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

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 .n ... .. ....811, .......... ...... ....n .... ............... .......-... ......I .... ...

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

1 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 STRUCTURES
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 Engineering 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 1965-1984 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

100r-

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'I Federal/Local Cost

$77,597,758.

S33.390.650.

$2,491,137.

1965-1970

No. Projects- 3
Miles Restored/
Nourished- 6.45

No. Projects -12
Miles Restored/
Nourished -17.12

1975-1980 1981-18U4 19o0-1U14
Total
No. Projects 6 No. Projects -7 No. Projects -28
Mies Restored/ Miles Restored/ Miles Restored/
Nourished- 13.35 Nourished 30.38 Nourished 6730

PERIOD OF TIME

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

801-

60-

401-

20o-

$557,920

Tl
Name of Project O
Mexico Beach Restoration $
Mexico Bch Renourishment
Pompano/Lauderdale By-The-Sea
Restoration
Pompano Beach Renourishinent
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
HIollywood/Hallandale 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)
.65

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 51.12
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
--w

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 m3 of 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 m3 (24.92 million yd3) 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 figure 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, $0.46/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 permitted.

3. Spreading the cost over a period is politically more palatable than one-
time 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 Km) 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

Realon II
Miles Completed
5.69

Federal/Local
Percent of
Reagin Total Cost

51%
. 67%
77%
73%
71%
71%

State Percent
Of Total Cost

Regional
Percent of
Air Cost

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

Region III
Miles Completed 10.50

Region IV
Miles Completed
12.10

.

*-**"" Realon V
Miles Completed
37.81

REGIONS

(Southeast) V

(East Central)
IV

(Northeast) III

(Southwest) II

(Panhandle) I

18.6 38.9 46.2
Total 103.7

32.5 53.0 51.5
I Tota

21.8 53.3 62.5

IMW Total

.I .v

1

.J ..

-- Critical Erosion
123 Non-Critical Erosion

CZ Stable or Accreting
Shoreline

I 137.0

l 137.6

1i

.6

STotal 177.4

58.1
STotal 219.2

100 150
SHORELINE (Miles)

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

II

IV
V
Total

200

%J

tl

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 m3 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 funding 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 funding. 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
S 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
Economy

Sediment Process

[ ,,,

TOOL
o Fill Factor
o Equilibrium Profile
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-Downdrift Impact
o Interactions (Inlet, Existing Engr. Works)
o Effectiveness
o Environmental Impact

CONSTRAINTS
Implementation o Cost
o Delivering System
o Time
14 ....., ..J,.,... vi.... !H!

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'

nVPoI nYMli
o Sand Sources
o Nourishment Method
o Cost

EVALUATION
o Effectiveness
o Longevity
o Environmental Impact

m

Figure 1.4.

TOOL
o Monkoring

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 Lower-
Atlantic 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 so-

called 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.O.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

4.

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INDIAN RIVER COUNTY

J00 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 ft or about 6 ft/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 useful to compute the

volumetric changes above the MHW and below the MHW separately. In theory,

this can be done simply through integrating the area between measured

profiles. In practice, considerable difficulty exists, particularly for the

below MHW 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 106 yd3
From NGVD to 5' 0.6 X 106 yd3
From NGVD to 10' 0.8 X 106 yd3
From NGVD to 15' 0.1 X 106 yd3
Total below NGVD -4.7 X 106 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
(R1, R18, R39 In North) (R90, R99, R114 In South)

.........-- ............... ................................-- R-1 ............................ .......................... ........... Nov. 72
June 86
l-

R-18

.-------J------l -- -i-----i-----------
--R-39

)0 0 400 800 1200 1600 2000 2400 2800 3200 36C
(A) Profiles at North End

R-90

R99

S ............ .... ..... ...... .

---- ----- --- ---- -R114

... -T--T-i--i--i-.T-.TTTTT-T--"Ti ""T-i"-'............................i""
II II I IIIl II I III I II I III II ii

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

0c 150.0
co

" 100.0
o
N
, 50.0

0l 0.0
u.
0
m -50.0

z
0 -100.0
4
ui
m
. -150.0
O
w
a -200.0
z

S-250.0

: -300.0

-350.0
O
:>

Therefore, depending upon the selection of offshore boundary, this coast

could appear to be accretional down to -15' 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, compar-

isons 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

-4000000
0o

-5000000
0
F-
-6000000

-7000000

1 -00000

0

CO
1-000000

C

-3000000

800.0

-15 -10 -5
-5ft
,=.. .. .. .. 'o

-15ft

-C

5 10 15
....--* -~"'* ,---"*

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

\ /

10 15 20

used as reference:

Positive Value means 1986 Profile Shifted Seaward).

11

-- C

900.0

200.0-

100.0-

.1

S.,-10tt
-- - ------- -- 5f It
.... ... .. \..A.

0
-25

Fiaure 2.
700.U

600.0

500.0

400.0

o0

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. Lucle 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, station number, period of 44001 77-81
record and approximate number of observations 41004 75-79
78-81 0. *41001
41005 .r 76-81
79-82.., *041002
... .. 75-81

"" 41006
83-86
S.42002 42001 42003
76-82 75-82 76-82

200 C PA=. :f--- oo20o

1000 800 600

Figure 2.8 North Atlantic and Gulf of Mexico Buoys.

800

600

COASTAL DATA NETWORK FIELD STATIONS
AND
YEARS OF INSTALLATION

* PRESSURE GAGE
P-U-V GAGES
-- TELEPHONE
--- RADIO

Figure 2.9. COE Wave Stations.

COASTAL DATA XETWORZ

Station: XARIBNLA9D
JANUARY, 1988

Rel.
Time: Depth: Is: Ta:
Day/Zr (a) (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
12.3
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
6.8

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
8.8
5.3
6.8

5.8
8.3
6.4
7.1

Monthly Wave Data Aalysis Report

% wave Energy Distribution

(Period BandviAth Liait -in seo)

21+

3.1
2.4
1.5
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

16-13 10.7-9.1 8-7.1 8.8-4
21-16 13-10.7 9.1-8 7.1-8.8

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 6.5
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

9.8
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
18.6
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

8.3
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.
6.3 8.8 24.
8.9 18.1 83.
8.6 14.4 52.

9.4 14.8 21.
10.0 16.4 29.
15.6 11.6 22.
8.4 11.7 34.

6.7
15.8
12.5
11.2

14.8
18.9
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.
18.1 19.
12.5 30.

10.2 24.
10.8 20.
8.3 19.
9.8 16.

5.6 12.
8.8 44.
8.2 38.
7.6 32.

9.9 20.
7.6 31.
6.9 81.
7.7 36.

7.3 31.
7.4 36.
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.Florida 32611

Table 2.1. Format for monthly Wave Data Analysis from Coastal Data Network,
COE, University of Florida.

Marineland
20

1 0
5 10 15 20 25 30
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 30043'N, 81019'W 14.2 yes
entrance 6/86- 7/86 II II yes
#4 8/87- 1/88 II It yes
11/83- 5/84 30040'N, 81016'W 17.5 yes
St. Mary's 7/84-12/84 It II yes
entrance 3/85- 4/85 II It yes
#5 7/85- 9/85 It It yes
8/87- 1/88 It it yes
Jacksonville 6/84-12/87 30018'N, 81022'W 10.1 no
Marineland 1/81- 4/86 29040'N, 81012'W 11.4 no
Cape Canaveral 3/82-12/87 28025'N, 80035'W 8.0 no
Cape Canaveral 5/84- 9/84 28020'N, 80025'W 18.0 yes
(offshore) 12/85- 5/86 II II yes
Vero Beach 10/86-12/87 27040'N, 80021'W 7.8 no
West Palm Beach 3/82-12/86 26042'N, 80002'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 I! 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, 7218'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, 70000'W 1300 no
44005 1/79- 4/86 42042'N, 68018'W 120 no
42001 8/75- 4/86 25054'N, 89042'W 3300 no
42002 3/77- 4/86 26000'N, 93000'W 2400 no
42003 7/77- 4/86 26000'N, 8618'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
=1(H) = exp [- exp (- s )] = 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)

-11 II
-111111111111~1111111

20
Oct. 1984

Sept.

Sept.

5

15

10

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, 5,s I 2p 59 s po

STATION: MRRINELRND
( 0(H,)=EXPC-EXP (- -) 3
C. C 1.60 d o..4g7
TYPE I LINE (GUMBEL'S APPROACH )
o ==CONTROL BAND(99X C.I.)
> MONTHLY ORTA(C.D.N.)

-

9-

I.oo -4.00 -2.00 0.00
REDUCED

2.00 4.00
VRRIRTE,

Figure 2.12.

o.ooc d.ot 'o.t o.s o.e o0. o. es o. o o:.e o:. so.se b.9eB
PROBRBILITT, 0 (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
c = 1.56-(tanh T60) and d = 4.15*tanh (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 3/2
c = 1.25*(tanh -- and d = 2.63.(tanh -) (in metric units) (2.3)

Estimates of 20, 50, and 100 year return values of Hs, 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) 3.32 4.94 7.28 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 6.42 8.37
100 (year) 3.18 4.91 6.85 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. Based 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-period-

direction 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.MARTY# GAGE

ST.MARYT4 GAGE

ST.MARY#a GAGE

87 MI i M>Hs
LEGEND: E 2M>Hs 21
S IIII 3M>Hs>2M
Hs>3M
VENICE GRGE
0% 5% 10%

Figure 2.14. Wave Roses Obtained at the St. Marys Entrance #4 and
Venice Gage Locations.

3. 2. 1. 0.

(DEG.)

PROBRBILITT DISTRIBUTION OF INCIDENT WAVE HEIGHTS AND DIRECTIONS

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

Water Depth = 10 m
(WIS # 152)

125

129 PHASE n

131
132 057 PHASE I
13. PHASE n
S134
JACKSONVILLE 135 059
136 ATLANrIC OCEAN
1 37
139 *60
41 PHAE

S% 14 7 PHASE
74 PHASE M

145

ISO PHASE n
48
151
15 P
VERO $EACH. 1S ASE

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 height-

direction 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 meteorological tide. In engineering work

such as beach nourishment, the meteorological 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.

S0

so 120

i i i I

oEC io o 0 ,u o \ 31 0 60 O

PROBABILITT DISTRIBUTION CF BREAKING WAVE HEIGHTS ANO
DIPECTIIONS T 63000 FEET

30

PRfqi0 [ ITI DISTRIBIIIION OF 8RERKING WOv
OIRECIIONS AT 3000 FEET

0 10000 20000 30000 40000 50000 60000 70000 8C

DISTANCE ALONG BASELINE (ft)

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

3. 2.cH<3.
1. 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 continuously 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
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
Alonashore Hurricanes

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

Rank Storm Tides
Correlate ResultsI Simulate Storm Tides- and Calculate R
of 2-D to 1-D Joint Probability AnalsisCalculate Return
Periods

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

| || |

Figure 2.17.

i

/e(

Approximate
Shoreline
Orientation 3 _

Alongshore
Hurricanes ,IS

0 o Exiting
Hurricanes 1490

Landfalling
Hurricanes

.~0 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 I

--------------------------- --------------------------------------
North Profile .
S'~ South Profile

---------- f^----.-- |-"-
...

-- ^---

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

It = k ss (2.5)

where It is the immersed weight transport rate and Pts is the longshore energy

flux factor. Based upon linear wave theory, P2s at the breaker line can be

estimated as:

Y 2
Ps Hb Cgbsin 2(ab- ) (2.6)

where y is the specific weight of sea water; Hb is the breaking wave height;

Cgb is the wave group velocity at the breaking point; ab is wave breaking

angle and B is shoreline normal. Since It and Pts 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

Qt(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

TN 10
(SEC)
5

0

3
3

1 5 10 15 20 25 30 111
1 5 10 15 20 25 30

1 5 10 15 20 25 30

10

Tn
(lo10 )

-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(TAR03)=-26523.4
AZIMUTH=2050

25
C
(0

U -25
a
cc cx
a:

s
-j

-25

5 0 t I I t I I I t I I I I I I I t i i i i 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 (YARD3)= -26523.4
AZIMUTH=2050

2
cc
o
z v

Q a:

S -2 -

I I I I I I I I I I I I I I I i t .A t t t t
1 5 10 15 20 25 30

DEC.,1987

Figure 2.22. Cumulative Longshore Sediment Transport Rate,
December 1987, Ponce de Leon, Florida.
Un -2

1 5 10 15 20 25 30
DEC. .1987

Figure 2.22. Cumulative Longshore Sediment Transport Rate,
December 1987, Ponce de Leon, Florida.

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

30

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
43.0(2) ? (2) 11.0
Nassau Sound 53.0 -
? 14.0
Ft. George 174.0 280.0
22.0(3) 186.0(2) 8.0
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) 16.0 12.0
Ft. Pierce 30.0 23.0
78.0(3) - -
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 8
10.0 .
Pt. Everglades *** 40.0
12.0 - -
Haulover 0.6 15.0
Gov'nt Cut *** **.0 -
5.0 -- -
Key West -- -
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 --
12.0(2) ..
Bunces P. -- -
30.0 --- --
Passage Key --- -
14.0(3) .
Longboat Key 8.0 47.0 1
1.0 --- ---
New P. 4.4 74.0
Big Sarasota P. 14.0 -
Midnight P. 0.6 -- -
Venice I. 0.4 7.0
5.0(2) .
Stump P. 4.00
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. --
4.0(2) .. .
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 from 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, reefs, 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-the-

Art 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/COEL-

87/015 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 linearizedd) 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) = Ay2/3 (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

-y = G a-Y (3.2)
at 2
ax

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 "non-

intersecting" profiles. 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.

2

DE

LU

-I--
LU
0)

C)
y?

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.

--AX- -W' -

oe e oo*

(a) Non-Intersecting Profiles

Figure 3.3. Two Generic Types of Nourished Profiles.

92.4m
SB = 1.5m

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

45.3m

b) Non-Intersecting
AN= AF = 0.1m1/3

5.9m

c) Non-intersecting Profiles
AN= O.1ml/3,AF = 0.09m113

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

1 1 1 I I I 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
-j
LLJ

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 non-

dimensional form as

I Ay 3 A 1 (3.3)
BW, W, 5 B W- A 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.
S3/2
w, = (-) (3.4)
AN

and the breaking depth, h* and breaking wave height, Hb are related by

h* = Hb/K

with K (" 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

A h* A AN 3/2 5/3 AN 3/2
2 A(YJ) 3( y ( -(7)} (3.5)
WB W, 5 B W- A AFF

It can be shown that the critical value (Ay/W*)c for intersection/non-

intersection of profiles is given by
3/2
(iY) i 1 (A!) ( 3. 6)
*c AF

with intersection occurring if Ay/W* is less than the critical value.

The critical volume associated with intersecting/non-intersecting

profiles is

Sh, A 3/2
( ) = + )[1 ) (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 AN
5 B 1) (3.8)
BW c2 5B A A(

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 non-

dimensional 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 shore-

line 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 3-

2
15 / -1 1
I L

o ,, / o

05 0 1" I 2 1 i 0
/ -
/(2/ -

0 1 2 3

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
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-by-

project 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 well-

defined 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

Ay = S -(3.10)
S h*+ B

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. AF = AN)

Ay N B (3.11)
N h + B

and is the beach nourishment volume per unit length of beach. Therefore

Ay = SW,] (3.12)
(h,+ B)

The above equation can be expressed in rates by,

d [dV W (3.13)
dt (h,+ B) dt dt
dS d
where for example, -- now represents the rate of sea level rise and is the
dt dt
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
df dS
rise the nourishment rate is related to the rate of sea level rise by
dt dt

dW dS
d- = W (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

SHb A W2/3
K *

then

H 3/2
W = ( (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

profile 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) + Q(y) dS (3.16)
dt dt s dt

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.S 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).

Z\
::: :

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)
Sdt.17)

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 Hb5/2 /g7 sin26b
8 (1-p)(s-1) 2 (3.18)

in which p is the sediment porosity (= 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, 8 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 /g/ sin2(B-ab)
8(l-p) (s-1) 2 (3.19)

where 8 = a tan- (y)
2 ax
Equation of Sediment Conservation The one-dimensional equation of

sediment conservation is

y (+ 1 Q 0 (3.20)
at +(h + B) ax

Combined Equation for Beach Planform Evolution

Differentiating with respect to x, the equation for longshore sediment

transport, Eq. (3.19), we find

5/2
KQ K Hb g/Kcos2(-a (3.21)
ax 8(l-p)(s-l) coB- ax

Recalling the definition of B and linearizing

I

Reference
Base Line

Definition Sketch.

Figure 3.9.

B -tan-1 (y --a- (3.22)
ax 2 ax

and considering the wave approach angle (B-ab) to be small such that

cos2(0-ab) 1, the final result is

K Hb5/2 /g7 2
aQ K Hb5/2 ~7 ay (3.23)
3x 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 = G y (3.24)
at x2

where

K Hb5/2
G F (3.25)
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 1.0-

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

-x-

Figure 3.11.

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

Result From This Study,
Santa Barbara

Relationship Suggested
Previously
,X\ *

jil

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
2
y(x,t) = exp ( 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-X24Gt
'4itGt

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/4r4dT

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)

K 5/2g7
K Hb
G = cos2(-ab) (3.27)
G = 8(s-l)(l-p)(h, + B) s2( (3.27)

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(B-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(x,t) = 2 {erf [ (x + 1)] erf [- (- I)]} (3.28)
4 Gt "* 4VGtT

where the error function "erf{ }" is defined as

z 2
erf(z) = e- 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.

1 2 3
x/(I /2)

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

S(3.30)
JGt

where is the length of the rectangle and G is the parameter in the diffusion

equation as discussed earlier. If the quantity ( ) is the same for two
JGt
different situations, then it is clear that the planform 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 ft and loses 50 percent of its material in a period of 2 years

then Project B with a similarly configured beach planform 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

MILLISECOND	CLASS.METHOD	MESSAGE
0	sobekcm_page_globals.constructor
0	sobekcm_page_globals.constructor	Application State validated or built
0	sobekcm_database.verify_item_lookup_object
0	sobekcm_page_globals.constructor	Navigation Object created from URI query string
0	sobekcm_database.verify_item_lookup_object
0	sobekcm_page_globals.display_item	Retrieving item or group information
0	sobekcm_page_globals.get_entire_collection_hierarchy	Retrieving hierarchy information
0	sobekcm_assistant.get_entire_collection_hierarchy
0	cached_data_manager.retrieve_item_aggregation
0	cached_data_manager.retrieve_item_aggregation	Found item aggregation on local cache
0	item_aggregation_builder.get_item_aggregation	Found 'all' item aggregation in cache
0	system.web.ui.page.page_load (ufdc.page_load)
0	sobekcm_page_globals.constructor.on_page_load
0	html_echo_mainwriter.add_style_references	Adding style references to HTML
0	html_echo_mainwriter.add_text_to_page	Reading the text from the file and echoing back to the output stream
98	html_echo_mainwriter.add_text_to_page	Finished reading and writing the file