorological Observations (SSMO)
B. Measured Wave Data
C. Wave Hindcasting Information Nearshore Wave Information STORM SURGE AND WATER LEVEL CHANGES
MORPHOLOGICAL AND SEDIMENTARY CONDITIONS
HYDROGRAPHIC SURVEY
LITTORAL DRIVE ENVIRONMENT
SAND SOURCES
BIOLOGICAL CONDITIONS AND WATER QUALITY
NATURAL AND MAN-MADE STRUCTURE S
REFERENCES
3 ENGINEERING DESIGN PRINCIPLES
PART II DESIGN
INTRODUCTION
CROSS-SHORE RESPONSE
Beach Width Gained vs. Sediment Quality
Effects of Sea Level Rise on Beach Nourishment Quantities Case I -Nourishment Quantities for the Case of No Onshore Sediment Transport Case II -Nourishment Quantities for the Case of Onshore Sediment Transport




PLANFORM EVOLUTION OF BEACH NOURISHMENT PROJECTS
The Linearized Equation of Beach Planform Evolution
Governing Equations
Transport Equation
Equation of Sediment Conservation
Analytical Solutions for Beach Planform Evolution
(1) A Narrow Strip of Sand Extending into the Ocean
(2) Initial Shoreline of Rectangular Planform
Effect of Ends on a Beach Fill
A Case Example Bethune Beach
Project Downdrift of a Partial or Complete Littoral Barrier
DAMAGE REDUCTION DUE TO BEACH NOURISHMENT
REFERENCES
4 SEDIMENT STORAGE AT TIDAL INLETS
INTRODUCTION
SEDIMENT BYPASSING
Natural Bypassing
Artificial Bypassing
SEDIMENT VOLUMES NEAR AN INLET
EVOLUTION OF EBB AND FLOOD SHOALS
SAND TRAPPING
Selected Inlets and Physical Environment
Volumetric Calculation
Summary of Results
EBB SHOALS
Florida Inlets Georgia Inlets
Ebb Shoal and Nearshore Environment
REFERENCES
5 THE BEACH RESTORATION PROCESS IN FLORIDA
INTRODUCTION
DESIGN
Silt & Clay Rock in Fill Beach Design Initial Fill
Design Cross-section
Storm Benefits
Recreation Benefits
Optimizing the Design
Advanced Fill
Construction Profile
Permits & Approvals




CHAPTER 1
OVERVIEW
Hsiang Wang
Coastal & Oceanographic Engine8ring Department University of Florida, Gainesville, Florida
AIM OF BEACH NOURISHMENT
At present, there are only three alternatives to shoreline recession; retreat as shoreline regresses, harden the shoreline with protective structures and replenish the beach. One should not, however, confuse them as
three coastal protective alternatives as the primary goal served by each alternative is different. Retreat from shoreline achieves the main purpose of seeking harmony with nature, it offers little or no help to coastal protection in the usual sense. Harden the shoreline with protective structures, on the other hand, is meant to protect upland; seeking harmony with nature, at best, is a constraint but not the goal. The primary aim of beach nourishment is to maintain a beach, although its benefit is often measured in terms of recreation, coastal protection or other social and economic factors.
Once communities have settled on the coast, coast and beaches become part
of the utility system much the same as highways and power supplies that the community relies upon. If society wants to use them, it must be prepared to pay to maintain and preserve them. Therefore, beach nourishment is a means to maintain the community utility at a cost.
Case review reveals that the decision to select beach nourishment over other alternatives is often based upon one or more of the following reasons:
1. Maintain a beach at a designated location.
2. Soften the impact on adjacent coast.
3. Offer a certain degree of upland protection.




4. Spread the cost.
5. Can be reversed to natural state with minimal effort.
Many people receive beach nourishment as a simple task of dumping sand on the beach. This simplistic view is similar to claiming that a highway is simply the pouring of asphalt over cowpath. In reality, beach nourishment, like any engineering work, in a harsh environment, is a complicated task. Our
present technology, however, is at its infancy. The intent of the short
course is to review the state of art and to present the essential elements of beach nourishment design.
HISTORY AND OUTLOOK
Americans were the pioneers in beach nourishment practice. The earliest documented beach nourishment work can be traced back to 1922, at Coney Island, New York. It was actually a fairly large scale operation at the time. Approximately 1.7 million cubic yards of material from New York Harbor was transferred to the 0.7 mile beach at Coney Island through hydraulic dredging, at a cost of about 21 cents per cubic yard. Numerous projects were carried out afterwards.
Hall (1952) compiled a list of 72 beach nourishment projects in the United States during the period of 1922 to 1950 (a number of them were actually one project of different segments). The majority of these projects were for the purpose of beach restoration and shore nourishment; 12 of these 72 projects were actually carried out for the primary purpose of dredge disposal. During this period, most of the nourishment projects were along the Southern California Coast and Mid Atlantic Coast of New York and New Jersey.
Only a handful of projects were along the SE Atlantic coast and Gulf Coast.




In this early stage, there was really no basic criterion pertaining to artificial beach nourishment. Hall did propose a set of design criteria
suggesting some simple rules on nourishment configuration and required quantity of material. Since there was no follow-up study on any of these projects, little knowledge was gained.
In the last three decades, the number of beach nourishment projects increased considerably, particularly along the east coast and the coast of Florida. Tonya and Pilkey (1988), for instance, identified more than 90 documented cases of replenishment in over 200 separate pumping operations along the U. S. Atlantic barrier shore (Long Island, New York to Key Biscayne, Florida) alone. Table 1.1 shows the number of locations in each state along the barrier shore that beach nourishment projects have been identified. Of
the 75 locations, 31 were in Florida, or more than 40%. Table 1.1 Locations in Each State Along the East Coast Barrier Shore with Nourishment Projects
State N Y NJ DE MD VA NC SC GA FL Total
Number of
Locations 5 17 1 1 1 13 4 2 31 75
In terms of expenditure, Florida was also the highest. Under the Florida
Beach Erosion Control Program, a total of 67.3 miles of beach has been restored or renourished during the period from 1965 to 1984 with a total cost
of some 115.6 million (Florida DNR report, 1984). Figure 1.1 shows funds
spent for restoration/ renourishment projects during 19 65-1984 in 5 year intervals. The trend of increased spending was clear. According to the data compiled by the Florida Department of Natural Resources 92.7 million were spent to restore 51.12 miles of shoreline and 22.9 million have been used to renourish (maintenance) 16.18 miles of beaches. Table 1.2 shows the actual




10 -Or

FLORIDA DEPARTMENT OF NATURAL RESOURCES
Division of Beaches and Shores
Funds Spent for Restoration/Renourishment Projects
1965 1984 $115,6321,597.
In Five Year Intervals

- M State Cost

-'-I Federal/Local Cost

$77,597,758.

Sa33390.650.

$2,491,137.
1965-1970

No. Projects 3 Miles Restored Nourished 6.45

1971-1975 I 1975-1980 1981-1854 1son-1UU4
Total
No. Projects -12 No. Projects 6 No. Projects -7 No. Projects -28 Miles Restored/ Mies Restored/ Miles Restored/ Miles Restored/ Nourished -17.12 Nourished -13.35 Nourished 30.38 Nourished 67.30

PERIOD OF TIME
Figure 1.1 Funds Spent for Restoration/Renourlshment Projects in Florida from
1965 1986 (DNR, 1984).

80-

60[

401-

20-

$557,920




T
Name of Project O
Mexico Beach Restoration $
Mexico Bhob Renourishment
Pompano/Lauderdale By-The-Sea Restoration
Pompano Beach Renouirishminent Virgina Key/Key Biscayne Rest.
Virginia Key Renourishment
Cape Canaveral Beach Restoration Hallandale Beach Restoration Delray Beach Restoration
Delray Beach Nourishment
Delray Beach Renourishment
St. Petersburg Beach Restoration Venice Beach Restoration Ft. Pierce Beach Restoration
Ft. Pierce Renourishment Bal Harbour Restoration Indialantic/Melbourne Restoration John U. Lloyd Restoration Hollywood/lHallandale Restoration Lido Key Restoration

otal Cost f Project
40,625

State Share Of Cost $ 20,312

1,873,437 468,359
577,075 69,249
1,050,000 241,055
779,977 292,491
3,015,383 976,044

682,716 49,700 621,288
4,962,420 3,582,000 2,945,262 7,743,376 360,000

305,109 36,668 150,041
819,154
1,162,911
784,340 2,825,513
150,000

Project Length (miles)
S65
3.30
2.50
2.80
.78
2. 67
.50
.17
1.30
.85 2.10 1.50
4.73 62

Miami Beach Restoration 49,892,000 14,530,114 9.65
North Redington Beach Restoration 369,000 247,125 .30
Jacksonville Beach Restoration 9,757,900 2,267,086 10.50 Mullet Key Restoration 649,878 97,483 1.20
Jupiter Island Restoration 3,574,221 716,332 4.60
Treasure Island Restoration 216,000 44,650 .40
Treasure Island Renourishment --- --- --Treasure Island Renourishment --- --- --Total Restoration Projects $ 92,742,258 $26,204,036 ST .12
Total Renourishment Projects --- --- --Note: Total Restoration
Renourishment $115,632,597 $33,390,650 67.12
Cost per mile = 1,718,166 Renourishment 1,944,214 Restoration
Total Number of Projects 28 Restoration

Total Cost Of Project
$ 41,155 10,273,340 2,381,742
1,660,584 3,949,117
1,559,431
1,228,000 1,796,970 $22,890,339

State Share
Of Cost
20,000 3,549.,453
262,516
564,423 1,408,713
493,259
314,500 573,750 $7,186, 614

Table 1.2.

Expenditure on Individual Beach Restoration/Renourishment Projects, 1965-1984 (DNR, 1984).

Project Length (miles)
.55
5.20 1.30
2.70 2.63
1.30
--
1.70
.80 16.18




expenditures of each individual beach nourishment project during this period.
As you can be seen, Maimi Beach restoration project was far the largest, with a listed cost of $49,892,000. The actual cost up to date probably exceeded 54 million. 14.4 million cubic yards of sand were placed on a stretch of beach about 10 miles long. More detailed information on beach restoration projects
in the State of Florida can be found in literature complied by Walton (1977) and Wang (1988).
During this period, technology of beach nourishment began to develop. The concept of overfill ratio was first proposed by Krumbein (1957) and Krumbein and James (1965) which allows rational estimation of the required volume of borrow material to retain a unit volume of beach material after nourishment and sorting by natural forces. The method of computation was
further refined by Dean (1974), James (1975) and Hobson (1977). The idea of
equilibrium beach profile (Brunn, 1954; Dean, 1977; Moore, 1982) was applied to beach nourishment to determine the shape of original and nourished beaches. Since the 1970s computer modelings on shoreline changes were developed and were being applied to beach nourishment design. These models
include one-line models, two-line models, N-line models, the GENESIS (a Generalized Shoreline Change Numerical Model for Engineering Use, Hanson, 1987), dune erosion models, etc. Methods of beach nourishment have also expanded. In addition to the conventional approach of placing sand on the beach face through hydraulic dredging, feeder beach, inlet sand by-passing, perched beach, sub-aqueous nourishment, beach scraping, stock piling, and other means were all experimented. There was also a growing awareness of
environmental concern. Environmental impact assessment now becomes an integral part of beach nourishment design. We also begin to see some effort in performance monitoring.




Outside the United States, the Netherlands and Germany are among the more active ones in beach nourishment engineering. Australia, Belgium and
Singapore have also seen some limited activities.
In the Netherlands, beach nourishment was experimented as early as 1953 when 70,000 m 3of sand was placed on the beach at Scheveningen (Edelman, 1960). Since then nourishment projects were carried out at numerous locations covering the entire coast of the country. Roelse (1986) compiled a list of 32
projects completed between 1952-1985. Figure 1.2 shows the locations of
artificial beach nourishment along the Dutch Coast. Of these projects, the
Hoek Van Holland project was the largest. During the years of 1971-72, 18.94 million m 3 (24.92 million yd 3) were dredged from the entrance channel of Europort via hopper dredgers to create a beach 3300 m long and 900 m wide. This project serves the dual purposes of dredge spoil disposal and land reclamation. The cost of the project was at an amazingly low f igure of 7.4 million DFL (approximately 3.9 million U.S. dollars). Even when converted to 1987 cost, it came to approximately 11 million dollars, or, $O.46/yd3 This was an exceptional case. In general, the cost of dredging and placement in
the Netherland is about half that of a comparable job in the States.
Since land reclamation and shore protection is a national priority in the
Netherland, considerable advances have been made there in beach nourishment technology even though they are a late comer on the scene. In fact, the first
and, at present, the only artificial beach nourishment design manual was published by the Dutches (Manual, 1986).
In Germany, the major beach nourishment effort is along the 40 km shoreline of Island of Sylt. Sylt is the popular resort island in Northern
Germany. It is under heavy erosional stress with dune recession in excess of 1 m per year along the entire coast. Various nourishment projects were




Figure 1.2. Locations of Artificial Nourishment Along the Dutch Coast
(Dutch Manual, 1986).
8




carried out since 1972 (Kramer, 1972, Fuhrboter, 1974, Gartner and Dette, 1987). On a per unit length basis, the stretch of beach is probably the most frequently nourished coast in the world. It is also the location where
various nourishment schemes were tested on a prototype scale including various planforms a unique sand groyne configuration, multiple sand groynes, rectangular shapes of different length to width ratios as well as various profile geometries different proportions and slopes at different elevations. A performance monitoring program has been instituted since 1972. Therefore, it is one of the few nourishment projects, systematic monitoring and documentation were carried out on a long term basis.
Since the first project in the early 1920s, beach nourishment practice has developed from a simple sand dumping exercise into a multi-facet engineering work. We also witnessed significant increases in project activities in the last two decades. The trend is most certainly to continue perhaps at an accelerated rate. The reasons behind the projected increase in activities are:
1. Shorelines are deteriorating at a national scale.
2. Shoreline hardening practice becomes increasingly undesirable and, at
certain instances, is no longer permited.
3. Spreading the cost over a period is politically more palatable than onetime large expenditure.
In the State of Florida, a coastal restoration task force was organized by the Governor in 1985 to examine the existing coastal condition and to provide guidance in the long term strategy of coastal restoration. Of the 800
miles of sandy shoreline around Florida, 543 miles were identified as erosional, again of which 140 miles (224 1(m) were considered critically eroding, (Figure 1.3). A ten-year program for the restoration and maintenance of Florida's critically-eroded beaches was proposed by the Florida Department




Reason I
Miles Completed 1.20

Reason 11
Miles Completed
5.69

Federal/Local
Percent of Realon Total Cost

51%
* 67% 77% 73% 71% 71%

State Percent
Of Total Cost

Reaion III
Miles Completed 10.50
Region IV
Miles Completed
12.10
! r
w-a' '' "Realon V
Miles Completed
37.81

Regional Percent of
Air Cost

49% .1%
33% 4.9%
23% 8.0%
27% 9.0%
29% 78%
29% 100.9%

REGIONS

(Southeast) V (East Central)
IV
(Northeast) III (Southwest) Ii (Panhandle) I

Total 103.7
51.5
Total 137.0
62.5
...I........ Total 137.6

Critical Erosion
Non-Critical Erosion r Stable or Accreting
Shoreline

112.5

Total 177.4

.1
Total 219.2

I I
50 100 150 200
SHORELINE (Miles)

Figure 1.3. Present Erosional Condition Along Florida Coast (DNR, 1985).

II Ill IV
V
Total




of Natural Resources (DNR) at an initial estimated cost of $362 million with an additional $110 million during that ten-year period to be used for periodic
renourishment of restored beaches (DNR, 1985, 1986). Similar programs are also expected in other coastal states and in other countries. Germany, for instance, has a five-year program to preserve the beach and dunes for the island of Sylt requiring 20 million m 3 of material at a cost of 80 million dollars. Japan, where coastal protection is of national priority but presently has no or very limited beach nourishment programs, is also aggressively looking into the soft structure approach as the future solution.
3. MAJOR STEPS IN PROJECT PLANNING
Beach nourishment project planning is still by and large a trial and error process requiring numerous iterations. It is complex and time consuming and it is not uncommon that a project from its incipiency to its implementation could take 5 to 10 years. Planning is, however, critical to the success or even the survival of the project.
In the State of Florida, dredge and fill operations, such as beach restoration which are conducted on the sovereignty lands of the State must be authorized by various regulatory agencies including the Department of Natural Resources, Department of Environmental Regulations, Department of State, Board of Trustees of the Internal Improvement Trust Fund and the U.S. Army Corps of Engineers. If the beach is in the county or city jurisdiction local permits have to be obtained as well. The process of obtaining all the various
approval and the collecting and providing of the necessary information to obtain these approvals is time consuming. If the project is to be cost shared by the Federal dollars, a feasibility study must be conducted to show justifiable cost/benefit from the Federal's criteria and to pass the test of environmental impact at the Federal level for project authorization. Projects




needing State and Federal fundings can then be submitted to the State Legislature or to the Congress for appropriation. During the process, if
excessive funds are expended for project preparation, cost overruns could dissuade the Legislators for project fundings. Furthermore, certain aspects of the project such as shoreline position and sand sources could change or become outdated requiring costly restudy. Therefore, timely and controlled
project planning is essential to insure successful project implementation.
The major steps involved in a beach nourishment project are illustrated by the following block diagram:

Elements required to accomplish each steps are given as follows:

1. Project Proposal
A). Problem Evaluation
Existing erosion problem
History of efforts and their effectiveness
B). Alternative Solutions




C). Project Definition
Requirements storm protection, recreation, shoreline
restoration
Project dimension planform, profiles and volumetric requirement Aternative sand sources offshore borrow areas, inlet by-passing,
etc.
D). Preliminary cost analysis
E). Beach access analysis F). Cost/benefit analysis
G). Environmental statement
2. Project Preparation
A). Engineering
B). Environmental Impact Study
C). Cost estimation
D). Financing E). Permiting
F). Project authorization and documentation
3. Project Implementation
A). Bidding and tendering
B). Pre-construction survey
C). Construction management and monitoring
D). Acceptance
E). Post-project monitoring and evaluation
F). Maintenance
The elements listed in each step are usually not independent of each other. Therefore, iterations are expected within each step and sometime across the steps.
Of course, the tangible product of the whole exercise is the engineering work of a nourished beach. This is also the main topic of the short course.




An engineering design is influenced by many factors, such as environmental effects, cost, sand sources, delivery systems, etc. The intent of the course is to provide an overview of a complete engineering design practice. A flow chart such as presented in the Dutch Manual on Beach Nourishment (1986) can be used to aid in the design process. Figure 1.4 present a flow chart for beach nourishment engineering.




CONSTRAINTS
o Storm Protection
o Recreation
o Beach Access
o Environment
Sediment Procss

TOOL
o Fill Factor o Equilibrium Profie o Survey
TOOL
o Shoreline Response Models o Dune Erosion Model o Wave and Storm Surge Models o Inlet Models o Data

Coastal and

4-

PROJECT EVALUATION
o Longevity o Updrift-Downdrft Impact o Interactions (Inlet, Existing Engr. Works) o Effectiveness o Environmental Impact
CONSTRAINTS Implementation o cost
o Delivering System o Time

Beach Nourishment Design Flow Chart.

BOUNDARY CONDITION
o Coastal Condition o Environmental Forces o Sediment Properties o Geometry and Structures

TOOL
o Historical Information o Wave Models o Littoral Environment o On/Off Shore Transport

PROJECT DEFINITION
o Geometry o Volumetric Requirement o Material Specification o Auxiliary Structures

A ILITL'

L,VP4 O I nM1I,4 I o
o Sand Sources o Nourishment Method o Cost

EVALUAION
o Effectiveness o Longevity o Environmental Impact

m

Figure 1.4.

o Montorig




References

Bruun, P. (1954) Coast Erosion and the Development of Beach Profiles, U. S.
Army Beach Erosion Board Tech. Memo, No. 44.
Dean, R. G. (1974) Compatibility of Borrow Material for Beach Fills, Proc.
14th Coastal Engineering Conf., ASCE, Copenhagen, Denmark.
Dean, R. G. (1977) Equilibrium Beach Profiles: U. S. Atlantic and Gulf Costs,
Tech. Rep. No. 12, University of Delaware, Newark.
DNR (1984) Beach Restoration: A State Initiative, Florida Department of
Natural Resources, Tallahassee, FL.
DNR (1986) A Proposed Comprehensive Beach Management Program for the State of
Florida, Florida Department of Natural Resources, Tallahassee, FL.
Dutch Manual (1986) Manual on Artifical Beach Nourishment, Rijkswaterstaat
(Dutch Public Works Department) Delft, The Netherlands.
Fuhrboter, A. (1974) A Refraction Groin Built by Sand, Proc. 147th Coastal
Engineering Conf. Copenhagen, Denmark.
Gartner, J., and Dette, H. H. (1987) Design and Performance of Large Scale
Nourishments Proc. Coastal & Port Engineering in Developing Countries
Beijing, China, pp 181-196.
Hall, Jr., J. V. (1952) Artificially Nourished and Constructed Beaches Beach
Erosion Board, Tech. Memo, No. 29.
Hanson, H. (1987) GENESIS, A Generalized Shoreline Change Numerical Model for
Engineering Use, Lund Univ. Pep. No. 1007, Lund, Sweden.
Hobson, R. D. (1977) Sediment Handling and Beach Fill Design, Coastal Sediment
77, ASCE, Charleston, S.C.
James, W. R. (1975) Techniques in Evaluating Suitability of Borrow Material
for Beach Nourishment, U.S. Army Coastal Engineering Research Ctr., Tech.
Memo, No. 60.
Kramer, J. (1972) Artificial Beach Nourishment on the German North Sea Coast,
Proc. 137th Coastal Eng. Conf., Vancouver, B.C., Canada.
Krumbein, W. C. (1957) A Method for Specification of Sand for Beach Fills,
Beach Erosion Board, Tech. Memo, No. 102.
Krumbein, W. C., and James, W. R. (1965) A Log-Normal Size Distribution Model
for Estimating Stability of Beach Fill Material, U. S. Army, Coastal Eng.
Res. Ctr. Tech. Memo. No. 16.




Moore, B. (1982) Beach Profile Evolution in Response to Changes in Water Level
and Wave Height, M.S. Thesis, Dept. of Civil Engr. Univ. of Del. Newark,
D.E.
Roelse, P. (1986) Artificial Nourishment as Coastal Defense in the Netherlands
Previous Fills, Future Development, Amex IV Artificial Beach Nourishment
Manual, Ministry of Transport and Public Work, The Netherland.
Wang, W. C. (1988) List of Literature Related to the Beach Restoration
Projects in the State of Florida. Technical Rep., Coastal Eng. Dept.
Univ. of Florida, Gainesville, FL (in preparation)
Walton, Jr., T. L. (1977) Beach Nourishments in Florida and on the LowerAtlantic and Gulf Coasts. UFL/COEL-77/031 Coastal and Ocean. Engr. Dept.,
Univ. of Florida, Gainesville, FL.
Toyna, C. and Pilkey, 0. (1988) An Historical Survey of Beach Replenishment on
the U.S. Atlantic Barrier Coast: Good News for Florida, Beach Preservation
Technology Conf. Gainesville, FL.




CHAPTER 2
ENGINEERING DESIGN PRINCIPLES
PART I BOUNDARY CONDITIONS
Hsiang Wang
HISTORICAL SHORELINE INFORMATION
In beach nourishment engineering, historical shoreline change information
is needed to assess the dynamics of the sediment process and the effects of man-made structures and constructions such as inlet improvement, jetties, groins, harbors, etc. This information is also needed for the prediction of the performance of a beach nourishment project and estimating the quantity and frequency of renourishment.
Historical shoreline changes can be deduced from three sources: hydrographic and beach surveys, maps and charts and aerial photographs. In
the state of Florida, shoreline maps from the U.S. Coastal and Geodetic Survey
(U.S. C&GS.) of reliable quality can be found as early as 1850s. The socalled T-sheet map series is available at varying scales from 1:10000 to 1:40000. One set of these T-sheet maps, the 7.5 minute series of Standard Topographic Quadrangle Maps (scale 1:24000), is the most complete one. The
shorelines are expressed as the Mean High Waterline (MHW).
Another map source is the TP-sheet series of Coastal Zone Ortho Maps (scale 1:10000), produced by the National Ocean Survey. This series of maps
was constructed from aerial photos and covered the period of the 1970s only. These maps were rectified for both the horizontal and vertical distortions and the shorelines were given as Mean High Waterline also.
The second source of shoreline information is the aerial photos. Usually
only vertically controlled photographs should be used. In the state of
Florida, the most complete set was collected by the Florida Department of




Natural Resources (DNR) from 1970s on. They were at scale of 1:1200 and/or
1:2400 and were used to produce the states' Coastal Construction Control Line maps.
The third and perhaps the most reliable source of shoreline information is the actual ground truth survey. The sources of this type of information are quite scattered from, for instance, U.S. C&GS, U.S. Corps of Engineers (C.0.E.), state, county and city agencies and engineering consulting firms. The most systematic beach surveys are conducted by DNR. They are available
since mid 1970s at approximately six year intervals. These data consists of
beach face surveys to wading depth at 1000 ft intervals and hydrographic surveys to 3000 ft offshore at 3000 ft intervals.
DNR has just completed an effort to digitize and map historical shoreline changes for the entire coast of Florida. These data set should consists of
the following information (Wang and Wang, 1987).
a. Digitized shoreline and offshore bathymetry at 6 ft, 12 ft, 18 ft, 24 ft, and 30 ft contours whenever available. All the data are referred to DNR monuments which, in turn, are referenced to State Plane Coordinates.
b. Composite historical shoreline change maps at a scale of 1:24000 and
1:2400.
c. Composite historical offshore depth-contour change maps at a 1:24000
scale.
Figure 2.1 is an example of the data file of the digitized shoreline information stored in DNR. Based upon our experience, the digitization error
is within 0.01 inch if done properly, which translates to 20 ft at 1:24000 scale.
For beach nourishment design, two kinds of information are useful-shoreline changes and volumetric changes. Figure 2.2 illustrates the shoreline change of Indian River County, FL. from 1972 to 1986. The data was




BREVARD COUNTYe FLORIDA
* SHORELINE POSITION DATA FILE .-- .- - - -*---- *------

MI M NT sUR FY 1.0. DAT(S)

R-IT R-IT
R: 1
R-iT
R- 2
It 2
f~t
R- 2
R-2 tR-Z
R:t
R-3
R:3
R-3 R-3
R-3 R-3
Rt-3
INli
3t-3
R-47 R-AT R:41
-4T
41 R-4T n-4
R-4T7
R
R-5
k-hS R-,-T
Pt-s
P- ". T
ft
R-6T
p-s.

SURVEY 0
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NOTIt I
N(FEET) (FEET)

SOURCE CALE SUUKE

1877-1 0 19
1929
941;194
1969-1971
1974
194 -1948
976
980
19685
11171;1979
976 96 196 7
9 7691
900
1877-1879 194o- 948
1969-1971
1974 S1 C
IC77-1879
19Z9
194 8
196J-)971
4
1976 980 1905
i877-1879
1912 94
196
1969-1971
1974 19P8 1980

146G906*5D
480906.50
88't: 8P
480906. 0 480906.53
8390605 483a )6.
480068.0
4 61,
479006.03
140068.00
148006.
478044jltlt 14t9086,50
1478094.00
1478094.0, 1476094.00 147609k.0,3
J4 8094:0:1 .478094, G 1478n94. ;,j
47717b:'. S 1471176. S'
1411116.;?
Itiftit I'd
4ITi*5d
1477176,5
147739,01
Ittill:.i I 476239.01
476239.01 1476239.01 47 6: 50
4 6 9c
1476239 .01 1476239 .01

631108.58 631tG.50 63 to 5
6 .
6 0.50
,,IlIll
631 106:
630630
1 Ii I
630673.00
6 6 C
6] .
630673.00
3 38l:88
630366.50
63U366.10 630366.5J
630366.5 630366.50
830103l: 630iC3. a.
tiillI:80
b30103-*00
600.00
titil11
63060 :06
629838.12
629838*12 629838.12 629838.12 639873*10
6 9630
629836.12 629838.12 143F3666.9

56.38 60.81
448,06 31653 417.138
ill I: us: '
44001
S69.
48.6:
Ill
12
14.11
-2093
11111
169:38
391.63
2 31.3
27 *3811.
'tid69
252.82 628. 397.63

MHM HMW
lMW MHMW
..
1!ilW
HHl
.
144Ww
NHM
MHW
144II NHM
NHH
MHM
M MMW
pall
Mid MHM
MMu wM
144W
Mu1W
P411
M41W 11W
194W
M41w

Figure 2.1. Example of Data File of the Digitized Shoreline Information
Stored in DNR.

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

0
It1
*S 6 4 6
IIII llhlill EI
II ..
,.oo,.. filllil' ,,,9sa .oil!! I ( '!88
1478094.00 630636.8 2400
It~llt I~i r S l III!Ssh h! I
6 2
140:18 t1iM 200
4 : *00 63069 0091 i
141r09*00 630466gi I il1il 3 il 14894.00 630636*88 2400
i t:18 H : 9 388 I t 1t1:08 00 8 I' lll 1 I ,!!
16 1 :0 6 9000O
476 *0 6 *1 S00 1476239.0 63257 40

U. S,*C&93 U.SS
a: 4iI UI.S, Ta)
ONRf("OO)
* S *os OMR T(PHOO)
U: all
U.S NTS U.S* tSS.
li .illi:
U.S .Cg.ss
US.G.S.
04lfill" ONR SURVEY) ONR PHOTO)
8:I::Et. 3:1:t OC. BibleA AS
U.S.SC*S UOCCGTO U.S.N.6O.S
ON 1PHOMO) U.So..S.
ONR(PHOTO)




INDIAN RIVER COUNTY

0OO 30000 40000 50000 60000 70000 80000 90000
DISTANCE ALONG BASELINE (ft)

Figure 2.2.

Total Shoreline Change and Annual Rate of Change of Indian River County, Florida (Between 1972 and 1986).

20.0 18.0
16.0
14.0 12.0 10.0 8.0
4.0
2.0 0.0
-2.0
-4.0
-6.0
-8.0
-10.0
-12.0
-14.0
-16.0
-18.0
-20.0




taken from the digitized shoreline information as mentioned above. Both data
sets are from DNR surveys; the 1972 survey was conducted during November but the 1986 survey was carried out in June. Therefore, they represent winter and summer shorelines respectively. The entire shoreline in the county is 22.4 miles (approximately 115 DNR monuments at 1000 ft intervals). The next inlet
at Ft. Pierce lies about 5.5 miles from the south county line. Vero Beach is located from R77 R82. From the plot, it can be seen the drastic effect of inlet on the downdrift side; immediately south of Sabastian Inlet, beach receded 80 f t or about 6 f t/yr. The shoreline, as a whole, has advanced on the average of 20 ft. The shoreline advance is most prominent just south of Vero Beach where the shoreline has a concaved shape.
The data of shoreline change is often quite noisy. Usually some form of smoothing is required.
To compute volumetric change requires hydrographic and topographic
information in addition to shoreline position. It is usef ul to compute the
volumetric changes above the MHW and below the MUW separately. In theory,
this can be done simply through integrating the area between measured profiles. In practice, considerable difficulty exists, particularly for the below MH-W portion. A number of problem areas are discussed here. A. Estimation of closure depth:
Closure depth is defined as the limiting water depth beyond which the sediment motion can be considered to be minimal at a time scale of engineering interest. This depth is obviously a variable, depending upon, among other factors, wave and current environment, tidal range, offshore slope and
geometry and sediment characteristics. It is a quantity difficult to be
determined accurately. For the Atlantic coast, a depth of 27 ft measured from the berm elevation was suggested as a representative value. Owing to the very




mild slope along the Atlantic coast, this depth could be way offshore (typically from 1000 to 4000 ft offshore but could be considerably further if offshore rock crops or reefs exist). At such a distance accurate profile date may not exist. The hydrographic survey by DNR, for instance, was carried out to approximately 3000 ft offshore at 3000 ft longshore intervals (every fourth monument).
Again using Indian River County as an example, Figure 2.3 shows the offshore topographies. The 30 ft contour line grows wider toward the south partially owing to the existence of a reef system (shown by hatched area). Therefore, in the northern end, the DNR survey reached beyond 27 ft but in the southern part of the county, the closure depth was never reached in either 1972 or 1986 survey series. A number of representative survey profiles in the
county are shown in Figure 2.4 (the monument numbers and their locations are identified in Figure 2.2).
The effects of choosing different offshore closure depths are further illustrated in Figure 2.5. In this Figure, volume changes along the shoreline computed to different elevations were shown. The solid line marked all means the closure depth was at the end point of the survey irrespective the depth at
this point. This point roughly (but not always) corresponds to the -30 ft depth. The total volumetric changes for the entire county which is the integration of volume along the shoreline are tabulated here:
Above NGVD 1.4 X 10o6 yd3
From NGVD to 5' 0.6 X 10o6 yd 3
From NGVD to 10' 0.8 X 10o6 yd3
From NGVD to 15' 0.1 X 10 6yd3
Total below NGVD -4.7 X 10o6 yd3




6= Reef Figure 2.3. Offshore Depth Contour of Indian River County (1972
DNR Survey).




40.0 20.0
0.0
,-20.0
-40.0
40.0 20.0 0.0
-20.0
-40.0
40.0 20.0 0.0
-20.0
-40.0
-40
40.0 20.0 0.0
-20.0
-40.0
40.0 20.0 0.0
-20.0
-40.0
40.0 20.0 0.0
-20.0
-40.0
-4O

00 0 400 800 1200 1600
HORIZONTAL DISTANCE TO
(B) Profiles at South End

2000 2400 2800
MONUMENT (IN FEET)

3200 3600

Figure 2.4. Representative Survey Profiles Along Indian River County Shoreline
(Ri, R18, R39 In North) (R90, R99, R114 In South)

.................................................... ........... ...... 1 1 1 1. R -1 ................................. ................. ........... ..... ... N ov. 72
June86
R-18
SR-39
...... ------ i- ------- I-O0 0 400 800 1200 1600 2000 2400 2800 3200 36C
(A) Profiles at North End
R-90
R99
-..-i-TT --... ..-I--- ----T ........
------------- --------- ---- -,
..... ..... .... ..... ....
1- 11- ... FI .. i ... i I .... r ... f..f..f...( i.i. I ..i ..(.. ..f.. ..I.. i ... I ... F1 ... Y ... iI i... i i.




INDIAN RIVER COUNTY

0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 110000 DISTANCE ALONG BASELINE (ft)

Figure 2.5.

Volumetric Changes as Influenced by Different Offshore Closure Depths (Indian River County).

200.0
ct 150.0 ED ED
o
" 100.0
o
N
C, 50.0
u- 0.0
.
0
- -50.0
0.
U -100.0
4 uJi
U. -150.0
0
w a .200.0
z
4 -250.0
.)
: -300.0
-350.0
0




Therefore, depending upon the selection of offshore boundary, this coast could appear to be accretional down to -151 NGVD. But if the closure depth was chosen beyond -15', this coast could become erosional.
B. Errors induced by survey inaccuracy.
The most serious survey error is the shift of horizontal and vertical datums between surveys as this error is cumulative. Because of the mild slope
and long horizontal distance, a small shift in either horizontal or vertical datum could translate into thousands cubic feet of sediment volume per lineal foot of beach front. Thus, the error could be in the same order of magnitude as the total volumetric change. A sensitivity analysis such as illustrated in Figure 2.6 would be helpful to establish the confidence level of the results. From this figure, it can be seen that if the volumetric change is small (mild erosion or accretion), the survey induced error (relative) could be very large. On the other hand, if the volumetric change is large (strong
erosion or accretion) the survey induced error, relatively speaking, is usually small.
The other source of error which by its nature is less serious is due to the motion of the survey vessel. Over a long distance the errors of this type tend to compensate each other as oppose to cumulative.
C. Seasonal variations.
The shape of the beach is known to vary seasonally. Therefore, comparisons of beach profiles surveyed at two different seasons could lead to wrong conclusions. Figure 2.2 shows that from 1972 (winter profile) to 1986 (summer profile), Indian River County had an apparent shoreline advance. Also, in shallow water up to -15 ft or so, the total volumetric change is also positive




INUIAN HIVLII UUUNIY

VJUUUUUU
2000000]

-- C
C

I-
w
-4000000
0
-5000000
O
-6000000
-7000000
oo
-1000000
W
-2000000
(0
o
-3000000 800.0

-15ft

-C

(5 10 15
... ... ... ... .... 4..............
..

All
-15tt

HORIZONTAL DATUM SHIFT (ft)

INDIAN RIVER COUNTY

-20 -15 -10 -5 0 5
HORIZONTAL DATUM SHIFT (ft) 6. Errors Induced by Shiftina of Datum
\ J/

10 15 20

used as reference:

Positive Value means 1986 Profile Shifted Seaward).
11

-1Oft
.......................-

-15 -10 -5
-5ft
. r .. . .. .. .. .. ... ... ... ..

900.0
200.0100.0-

.1

..... .............. -5f,,
...~ ~ /..... .............All
----.. .. ------ ,---

0
-25
Fia re 2. 700.0
600.0 500.0
400.0

o>

300.0

I




(Figure 2.5). St. Lucie County which is next to the Indian River County on the south also had two hydrographic surveys by DNR, one in 1972 and the other in 1987. However, the survey in 1972 was carried out in the summer whereas the 1987 survey was completed in the winter, exactly the opposite to the Indian River County case. Now as shown in Figure 2.7, the shoreline had an apparent retreat downdrift from the Fort Pierce Inlet; the volumetric change to the near-closure depth was actually accretional. This is, of course,
exactly opposite to the situation in the Indian River County. Thus, comparing data obtained from different seasons raises the possibility of false signals.
LONG-TERM AND EXTREME SEA CONDITIONS
Wave is the prime mover of coastal sediment. Long-term wave information
is the necessary input for computing littoral drift quantity and shoreline evolution which, in turn, governs the effectiveness of beach nourishment and the required frequencies of renourishment. The extreme sea conditions are
needed to estimate short-term shoreline retreat and dune erosion due to design storm; both are important boundary conditions for beach nourishment design.
Long-term wave information along the Florida Coast can be derived from a number of sources:
A. Summary of Synoptic Meteorological Observations (SSMO).
SSMO was prepared under the direction of the U.S. Naval Weather Service Command by the National Climatic Center. All the data were obtained from
Marine surface observations by ships. It is one of the most commonly cited
data sources for surface winds and ocean waves. Along the Florida coast these
marine conditions are divided into five regions Jacksonville, Miami, Key West, Fort Myers, Apalachicola and Pensacola. Statistics of percent frequency




ST. LUCIE COUNTY

0 20000

40000 60000 .80000 100000 120000 140000 160000

DISTANCE ALONG BASELINE (ft)

Figure 2.7. Total Shoreline Change of St. Lucie County.




of wind speed and direction versus sea height were given on a monthly basis as
were the percent frequency of wave height versus wave period. Based upon
these data, the statistics of wave height versus wave direction in deepwater condition can be inferred. The joint distribution of wave height, wave period
and direction cannot be established with this set of data without further assumptions. Since SSMO data are biased to calm weather they are not suitable for extreme condition analysis.
B. Measured Wave Data.
The National Oceanic and Atmospheric Administration (NOAA) maintained a number of meteorological buoys along the coast of the United States. The
locations of the North Atlantic and Gulf coast buoys are shown in Figure 2.8. They are all in deep water with water depths ranging from 120 m to 4,000 m (Wilson, 1975-1986). These buoys record wave height and period as well as wind conditions at the 5-meter level. The wave directions have to be inferred from wind information.
Along the coast of Florida, the Department of Coastal and Oceanographic Engineering (COE), University of Florida, maintains a coastal data network (CDN) that contains twelve gage stations at present. Their water depths range from 5.8 m to 18.0 m. These gages record wave height, wave period and water level variations. A few of the gages also can provide wave directional information by simultaneously measuring oscillatory current velocities in the horizontal plane. The locations of these gages are also shown in Figure 2.9. At certain locations, up to 10 years of data have been recorded. All the data are archived in COE and monthly summary reports are available. Table 2. 1
illustrates the format of the monthly wave information summary and Figure 2.10 shows the graphic display of the monthly wave information.




1000

400.... 77-82 400
NORTH ATLANTIC and GULF COAST BUOYS 44004
Plots show location, staton number, period of 44001 77-81
record and approximate number of observations 41004 75-79
78-81 041001
41005 76-81
79.8 .., 0 41002 75-81
:" 'i' """;" ":""" 41006
*42002 42001 42003 76-82 75-82 76-82
20 CP= .o200
1000 800 600
Figure 2.8 North Atlantic and Gulf of Mexico Buoys.

800

600




COASTAL DATA NETWORK FIELD STATIONS AND
YEARS OF INSTALLATION

e pRESSURE GAGE P-U-V GAGES
- TELEPHONE
--- RADIO

Figure 2.9. COE Wave Stations.




COASTAL DATA WETWORZ

Station: ARINEIAD
JANUARY, 1988

Rel.
Time: Depth: Is: Tm: Day/Er (m) (a) (seo)

/0 /6
/12 /18
/0 /6
/12 /18
/0 /6
/12 /18
/0 /6
/12
/18
/0 /6
/12 /18
/0 /6
/12 /18
/0 /6
/12 /18

10.8 12.53 10.8 11.8
10.6
12.2 11.0
12.0
11.0
12.4 11.3 11.9
11.0
12.0 11.3 11.6
11.0
11.7 11.5
11.4
11.3
11.5 11.6
11.3
11.5
11.4 11.9
11.2

1.45 1.16 1.18 1.09
0.88
0.84 0.77 1.23
1.47 1.64 1.84
1.68
1.25
1.12
0.82 0.89
0.74 1.45 1.23 1.29
0.93 1.25 1.28
1.22
1.12 1.24 1.38
1.74

12.8 12.8 6.4
5.8
7.1 7.1 8.0 5.3
8.8
8.0 7.1
6.4
8.0 9.1 8.0 9.1
9.1
5.8
6.4 6.4
4.9 5.8 8.3
5.8
5.8 8.3
6.4 7.1

Xonthly Wave Data Awaysis Report
% wave Energy Ditributiton
(Period BandviAth LEit -in seo)

21+
8.1
2.4 1.8 1.5
1.6 1.6 1.6
1.2
0.7 1.0 1.1 1.1
1.2 1.8
1.4 1.3
1.4 0.6 0.7 0.9
1.1
0.6 0.6 0.7
0.9 0.7 0.7 0.7

16-15 10.7-9.1 8-7.1 5.8-4 21-16 15-10.7 9.1-8 7.1-5.8

2.6 19.8 6.8 16.6 2.5 11.1 1.6 8.4
1.6 12.6 1.5 8.6 2.2 6.2 1.1 1.8
0.5 0.9 0.7 0.8 1.1 6.53 0.6 4.2
0.6 3.0
1.4 1.7 1.6 2.6 1.6 2.4
1.6 -.2.6
0.5 0.7 0.5 1.0 0.6 1.0
1.4 2.6 1.3 1.6 0.8 2.2 1.0 2.3
0.9 2.5 0.5 1.7 0.6 2.0
0.3 0.9

9.85 8.0*
6.4 9.1
8.2 6.5 8.8
2.8
1.9
2.4 13.8
12.6
12.8 10.8 15.6 8.8
14.6 2.1 3.4 3.9
7.3
4.9 6.3
5.4
11.2 6.3 7.6 3.9

6.9 9.5 6.9 7.0
5.5 6.8
7.8
4.7
4.5 8.5
12.1 11.7
13.9
24.2 16.9
20.5
18.0 8.5 7.7 12.8
9.2 9.8
7.6
7.8
6.7
5.0 6.1 8.1

5.7 4.9 16. 6.8 8.8 24. 8.9 15.1 835. 8.6 14.4 52.
9.4 14.8 21. 10.0 16.4 29. 15.6 11.8 22. 8.4 11.7 54.

6.7 15.8 12.5
11.2
14.8
15.9 17.3
17.7
15.4 7.8
8.4
9.5
9.2
6.4 7.2
4.4
6.1
3.6
6.4
18.6

10.2 36.
14.7 29. 15.1 19. 12.5 30.
10.2 24.
10.8 20. 8.3 19. 9.8 16.
5.6 12. 8.3 44.
8.2 88. 7.6 32.
9.9 20. 7.6 51. 6.9 81. 7.7 6.
7.3 31. 7.4 35. 12.4 41. 25.7 24.

31.
18. 17. 18.
26. 23.
24. 34.
39.
27. 19. 16.
20. 13. 18.
22.
29. 28.
32. 32.
40. 37. 38.
35.
33.
40. 23.
18.

CDN.FORMAT A/Version 1987.1 COEL.University of Florida.Gainesville.Florlda 32611
Table 2.1. Format for monthly Wave Data Analysis from Coastal Data Network,
COE, University of Florida.




Marineland 20
CD
o1 0
0 52
01 5 10 15 20 25 30

JANUARY, 1988

JANUARY, 1988
Figure 2.10. Graphic Display of Monthly Wave Information.

IVIP




A list of information concerning the wave data lengths, types, and mean water depths and locations where data are being collected by the CDN wave gages and the NOAA buoys is given in Table 2.2. The CDN wave gages are
identified by the names of the nearby cities or bay systems. The NOAA buoys are identified by the location identification numbers. Most of the wave data retrieved from the CDN wave gages have data length more than five years while most of the buoy data have data length longer than ten years.
C. Wave Hindcasting Information.
At present, there are a number of operational wave hindcast models for the Atlantic Ocean along the eastern seaboard of the United States. The Fleet Numerical Oceanography Center (FNOC), U.S. Navy, for instance, provides routine wave hindcasting based upon their Global Spectral Ocean Wave Model (GSOWM). The GSOWM is based on a 2.5 by 2.5 degree latitude/longitude grid. It provides deepwater wave information in terms of wave energy-frequencies versus direction. This hindcast information is available on magnetic tape for the period from October 1, 1975 to present (from National Climatic Data Center in Asheville, N.C.).
The other main operational model is the discrete spectral model developed by the Wave Information Study (WIS) group of the Waterways Experiment Station (WES), U.S. Army. The modeling was originally designed to have three separate phases: deepwater wave hindcasting, wave modification in shelf zone, and finally, transformation into nearshore shallow water zone. The main intent of the model is to provide hindcast wave information along the coastal waters on both sides of the continent of the United States. A 20-year hindcast
information was generated at 13 stations along the edge of the continental shelf of the eastern United States. The hindcast was further extended to shallow water through linear shoaling and refraction by assuming plane beach




Table 2.2 Summary of wave gage and floating buoy data informations
CDN underwater wave gage data
station data length latitude and water directional
or ID.#, (from to) longitude depth(m) data
St. Mary's 11/83- 5/84 30-43'N, 81-19'W 14.2 yes
entrance 6/86- 7/86 II II yes
#4 8/87- 1/88 It It yes
11/83- 5/84 3040'N, 81016'W 17.5 yes
St. Mary's 7/84-12/84 It It yes
entrance 3/85- 4/85 It It yes
#5 7/85- 9/85 It It yes
8/87- 1/88 It it yes
Jacksonville 6/84-12/87 30"18'N, 81-22'W 10.1 no
Marineland 1/81- 4/86 2940'N, 8112'W 11.4 no
Cape Canaveral 3/82-12/87 28025'N, 80-35'W 8.0 no
Cape Canaveral 5/84- 9/84 28020'N, 8025'W 18.0 yes
(offshore) 12/85- 5/86 It It yes
Vero Beach 10/86-12/87 2740'N, 8021'W 7.8 no
West Palm Beach 3/82-12/86 26042'N, 80-02'W 9.9 no
Miami Beach 7/83-12/87 25046'N, 80007'W 6.5 no
2/86- 3/87 27004'N, 82027'W 7.5 no
Venice 4/87- 5/87 It It yes
6/87-12/87 It It no
Clearwater 3/82-12/87 27059'N, 82051'W 5.8 no
Steinhatchee 2/86- 7/86 29042'N, 83046'W 9.2 no
NOAA maintained buoy data
station data length latitude and water directional
or ID.# (from to) longitude depth(m) data
41001 6/76- 4/86 35000'N, 72018'W 4000 no
41002 11/75- 4/86 32018'N, 75012'W 3900 no
41006 5/82- 4/86 29018'N, 77018'W 1200 no
44003 3/79- 4/86 40048'N, 68030'W 150 no
44004 9/75- 4/86 39000'N, 7000'W 1300 no
44005 1/79- 4/86 4242'N, 68018'W 120 no
42001 8/75- 4/86 2554'N, 89042'W 3300 no
42002 3/77- 4/86 26000'N, 93000'W 2400 no
42003 7/77- 4/86 26000'N, 86018'W 3250 no




(Jensen, 1983). A similar 20-year wave hindcasting is just becoming available for the Gulf Coast also.
Recently, the Department of COE has just modified the WIS model for the Florida coast along the Atlantic seaboard (Lin, 1988). The model is more
rigorous in shallow water wave hindcasting and was calibrated using shallow water directional wave data collected by COE. The model has been applied to hindcasting wind waves along the east coast of Florida and it performed well for both low- and high-pressure weather systems. Figure 2.11 shows the
comparisons between the hindcasted and the measured waves at Marineland station for a two months period in 1984 (September and October) when three hurricanes and two northeasters hit the coast.
Based upon the actual wave data collected at those stations with duration of more than four years, extreme wave height analysis was performed by Lin and Wang (1988). Using monthly maximum waves as data base, they have shown that Fisher-Tippett Type I distribution, or commonly known as the Gumbel distribution, to have the best fit for both east coast and west coast waves and in both deep and shallow water.
By denoting the significant wave height as Hs, the Type I distribution of the significant wave height is expressed as H -d
=l(Hs exp [- exp (- s c = exp[- exp(-y)], c > 0, d > 0 (2.1)
where c and d are the data-dependent shape factors and y is known as the reduced variate. Table 2.3 summarizes the values of c and d for the best fit at 15 selected study sites (9 deep water and 6 shallow water). All these data sets are found to lie within a 99 percent confident limit. An example is
given in Fig. 2.12.




Marineland Station

S
E
N
W
S
1

10 20 30 10 20

Oct. 1984

1 10 20 30 10 20

Oct. 1984

Figure 2.11. Comparisons of CDN and UCWP Average Wave Direction,
Significant Wave Heights and Peak Energy Frequencies
at the Marineland Gage Location.

Computed Data (UCWP)
IIIIIIIIIIIIII11ll1IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

20
Oct. 1984

Sept.

Sept.

5
0
25
20 1510

Sept.

-




Table 2.3 Summary of the values of c and d at the 15 selected study sites
CDN wave gage data
station data length c d water depth
or ID# (from to) (m) (m) (m)
Jacksonville 6/84-12/87 0.457 1.59 10.1
Marineland 1/81-12/87 0.497 1.80 11.4
Cape Canaveral 3/82-10/87 0.412 1.23 8.0
West Palm Beach 3/82-12/86 0.444 1.55 9.9
Miami Beach 7/83-12/87 0.394 1.02 6.5
Clearwater 3/82-12/87 0.373 0.92 5.8
WIS hindcasted wave data
station data length c d water depth
or ID# (from to) (m) (m) (m)
Jacksonville 1/56-12/75 0.472 1.80 10.0
Cape Canaveral 1/56-12/75 0.450 1.62 10.0
West Palm Beach 1/56-12/75 0.456 1.57 10.0
mean: 0.459 1.66 10.0
(s.d.*) (0.011) (0.12)
NOAA buoy data (Atlantic Ocean)
station data length c d water depth
or ID# (from to) (m) (m) (m)
41001 6/76- 4/86 1.639 4.21 4000
41002 11/75-4/86 1.587 4.00 3900
41006 5/82- 4/86 1.563 4.16 1200
44003 3/79- 4/86 1.563 4.20 150
44004 9/75- 4/86 1.538 4.21 1300
44005 1/79- 4/86 1.471 4.12 120
mean: 1.560 4.15
(s.d.*) (0.055) (0.08)
NOAA buoy data (Gulf of Mexico)
station data length c d water depth
or ID# (from to) (m) (m) (m)
42001 8/75- 4/86 1.250 2.59 3300
42002 3/77- 4/86 1.282 2.71 2400
42003 7/77- 4/86 1.235 2.59 3250
mean: 1.256 2.63
(s.d.*) (0.024) (0.07)
* s.d. stands for standard deviation.




o RETURN PERIOD(TERR)
9; 2, s p 29 59 1po
STATION: MRRINELRNO (H,- C
9 0(H3) =EXPE-EXP (---- 3
C- 1.604 d. 0o.49g7
- TYPE I LINE (GUMBEL'S APPROACH ) o ==CONTROL BRND(99Z C.I.)
S MONTHLY ORTA(C.D.N.)
-
9--

.Do -.00 -,.00 0.00
REDUCED

2.00 4.00 VARIRTE, T

Figure 2.12.

o.ood d.ot 'o.t o'. s o .e o'. s o.e s o. 99 o :ea s oese b.es
PROBABILITY, e (Hs)
Probability Distributions of the Monthly Largest Wave Heights at the Wave Gage Location near Marineland, Florida.

6.00

8 .00




It is observed that estimated values of both parameters c and d increase monotonously with increasing water depth. Both parameters, c and d, are
plotted against the mean water depth as shown in Figure 2.13. Knowing that
both c and d should be zero when the water depth is zero and that the upper bound values of c and d should approach the deepwater values from the NOAA buoy data empirical formulas can be developed. For the east coast the
following formulas are proposed:
3/7 h
c = 1.56-(tanh T60) and d = 4.15.tanh T (in metric unit) (2.2)
based on the mean values obtained by the deepwater buoy data. For the west
coast of Florida, the c and d parameters in the extreme wave height statistics can be approximated by the following formulas:
3/7 h 3/2
c = 1.25"(tanh -0 and d = 2.63.(tanh-1-) (in metric units) (2.3)
Estimates of 20, 50, and 100 year return values of H., at the different water depths of 5, 10, 20, and 50 m, based on Eqs. 2.1, 2.2 and 2.3, are given in Table 2.4. The significant wave heights predicted to the west coast of Florida are in general smaller than those to the east coast of Florida. This is because the fetch is limited in the Gulf of Mexico.
Nearshore Wave Information
In the nearshore region waves usually have onshore directions. Even
under the offshore winds, the waves may still have overall onshore direction due to propagation of distant waves. This is often the case for the waves observed near the Florida coast at the CDN wave gages. Examples displaying
the wave roses, which show the information of percentage wave energies found




3 6 9 12

WATER DEPTH (m) Figure 2.13. Plots of the Proposed and Esitmated Values of c and d.




Design H, (m) at the east coast of Florida
water depth 5 10 20 50
return period (M) (M) (M) (M)
20 (year) 2.75 4.18 6.25 9.12
50 (year) 3.08 4.62 6.84 9.98
100 (year) 1 3.32 1 4.94 7.28 1 10.63
Design H. (m) at the west coast of Florida
water depth 5 10 20 50
return period (M) (M) (M) (M)
20 (year) 2.63 4.16 5.85 7.55
50 (year) 2.94 4.58 .42 8.37
100 (year) 1 3.18 1 4.91 6.85 1 9.00

Table 2.4 Predictions of 20, 50, and 100 year return values of H.




in each of the 32 evenly-divided circular directional bands, at the location of St. Mary's entrance near Georgia and Florida border and the Venice gage are given in Figure 2.14.
At present, the directional wave data collected by the CDN wave gages are not of sufficient duration to facilitate the long-term statistical study. The hindcasted directional wave information is available from the 20-year hindcast data by the WIS group of the Waterways Experiment Station, the U.S. Army Corps of Engineers (Jensen, 1983). The information does not include the hurricane waves.
To determine littoral drift environment, the most pertinent wave information is the wave height versus direction distributions just outside the
surf zone (wave period only plays a minor role in the littoral drift equation). To establish such information, the following simplified procedures are suggested:
a. Prepare a joint probability table of wave direction. Establish a
grid system encompassing the coastline of interest and extend the grid to offshore to deep water condition or to the location where the offshore wave information is available. The grid size depends on offshore topography. In general, a half mile should be a reasonable choice to 30 ft contour. Within
the 30 ft contour, the grid size should be reduced further.
b. Eased upon the shoreline orientation, select wave directions that will impact the shoreline. For the east coast of Florida, waves from NE, E.
SE and S should probably be included. Wave statistics of height-perioddirection distributions at the offshore boundary should be established based upon available wave information. An example for the wave conditions, offshore
Indian River County, is given in Figure 2.15 based upon WIS model output (30 ft contour line).




~S
ST.MART:Y#4 GAGE
ST.MARYTu GAGE

ST.MARY#4 GAGE

87 M 1 M>Hs
LEGEND: EM 2M>Hs21m S IIIIIIl 3 M> HS>2M
- Hs23M
VENICE GAGE ,
0% 5% 10%
Figure 2.14. Wave Roses Obtained at the St. Marys Entrance #4 and
Venice Gage Locations.




3. 1. 0.
(DEG.I

PROBABILITY DISTRIBUTION OF INCIDENT WAVE HEIGHTS AND DIRECTIONS

The Location of #152: Riomar, Florida
Depth = 10 m

Water Depth = 10 m
(WIS # 152)

.. 125
j126
127
128
665
S 129 PHASE n
BU 130 *
131
* 132 957 PHASE I
13 PHASE n
2 134
JACKSONVILLE 135 059
PHASE 2
136 ATLANrc OCEAN
41 PHASE
DAYTONA BEACH 142
144 PHASE U
145PHASE
146 1
147 PHASE M
148 149
150 PHASE n
151
VERO SEA 53 PHASE 1

Figure 2.15. Wave Roses at St. 152 (Offshore Indian River County) Based
upon WIS Hindcast at 10 m Depth.




c. Construct wave refraction diagram for each of the wave periods used in the wave statistics. For the present example four wave periods 5, 7, 9, and 12 sec. were used. Wave rays from the four directions, for each of the four periods, were generated using a reference deep water wave height of 1 m. The wave amplification factors for each wave period from each direction can thus be established.
d. Compute shallow water wave height through multiplying deep water wave height by the amplification factor. The distributions of wave height wave period direction in the nearshore area can then be established. Since wave period is not important in littoral drift computation, often only wave heightdirection distribution information is required. Figure 2.16 shows the
nearshore wave height roses along Indian River County based upon the WIS output at 30 ft. contour given in Figure 2.15.
STORM SURGE AND WATER LEVEL CHANGES
Water level rise is perhaps the most damaging factor causing beach and dune erosion. This is because water level rise will submerge the backshore that is not in a state of equilibrium and will increase wave energy by sustaining larger waves owing to the increase in water depth.
Water level change consists of three main components: long term mean sea level change, astronomical tide and meterological tide. In engineering work such as beach nourishment, the meteorlogical tide also known as the storm surge is by far the most important factor because of its transient nature, large magnitude and unpredictability.
Along the Florida Coast, storm surges are generated by three types of storms: extratropical cyclone, tropical cyclone and intermediate type of storm.




0
so 120
0 bSO
.0 c I teeJ i
PROBABILITY DISTRIIBUTION CF BREKING W AVE HEIGHTS AND
DIRECTIONS AT 63000 FEET

30

30
PRMf9i IL IT DISTRIBIuIIN OF 8RERKING WAY DIRECTItONS I 3000 FEET

0 10000 20000 30000 40000 50000 60000 70000 SC DISTANCE ALONG BASELINE (ft)

Figure 2.16. Nearshore Wave Height Roses Along Indian River County Shore.

3. 0.



The extratropical cyclones usually originate in high and mid latitude. They are large scale system of 500 miles to over 1000 miles and are relatively stationary. They are not a major threat to the Florida Coast in terms of high winds. However, because of their scale and duration, they are responsible for most of the severe winter erosions along the east coast of Florida, particularly, in the northern portion of the State.
Most of the severe storm surges recorded in Florida were caused by hurricanes or tropical storms of a severe nature (wind speed exceeds 74 miles per hour). They are intense systems of a much smaller scale, about 10 to 50 miles from the center to maximum wind known as the radius of the hurricane. They are also more rapid-moving than northeasters with widely varying tracks. Along the Florida coast, severe hurricanes and associated storm surges occur somewhere two to three times per decade.
The intermediate type of storm, called a "subtropical storm" is a mixed type of extratropical and tropical characteristics. Six subtropical storms
have been identified in or near Florida (Harris, 1982). They are infrequent
and not a major threat.
Since high storm surges are localized phenomenon induced by infrequent high-intensity landfall or near landfall storms, field record is usually not sufficient to determine the design value through statistical analysis.
Numerical simulation coupled with storm surge model is usually employed to generate design information. Storm surge modeling is quite an advanced
field. There are numerous storm surge models; most of them are adequate for their intended area and weather conditions.
In Florida, a Coastal Control Construction Control Line (CCCL) program was instituted in the 1970s that mandates all the new constructions have to set back behind the 100-year coastal flood line. Therefore, adequate storm




surge model is available. Federal Emergency Management Administration (FEMA) is also continously updating their coastal flood levels. The current
methodology used by the Florida Department of Natural resources for generating storm surge information is illustrated by the Flow Chart shown in Figure
2.17. The procedure consists of developing and verifying a 2-dimensional hurricane storm surge model for regional application (county by county
basis). The model is calibrated and adjusted with real storm surge record. A 1-dimensional simplified model is then calibrated against the 2-dimensional model and used to reduce the cost of computations for a large number of runs simulating a 500-year duration of storm tides. The dynamic waves set-up is also included in the simulation.
The input wind fields are generated by a 5-parameter wind model. The
five parameters are: central pressure, radius of maximum wind, forward speed and hurricane translation direction and landfall characteristics. The
landfall characteristics are defined as "landfalling" and "along shore" as shown in Figure 2.18. Historical hurricane data from 1871 to the present are then used as the statistical base for generating these parameters. An example of the simulated storm surge level vs return period is given in Figure 2.19. Detailed description of the storm surge simulation model for the State of Florida can be found in Dean and Chiu (1981). MORPHOLOGICAL AND SEDIMENTARY CONDITIONS
Morphological conditions and sediment property greatly affect the shore process and the littoral drift environment which, in turn, govern the rate and shape of shoreline changes. Inlets often behave as littoral drift barriers depriving sand to the down drift side; river mouths, on the other hand, often serve as sand sources transporting material from upland to the beach. Headlands and rock outcrops are stable morphological features and often cause




Choose Hurricane
D Calibrate 2-D Variable Characteristics in
Develop 2-D Variable Grid Model Against Accordance with
Grid Model Recorded Storm Tides Historical Data
for the Study Area

Develop 1-D Model and Run the Same Cases for Landfalling, Exiting and Alonqshore Hurricanes

Run 11 cases each for Landfalling, | Exiting and Alongshore Hurricanes
with 2-D Variable Grid Model

Correlate Results Simulate Storm Tides- and Cacorm Tides
of 2-D to 1-D Joint Probability and Calculate Return
_j Jint robbiliy Aalyss Periods

Flow Chart for Storm Surge Simulation (Dean and Chlu, 1981).

| || |

Figure 2.17.




Approximate Shoreline Orientation 3A .
Alongshore 0
Hurricanes ,3,
bo Exiting
Hurricanes 1490
Landfalling Hurricanes
.I@o Alongshore Hurricanes
Figure 2.18. Designation of Alongshore, Landfalling and Exiting Hurricanes
depending on Track Directions Relative to Shoreline Orientation
(Dean and Chlu, 1981).




CHARLOTTE COUNTY
Middle Profile...... North Profile-/ '. South Profile
/.. '"

100

200

RETURN PERIOD (years)

Figure 2.19.

Combined Total Storm Tide Elevation Versus Return Period for Three Repersentative Transect Lines in Charlotte County (DNR, CCCL Program).

500




abrupt change or reversal of littoral drift pattern. Offshore reefs and
outcrops provide natural shields against wave attacks and create discontinuity of offshore profiles. Spits are usually unstable and are commonly associated with adjacent shoreline rotations and/or elongations. The occurrence of large
scale sand waves, a not well understood phenomenon, creates a migratory shoreline deformation along the coast. Sand dunes provide added protection for the upland and on the same time supply sand to the beach during storms. Major or drastic shoreline changes are usually related to morphological changes such as opening and closure of inlet, offshore dredging or the construction of man-made structures. Therefore, a survey of morphological condition is essential for the planning of beach nourishment projects and for aid in the interpretation of dynamic processes.
Sediment property is the single most important factor affecting the beach profile shapes, particularly, the so-called equilibrium profile which plays an important role in beach nourishment engineering. Referring to the definition sketch of beach profile in Figure 2.20 the most active portion of the beach is
within the foreshore and inshore zones. Under steady wave actions, this
portion of the beach tends to reach a stable shape. Based upon field
evidence, Bruun (1954) and later Dean (1977) found this stable profile can be expressed by a power function:
h(x) = A xm (2.4)
where x is the axis normal to the shoreline and h is the water depth along the profile. In application, the origin is selected at the mean high water (MHW) with positive axis pointing offshore. The value m is found to be approximately equal to 2/3, which is consistent with a model proposed by Dean




Figure 2.20. Beach Profile Definition Sketch (CERC, 1973).
39




(1983) assuming spilling breaker and uniform wave energy dissipation per unit water volume inside the surf zone as the mechanism of sediment suspension. The coefficient A was evaluated by Moore (1982) and Dean (1984) and found to be mainly a function of sediment grain size (or more appropriately sediment particle fall velocity). More detailed treatment on the equilibrium profile and its application to beach nourishment is given in the next chapter.
One should realize that the proposed equation only represents an approximation of a typical beach shape under mild wave condition. Field
survey including profiling and sediment sampling is essential to establish correctly the typical profile for the region of interest. It is also
important to differentiate the normal and storm profiles of the region and their influence on beach width and storm protection.
Sediment property is also important for determining the compatibility of nourishment material. There is no central data inventory in the State of Florida on beach sand property. Sand sampling and analysis should be an integral part of the nourishment project. U. S. Corps of Engineers,
Jacksonville District does maintain records of offshore core samples, which are useful for preliminary analysis of potential borrowing material.
HYDROGRAPHIC SURVEY
Detailed hydrographic survey information is required for the following purposes:
a. To calculate the required quantity of beach fill.
b. To serve as baseline for the future monitoring and performance
analysis.
c. To use as input for littoral drift and shoreline change computations.
A number of essential points should be observed, whenever possible:




a. The survey should tie in with the DNR monuments and the state's plan
coordinates.
b. The survey should cover from the dune line (or hard structure) to the
closure depth, if possible.
c. MHW line should be noted in the survey.
d. The survey should cover both summer and winter seasons and/or at the
same season that the DNR survey information in the past is available.
e. Based upon the analysis of historical shoreline and volumetric
changes and the accompanying sensitivity analysis as illustrated in the Section "Historical Shoreline Information" areas requiring special attention should be noted. The requirement of survey
accuracy and error tolerance should also be established to insure
useful survey results.
LITTORAL DRIFT ENVIRONMENT
To estimate the rate of littoral drift in the absence of actual field measurement, the accepted practice is to relate the longshore sediment transport rate to the longshore component of "wave energy flux", or
t= k Ptas(2.5)
where It is the immersed weight transport rate and Pits is the longshore energy flux factor. Based upon linear wave theory, P ts at the breaker line can be estimated as:
y 2
P2, =Y N Cgbsin 2(ab ) (2.6)
where y is the specific weight of sea water; 11b is the breaking wave height; Cgb is the wave group velocity at the breaking point; ab is wave breaking angle and 0 is shoreline normal. Since It, and P2,5 have the dimension (force/time), a should, in theory, be unity. Various K values have been




suggested. The value recommended by SPM (1984) is 0.39 if wave energy is based upon significant wave height. Komar and Inman (1970) recommended K = 0.77 using wave energy based upon HRMS value. It is often more practical for engineering application to express the sediment transport rate in terms of volumetric transport rate. In this case, the coefficient of proportionality is no longer dimensionless and we have
Q (m3/yr) = 1290 (m3-s/N-yr) P~s(N-m/m-s)
(2.7)
Qp(yd3/yr) = 7500 (yd3-s/lb-yr) Pps(ft-lb/ft-s)
using Hs as basis for energy computation.
The value of K suggested above is suitable for straight shoreline of normal sandy beach. The actual value of K for a specific shoreline is influenced by the material, foreshore geometry, man-made structures and natural changes, etc., and is, therefore, expected to vary from the suggested value.
Based upon the wave information and the longshore transport equation, long-term or short-term littoral drift environment can be established. Figure 2.21 shows an example of longshore sediment transport computation for the month of December 1987, near Ponce de Leon, Florida. The computation started with wind as input to generate waves in deep water. The waves were then
carried into shallow water, which in turn, were the input to the longshore transport equation. In the example given here the time increment in the computation was 10 min. The wind information was reported at 3 hrs interval. Linear interpretation was used to establish wind condition at 10 min. interval. Figure 2.22 shows the cumulative transport rate. The impact




LONGSHORE SEDIMENT TRANSPORT

20
15 T.10 (SEC)
5 0
3LI 3

1 5 10 15 20 25 30 I I I
15 10 15 20 25 30

1 5 10 15 20 25 30

10
Tn
(10 )
-10

Figure 2.21.

DEC..1987
Example of Longshore Transport Computation based upon Wind Information for 1 hour, Month of December 1987, near Ponce de Leon, Florida.




LONGSHORE SEDIMENT TRANSPORT
5o
N PONCE DE LEON TOTAL VOLUME(AR03)=-26523.4
AZIMUTH=2050
25
C
cn
8 -25
S
- R 0 t I I I I I I ft I 1 I I I I I t i I I 1 i I i I i I i i I i
1 5 10 15 20 25 30
DEC.,1987
N PONCE DE LEON TOTAL VOLUME (YARD )= -26523.4
AZIMUTH=205o
2
cc x
-j
-2
S
1 5 10 15 20 25 30
DEC.,1987
Figure 2.22. Cumulative Longshore Sediment Transport Rate,
D7e
N PONCE DE LEON TOTAL VOLUME (rARI3:'-26523. 4
AZ IMUTH=2050
2
c
CD
LU
(n-2
z
1 01 2 53
DE.18
Fiue22.Cmltv0oghoeSdmn rnpr ae
Decem DEC. 197.1987 eLon loia
44




of episodic events is clearly seen. Figure 2.23 shows the histogram of
longshore transport at the same site for year 1987. Based upon this computation, the annual net littoral drift is estimated to be around 123,000 cu. yd/year. This value falls in between the estimate of 500,000 cu. yd/year
made by Corps of Engineers and the estimate by Walton (1973) of 77,000 cu. yd/year. The estimate made by Corps was based on analysis of dredging records, volumetric surveys, and pumping records at existing by-pass plants. Walton's estimate was based upon SSMO wave data.
SAND SOURCES
The economic feasibility of beach nourishment project depends heavily upon the availability of suitable sand sources. There are three major sand
sources from offshore, (1) inlet dredging and maintenance, (2) ebb tidal shoals, and (3) offshore borrow sites. Various Federal, State and local
interests have undertaken investigations in attempts to locate and quantify the sand sources. Recently, Bodge and Rosen (1988 a.b) have attempted to summarize the offshore sand sources for beach nourishment along the Atlantic
and Gulf coasts of Florida. Marino and Mehta (1986) have compiled the
sediment volumes around Florida's east coastal tidal inlets. Many of the
offshore sand sources can be found from the Inner Continental Shelf Sediment and Structure (ICONS) studies conducted by U.S. Army Corps of Engineers. Table 2.5a,b provides a list of sand sources along the Florida coast.
The suitability and potential available volume of offshore and inlet related sources are limited by several factors, among them (Bodge and Rosen, 1988a):




LONGSHORE SEDIMENT TRANSPORT

a:
cc
0

-30

JAN FEB MAR APR MAY JUN JUL RUG SEP OCT NOV DEC 1987
Figure 2.23. Histogram of Longshore Sediment Transport Rate
at Ponce de Leon Inlet, 1987.




Table 2.5a Sand inventory along Atlantic coast, FL.

Ebb shoal Dredging/ Nearshore Offshore
Inlet by passing site site
Vol. x 10-6 Vol. x 10-3 Vol. x 10-6 Vol. x 10-6 Distance (cu.yd) (cu.yd/yr) (cu.yd) (cu.yd) (Mi)
St. Marys 126.0 1000.0
Nassau Sound 53.0 --- - ?14.0
Ft. George 174.0 280.0
St. Augustine 110.0 200.0
Matanzas 6.0 -50.0 105.0(4) 11.0
Ponce de Leon 22.0 140.0
50.0 ..
Port Canaveral 6.0 200.0
Sabastian 0.1 100.0 56.0(5)
5.5)16.0 12.0
Ft. Pierce 30.0 23.0
St. Lucie 22.0 260.0
77.0 -
Jupiter 0.4 35.0
100.0 ......
Lake Worth 3.8 70.0
100.0 ......
S. Lake Worth 1.4 60.0
76.0 ..
Boca Raton 0.8 60.0
8.0 ......
Hillsboro 60.0
10.0 ..
Pt. Everglades 40.0
12.0 .....
Haulover 0.6 15.0
Gov'nt Cut 3.0 --K ey W est -5.0 .. .
1.0 --Number in parenthesis indicates number of sites more than one ? Quantity unknown
***Quantity negligible
- - No estimate




Table 2.5b Sand inventory along Gulf coast, FL.

Ebb shoal Dredging/ Nearshore Offshore
Inlet by passing site site
Vol. X 10-6 Vol. X 10-3 Vol. X 10-6 Vol. X 10-6 Distance (cu.yd) (cu.yd/yr) (cu.yd) (cu.yd) (Mi)
Hurricane P. 0.2 --Dunedin P. 0.2 ---
Clearwater P. 0.2 40.0
Johns P. 0.6 60.0
0.2 ..
Blind P. 0.2 ---
Bunces P. --- 12.0(2)
30.0 ......Passage Key ......
Longboat Key 8.0 47.0 14.0(3)
1.0 ..
New P. 4.4 74.0
Big Sarasota P. 14.0 - --Midnight P. 0.6 ---
Venice I. 0.4 7.0
Stump P. -- 4.0 5.0(2)
Gasparilla P. 3.5 ---
Boca Grande P. 160.0 290.0
Captiva P. 12.0 -
Redfish P. 3.0 ---
San Carlos/
Ft. Myers 26.0 31.0 18.0(5)
Doctors P. --Gordon P. 0.6 32.0 4.0(2) --Number in parenthesis indicates number of sites more than one ? Quantity unknown
***Quantity negligible
- - No estimate




1). sediment grain size,
2). population of clays, silts, and rock,
3). local water depth,
4). environmental considerations,
5). gross size of sand deposit,
6). distance to the project area, and
7). potential impacts of borrowing to local littoral process.
BIOLOGICAL CONDITIONS AND WATER QUALITY
In the United States, environmental impact study becomes an integral part on any dredging and beach fill project. Although the scope of environmental
impact is expanding and varies f rom region to region, the primary concern is still the impact on the biological communities and water quality during the following three phases:
- dredging transport placement
Since biological communities are closely related to site and the
implementation method of nourishment, a site -and method specific analysis is usually required.
In the State of Florida, the common questions addressed by the regulatory agencies include:
detailed biological sampling data from the borrow sites and
nourishment sites;
detailed surveys of rock outcrops, reef s, grass beds, and any other
features in the areas of the borrow and nourishment sites;




a survey of turtle nesting sites;
details on dredging, transport and placement methods and the techniques to maintain water quality standards, particularly in
relation to turbidity monitoring and control.
Although there is no central data bank on biological communities along the Florida coast, a considerable amount of information is available in open literatures. Nelson (1985) gave an excellent account on the background information of biological effects of beach nourishment. He stated that there
is considerable more information on the effects of dredging on benthic communities but much less is known about the specific environmental consequences of beach nourishment.
The area that a major void exists is the lack of background information on water quality and the effects of turbidity created by the nourishment operation.
Nelson also suggested biological monitoring procedures on beach nourishment project.
NATURAL AND MAN-MADE STRUCTURES
An inventory of natural and man-made structures is also important for beach nourishment design. Since a nourishment project is expected to interact
with its adjacent beaches, the inventory should include zones beyond the immediate nourishment area to the boundaries of a natural littoral drift cell. In Florida, this often means between two adjacent inlets. The
following types of structures are particularly significant:
- inlets (existing and old)
- seawalls and revetments
- past nourishment projects sand dunes and vegetations
- outcrops




References
Bodge, K. R., and Rose, D. S. (1988) Offshore Sand Sources for Beach Nourishment in Florida; Part 1: Atlantic Coast, Proc. National Beach Preservation Technology 88, Gainesville, FL, Florida Shore and Beach
Preservation Association.
Bodge, K. R., and Rose, D. S. (1988) Offshore Sand Sources for Beach
Nourishment in Florida; Part 2: Gulf Coast, Proc. National Beach Preservation Technology 88, Gainesville, FL, Florida Shore and Beach
Preservation Association.
Dean, R. G. (1983) Shoreline Erosion Due to Extreme and Sea Level Rise,
UFL/COEL-83/007, Coastal and Ocean. Engr. Dept. Univ. of Fla.,
Gainesville, FL.
Dean, R. G. (1984) Application of Equilibrium Beach Profile Concepts, 19th
International Coastal Engr. Conf. ASCE, Houston, TX.
Dean, R. G. and Chiu, T. Y. (1981) Hurricane Tide Frequency Analysis for
Broward County, Florida, UFL/COEL-81/001 Coastal and Ocean. Engr. Dept.
Univ. of Fla., Gainesville, FL.
Harris, D. L. (1982) The Prediction of Hurricane Storm Surges, a State-of-theArt Survey, SGR 49, Florida Sea Grant College, Univ. of Fla.,
Gainesville, FL.
Jensen, R. E. (1983) Atlantic Coast Hindcast, Shallow-water, Significant Wave
Information, Wave Information Study, Report 9, U.S. Army Engineer
Waterways Experiment Station, Vicksburg, Mississippi.
Lin, L. (1988) A Coupled Discrete Spectral Wave Hindcast Model, Technical
Report, TR-076, Dept. of Coastal and Oceanographic Engineering,
University of Florida, Gainesville, Florida.




Lin, L., and Wang, H. (1988) Analysis of Extreme Wind Speed and Significant
Wave Height Along Florida Coast, Proc. Ocean Structural Dynamics
Symposium '88, Oregon, Oregon State University Press.
Moore, B. (1982) Beach Profile Evolution in Response to Changes in Water Level
and Wave Height, M.S. Thesis, Dept. of Civil Engr. Univ. of Del. Newark,
DE.
Nelson, W. G. (1985) Guidelines for Beach Restoration Projects, Part 1
Biological, SGR-76, Florida Sea Grant College.
Walton, T. L. (1973) Littoral Drift Computations Along the Coast of Florida by
Means of Ship Observations, Rep. UFL/COEL/TR-015, Univ. of Florida
Coastal Engineering Laboratory, Gainesville, FL.
Wang, W. C. and Wang, H. (1987) Data Compilation of the Historical Shorelines
and Offshore Bathymetry for the Southeast Coast of Florida UFL/COEL87/015 Coastal and Ocean. Engr. Dept. Univ. of Fla., Gainesville, FL.
Wilson, E. E. (1975-1986) Mariners Weather Log, National Oceanic and
Atmospheric Administration, Environmental Data and Information Service,
U.S. Dept. of Commerce, Volumes 19-30. WIS Wave Models
Corson, W. D., et al. (1981) Wave Information Studies of U. S.
Coastlines; Atlantic Coast Hindcast, Deepwater, Significant Wave Information, WIS Report 2, U.S. Army Engineer Waterways Experiment
Station, CE, Vicksburg, Miss.
(1982) Wave Information Studies of U.S. Coastlines; Atlantic Coast Hindcast, Phase II Wave Information, WIS Report 6, U. S.
Army Engr. Waterways Experiment Station, CE, Vicksburg, Miss.
Jensen, R. E. (1988) Wave Information Studies of U. S. Coastlines, Methodology for the Calculation of a Shallow-Water Climate, WIS Report 8,
U. S. Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss.
52




(1983) Atlantic Coast Hindcast, Shallow-Water Significant Wave Information, WIS Report 9, U. S. Army Engr. Waterways Experiment Station, CE, Vicksburg, Miss.




CHAPTER 3
ENGINEERING DESIGN PRINCIPLES
PART II DESIGN
Robert G. Dean
Coastal and Oceanographic Engineering Department University of Florida, Gainesville
INTRODUCTION
It is convenient to discuss the physical performance of beach nourishment
projects in terms of the cross-shore response (or profile adjustment) and longshore response, i.e. transport of sand out of the area placed. It is also convenient in exploring performance at the conceptual level to utilize idealized considerations and simplified (linearized) equations in some cases. This allows one to obtain a grasp or overview of the importance of the
different variables without the problem being clouded by complications which may be significant at the 10% 20% level. To simplify our cross-shore
considerations, we will use the so-called equilibrium beach profile concept in
which the depth h(y) is related to the distance offshore, y, by the scale parameter, A, in the form
h(y) = Ay 2/3 (3.1)
Although this is not a universally valid form, it serves to capture many of the important characteristics of equilibrated beach profiles. To assist in
providing an overview of transport in the longshore direction, we will utilize
the linearized combined form of the transport and continuity equations first developed by Pelnard Considere'
D_ = G a 2y (3.2)
at a




where x is the longshore distance, t is time, G is a longshoree diffusivity" which depends strongly on the wave height mobilizing the sediment and Eq. (3.2) is recognized as the "heat conduction equation".
CROSS-SHORE RESPONSE
Beach Width Gained vs. Sediment Quality
From Fig. 3. 1, it is seen that the scale parameter, A, in Eq. (3. 1) decreases with decreasing sediment size. Thus, as presented in Fig. 3.2, a finer sediment will be associated with a milder sloped profile than one composed of coarse sediment. We will denote the native and fill profile scale parameters as AN and AF, respectively. The consequence of sand size to beach nourishment is that the coarser the nourishment material, the greater the dry beach width per unit volume placed.
Nourished beach profiles can be designated as "intersecting" and "nonintersecting" prof iles. Figure 3.3 presents examples of these. As will be presented, a necessary but not sufficient requirement for profiles to intersect is that the placed material be coarser than the native. Fig. 3.4
illustrates the effect of placing the same volume of four different sized sands is shown. In Fig. 3.4a, sand coarser than the native is used and a relatively wide beach Ay is obtained. In Fig. 3.4b, the same volume of sand of the same size as the native is used and the dry beach width gained is less. More of the same volume is required to fill out the milder sloped underwater profile. In Fig. 3.4c, the placed sand is finer than the native and much of the sand is utilized in satisfying the milder sloped underwater profile requirements. In a limiting case, shown in Fig. 3.4d, no dry beach is yielded with all the sand being used to satisfy the underwater requirements.




DE
(I)
I
z
(I)

SEDIMENT SIZE, D (mm)

Beach Profile Factor, A, vs. Sediment Diameter, D, In Relationship h = Ax2/3 (modified from Moore, 1982).

1.0
0.10
0.01
0.01

0.1 1.0 10.0 100.0

Figure 3.1.




DISTANCE OFFSHORE (m)
100

200

Equilibrium Beach Profiles for Sand Sizes of 0.2mm and 0.6mm A(D = 0.2mm) = 0.1 m 1/3, A(D = 0.6mm) = 0.20 m 1/3

Figure 3.2.




(a) intersecting Profiles
L~AX1
(b) Non-Intersecting Profiles
Figure 3.3. Two Generic Types of Nourished Profiles.




92.4m
7B = 1.5m

a) Intersecting Profiles, AN= 0.1mI 3,AF = 0.14ml /3

45.3m
-p1_ he-_

5.9m

c) Non-intersecting Profiles AN= 0.1ml /3,Ap = 0.09ml /3

- d) Limiting Case of Nourishment Advancement, 1 Non-Intersecting Profiles, AN= 0.1m1 /3,AF = 0.09m /3
1 1 1 I I 1 I

100

200

300

400

500

600

OFFSHORE DISTANCE (m)

Effect of Nourishment Material Scale Parameter, A F, on Width of Resulting Dry Beach. Four Examples of Decreasing AF -

Z 10
0
> 5
w
-j
wL

Figure 3.4.




We can quantify the results presented in Fig. 3.4 by utilizing the equilibrium profile concepts. It is necessary to distinguish two cases. The first is with intersecting profiles such as indicated in Fig. 3.4a and requires AF > AN. For this case, the volume placed per unit shoreline
length, 4 1 associated with a shoreline advancement, Ay, is presented in nondimensional form as
I= y +3h, A 5/31 (3)
BW-- W--y --(,) 1
BW W 5- (AN)3/2 2/3
in which B is the berm height, W* is a reference offshore distance associated with the breaking depth, h*, on the original (unnourished) profile, i.e.
h, 3/2
w, = (A (3.4)
and the breaking depth, h* and breaking wave height, Hb are related by
h, = Hb/K
with K (p 0.78), the spilling breaking wave proportionality factor.
For non-intersecting profiles, Figs. 3.3b and 3.4b,c and d, the corresponding volume, 2 in non-dimensional form is hA N 3/2 5/3 A 3/2
2 [w, + .){[., () (4(3
It can be shown that the critical value (Ay/W*)c for intersection/nonintersection of profiles is given by 3/2
(AY) -1-(Ai)(36
wt C f
with intersection occurring if Ay/W, is less than the critical value.




The critical volume associated with intersecting/non-intersecting profiles is
3 h A N 3 / 2( 3 7
( -) = i+ -)I- IAF (3.7)
cl F
and applies only for (AF/AN) > 1. Also of interest, the critical volume of sand that will just yield a finite shoreline displacement for non-intersecting profiles (AF/AN < 1), is
S=3 h* AN 3/2 A N
5 B (A (3.8)
Figure 3.5 presents these two critical volumes versus the scale parameter ratio AF/AN for the special case h*/B = 4.0.
The results from Eqs. (3.3), (3.5) and (3.6) are presented in graphical form in Figs. 3.6 and 3.7 for cases of (h*/B) = 2 and 4. Plotted is the nondimensional shoreline advancement (Ay/W*) versus the ratio of fill to native sediment scale parameters, AF/AN, for various isolines of dimensionless fill volume V (= W-) per unit length of beach. It is interesting that the shoreline advancement remains more-or-less constant for AF/AN > 1; for smaller values the additional shoreline width decreases rapidly. For AF/AN values
slightly smaller than plotted, there is no beach width gain, i.e. as in Fig. 3.4d.
Effects of Sea Level Rise on Beach Nourishment Quantities
Recently developed future sea level scenarios developed based on assumed fossil fuel consumption and other relevant factors have led to concern over the viability of the beach nourishment option. First, in the interest of
objectivity, it must be said that the most extreme of the scenarios published




15 1 1 3
_~
- LL
OO_ 10 ;-2 OO
00 I" 200
5 (2- ) -/ 1
C
OI O0 I 0
0 0
z 0 1 1l 1 1-1 z
0 1 2 3
AF/AN
Figure 3.5. (1) Volumetric Requirement for Finite Shoreline Advancement
(Eq. 3.8); (2) Volumetric Criterion for Intersecting Profiles
(Eq. 3.7). Variation with A F/AN. Results Presented for H./B 4.0.




0.001 Deflnitlon Sketch
0 1.0 2.0 2.8
A' = AF/AN
Figure 3.6. Variation of Non-Dimensional Shoreline Advancement Ay/W. with A' and V'. Results Shown for h, /B = 2.0.
10




1.0 0.1
0.01 0.001
0.0001 L
0

Variation of Non-dimensional Shoreline Advancement Ay/W,, with A' and V. Results shown for h, /B = 4.0.

1.0 2.0 2.8
A' = AF/AN

Figure 3.7.




by the Environmental Protection Agency (EPA) which amounts to over 11 ft. by the year 2100 are extremely unlikely. While it is clear that worldwide sea level has been rising over the past century and is highly likely to increase in the future, the future rate is very poorly known. Moreover, probably at least 20 to 40 years will be required before our confidence level of future sea level rise rates will improve substantially. Within this period, it will be necessary to assess the viability of beach restoration on a project-byproject basis in recognition of possible future sea level increases. Presented below is a basis for estimating nourishment needs for the scenario in which there is no sediment supply across the continental shelf and there is a more-or-less well-defined seaward limit of sediment motion; in the second case the possibility of onshore sediment transport will be discussed.
Case I Nourishment Quantities for the Case of No Onshore Sediment Transport
Bruun's Rule (1962) is based on the consideration that there is a welldefined depth limit of sediment transport. With this assumption, the only
response possible to sea level rise is seaward sediment transport. Considering the shoreline change Ay, to be the superposition of recession due to sea level rise AyS and the advancement due to beach nourishment, AYN,
Ay = AyS + AyN (3.9)
and, from Bruun's Rule
AyS = S (3.10)
S S*+
in which S is the sea level rise, W* is the distance from the shoreline to the depth, h*, associated with the seaward limit of sediment motion and B is the berm height. Assuming that compatible sand is used for nourishment (i.e. A F = AN)




Ay N = h,+ B (3.11)
and is the beach nourishment volume per unit length of beach. Therefore
S1 l[V_ SW,] (3.12)
(h,+ B)
The above equation can be expressed in rates by,
1 (3.13)
dt (h,+ B) *
dSd4
where for example, -S now represents the rate of sea level rise and- is the rate at which nourishment material is provided. It is seen from Eq. (3.3) that in order to maintain the shoreline stable due to the effect of sea level rise the nourishment rate is related to the rate of sea level rise by
riedt dtb
d-= dS (3.14)
dt *dt
Of course, this equation only applies to cross-shore mechanisms and therefore
does not recognize any background erosion, or longshore transport (so-called "end losses"). It is seen that W* behaves as an amplifier of material required. Therefore, it is instructive to explore the nature of W, and it will be useful for this purpose to consider an equilibrium profile given by
h = Ay2/3
in which A is the scale parameter presented in Fig. 3.1. Using the spilling breaking wave approximation
h, Hb A W,2/3
K
then




H 3/2
= KA(3 15
i.e. W* increases with breaking wave height and with decreasing A (or sediment size).
Case II Nourishment Quantities for the Case of Onshore Sediment Transport
Evidence is accumulating that in some locations there is a substantial amount of onshore sediment transport. Dean (1987) has noted the consequences
of the assumption of a "depth of limiting motion" in allowing only offshore transport and proposed instead that if this assumption is relaxed, onshore transport can occur leading to a significantly different response to sea level rise. Recognizing that there is a range of sediment sizes in the active prof ile and adopting the hypothesis that a sediment particle of given hydraulic characteristics is in equilibrium under certain wave conditions and
at a particular water depth, if sea level rises, then our reference particle will seek equilibrium which requires landward rather than seaward transport as resulting from the Bruun Rule. Figure 3.8 summarizes some of the elements of this hypothesis.
Turning now to nourishment requirements in the presence of onshore sediment transport, the conservation of cross-shore sediment yields
dy (h(y) + B) = d*+ Q (y) -ydS (3.16)
which must be balanced at each position, y, across the active zone. Without
some historical data, application of Eq. (3.16) is not possible. Stressing
again that Eq. (3.16) addresses only cross-shore sediment transport, to determine the background information, it is recommended that a representative




POSSIBLE MECHANISM OF SEDIMENTARY EQUILIBRIUM

Increased Sea Level
- S .A- Originlal Sea Level

Sediment .......
Particle
"Subjected to a Given Statistical Wave Climate, A Sediment Particle of a Particular Diameter Is in Statistical Equilibrium When in a Given Water Depth"
Thus When Sea Level Increases, Particle Moves Landward

Possible Mechanism of Sedimentary Equilibrium (After Dean, 1987).

Figure 3.8.




time period be selected over which reasonable estimates are available. Recognizing that the short-term response time scales of cross-shore transport are associated with sediment mobilization by breaking waves, it is recommended that a depth h* = Hb/K be used; in Florida, values of 15-20 ft. are suggested for h*. In the absence of beach restoration, the long-term value of Qs is
Qs = W,-{ + (h, + B) dy (3.17)
dS dt
where, again it is emphasized that all effects of longshore gradients in sediment transport are to be removed from the available dy/dt data. For
Florida, long-term trend estimates of dS/dt over the last 60 or so years are 0.01 ft./year although there is considerable variability in the year-to-year values of sea level changes, including interannual increases and changes which can amount to 40 times the annual trend value.
PLANFORM EVOLUTION OF BEACH NOURISHMENT PROJECTS
To a community that has allocated substantial economic resources to nourish their beach, there is considerable interest in determining how long those beaches can be expected to last. Prior to addressing this question, we will develop some tools.
The Linearized Equation of Beach Planform Evolution
The linearized equations for beach planform evolution were first combined and applied by Pelnard Consider6 in 1956. The combined equation is the result of the sediment transport equation and the equation of continuity.




Governing Equations
Transport Equation Utilizing the spilling breaker assumption, the
equation for longshore sediment transport has been presented as
K b 5/2 /g7 sin2eb
T (I-p)(s-l) 2 (3.18)
in which p is the sediment porosity (z 0.35-0.40) and s is the sediment specific gravity (= 2.65). Equation (3.18) will later be linearized by considering the deviation of the shoreline planform from the general shoreline alignment to be small. Referring to Fig. 3.9, denoting v as the azimuth of the general alignment of the shoreline as defined by a baseline, a as the azimuth of an outward normal to the shoreline, ab as the azimuth of the direction from which the breaking wave originates, then
K Hb5/2 KgI sin2(-ab)
q 8(l-p) (s-i) 2 (3.19)
where B = 2 tan- (x)
2 ax
Equation of Sediment Conservation The one-dimensional equation of
sediment conservation is
ay + 1 9Q = 0 (3.20)
at +(h *+ B) a x
Combined Equation for Beach Planform Evolution
Differentiating with respect to x, the equation for longshore sediment transport, Eq. (3.19), we find
DQ =K H b 52g7K cosB- (3.21)
ax = 8(l-p)(s-l) cos2(-b) ax
Recalling the definition of a and linearizing




0

Reference Base Line

Definition Sketch.

Figure 3.9.




tan'l ( a ax (3.22)
ax2 ax
and considering the wave approach angle (0-cb) to be small such that cos2(0-ab) 1 1, the final result is
aQ K H5/2 K ay (3.23)
ax 8(1-p)(s-1) ax2
Combining Eqs. (3.20) and (3.23), a single equation describing the
planform evolution for a shoreline which is initially out of equilibrium is obtained as
Y = Ga 2y (3.24)
at Dx2
where
Kb5/2/g-7/
G 8(s-l)(l-p)(h+ B) (3.25)
The parameter G may be considered as a "shoreline diffusivity" with dimensions of (length)2/time. Field studies have documented the variation of K with sediment size, D, as presented in Fig. 3.10. It is recognized that the form of Eq. (3.24) is the heat conduction or diffusion equation for which a number of analytical solutions are available. Several of these will be explored in the next section.
It is of interest to know approximate values of the shoreline diffusivity, G. It is seen that G depends strongly on Hb, and secondarily on Hb, (h, + B) and K. Table 3.1 presents values of G for various wave heights in several unit systems.




2.0

d 1.01-

0.5 1.0
DIAMETER, D (mm)

Figure 3.10.

Plot of K vs. D. Results of Present from Dean, 1978).

Ax M=

and Previous Studies (modified
YAx
0 x

Figure 3.11.

Initial Beach Planform. Narrow Strip of Sand Extending from Unperturbed Shoreline.

Result From This Study,
Santa Barbara
Relationship Suggested
Previously
I I I I




Table 3.1. Values of G for Representative Wave Heights Value of G in
Hb
(ft.) ft2/s mi2/yr m2/s km2/yr
1 0.0214 0.0242 0.00199 0.0626
2 2.121 0.137 0.0112 0.354
5 1.194 1.350 0.111 3.50
10 6.753 7.638 0.628 19.79
20 38.2 43.2 3.55 111.9
Note: In this table the following values have been employed: K = 0.77, K =
0.78, g = 32.2 ft/s2, s = 2.65, p = 0.35, h* + B = 27 ft. Analytical Solutions for Beach Planform Evolution
Examples which will be presented and discussed include: (1) the case of a narrow strip of sand protruding a distance, Y, from the general shoreline alignment, and (2) a rectangular distribution of sand extending into the ocean which could provide a reasonably realistic representation of a beach nourishment project.
(1). A Narrow Strip of Sand Extending into the Ocean
Consider the case of a narrow strip of sand extending a distance, Y into the ocean and of width Ax such that M = YAx, Fig. 3.11. The total area of the sand is designated M and the solution for this initial condition and the differential equation described by Eq. (3.24) is the following
y(x,t) = M x (3.26)
1'41TGt exp
which is recognized as a normal distribution with increasing standard
deviation or "spread" as a function of time. Figure 3.12 shows the evolution originating from the initial strip configuration. Examining Eq. (3.26), it is seen that the important time parameter is Gt. The quantity, G, which is the




y(x,t) m e-x2 /4Gt
7'4tG t

Figure 3.12. Evolution of an Initially Narrow Shoreline Protuberence.

1.0

Gt = 0.1

2.0,

5.0.

-10 -5 0 5 10
x/ 4dt




constant in Eq. (3.24) serves to hasten the evolution toward an unperturbed shoreline. In Eq. (3.25) it is seen that the quantity, G, is proportional to the wave height to the 5/2 power which provides some insight into the significance of wave height in remolding beach planforms which are initially out of equilibrium.
It is interesting that, contrary to intuition, as the planform evolves it remains symmetric and centered about the point of the initial shoreline perturbation even though waves may arrive obliquely. Intuition would suggest that sediment would accumulate on the updrift side and perhaps erosion would occur on the downdrift side of the perturbation. It is recalled that the
solution described in Fig. 3.12 really only applies for the case of small deviations of the shoreline from the original alignment and may be responsible for the difference between the linear solution and intuition.
For purposes of the following discussion, we recover one of the
nonlinearities removed from the definition of the "constant" G from Eqs. (3.20) and (3.21)
GK b 5/2g c (3.27)
8(s-1)(1-p)(h* + B) os2(B-b)
it is seen that if the difference between the wave direction and the shoreline orientation exceeds 450 then the quantity, G, will be negative. Examining the results presented earlier, it is clear that if this should occur then it is equivalent to "running the equation backwards". That is, if we were to
commence with a shoreline which had a perturbation represented by a normal distribution then rather than smoothing out, the perturbation would tend to grow, with the ultimate planform being a very narrow distribution exactly as was our initial planform! In fact, regardless of the initial distribution one




would expect the shoreline to grow into one or more accentuated features. Shorelines of this type (cos2(0-ab) less than zero) can be termed "unstable" shorelines and may provide one possible explanation for certain shoreline features including cuspate forelands.
(2). Initial Shoreline of Rectangular Planform
Consider the initial planform presented in Fig. 3.13 with a longshore length, t, and extending into the ocean a distance, Y. This planform might
represent an idealized configuration for a beach restoration program and thus its evolution is of considerable interest to coastal engineers, especially in interpreting and predicting the behavior of such projects.
It is seen that in a conceptual sense it would be possible to consider the problem of interest to be a summation of the narrow small strip planforms presented in the previous example. In fact, this is the case and since Eq. (3.24) is linear, the results are simply a summation or linear superposition of a number of normal distributions. The analytic solution for this initial planform can be expressed in terms of two error functions as
Y [ Z___ 2 _ 2x
y(x,t) = 2 {erf [ (2 + I)] erf (T- I)] (3.28)
where the error function "erf{ }" is defined as z 2
erf(z) = f e-u du (3.29)
and here u is a dummy variable of integration. This solution is examined in Fig. 3.13 where it is seen that initially the two ends of the planform commence spreading out and as the effects from the ends move toward the center, the planform distribution becomes more like a normal distribution. There are a number of interesting and valuable results that can be obtained by examining Eq. (3.28). First, it is seen that the important parameter is




1.0 0.8 0.6
0.4 0.2

0
Figure 3.13.

2 3
x/(Ie /2)

Evolution of an Initially Rectangular Beach Planform on an Otherwise Straight Beach.




I

(3.30)
Gt
where k is the length of the rectangle and G is the parameter in the diffusion
k
equation as discussed earlier. If the quantity (=) is the same for two i/Gt
different situations, then it is clear that the platform, evolutions are also the same. Examining this requirement somewhat further, if two nourishment projects are exposed to the same wave climate but have different lengths, then the project with the greater length would tend to last longer. In fact, the longevity of a project varies as the square of the length, thus if Project A with a shoreline length of one mile "loses" 50 percent of its material in a period of 2 years, Project B subjected to the same wave climate but with a length of 4 miles would be expected to lose 50 percent of its material from the region where it was placed in a period of 32 years. Thus the project
length is very significant to its performance.
Considering next the case where two projects are of the same length but located in different wave climates, it is seen that the "activity" varies with the wave height to the 5/2 power. Thus if Project A is located where the wave
height is 4 f t and loses 50 percent of its material in a period of 2 years then Project B with a similarly configured beach platform located where the wave height is 1 foot would be expected to last a period of 64 years.
Figure 3.14 presents a specific example of beach evolution and Fig. 3.15 presents results in terms of the proportion of sediment remaining in front of the beach segment where it was placed as a function of time. These results
are presented for several examples of combinations of wave height and project lengths. As an example of the application of Fig. 3.15, a project of 4 miles length in a location where the wave height is 4 feet would lose 60 percent of its material in 7 years and the second project in a location where the wave