Short course on principles and applicatins of beach nourishment, February 11-12, 1992

Material Information

Short course on principles and applicatins of beach nourishment, February 11-12, 1992
Series Title:
UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 92/001
Campbell, Thomas
Dean, Robert C.
Wang, Hsiang
Place of Publication:
Gainesville, FL
Coastal and Oceanographic Engineering Department
Publication Date:


Subjects / Keywords:
Beach nourishment


General Note:
Organized by Florida Shore and Beach Preservation Association and Coastal and Oceanographic Engineering Department, University of Florida
This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.

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Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.


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UFL/COEL 92/001

FEBRUARY 11 -12, 1992



... Instructors..
Thomas Campbell Robert G. Dean
Hsiang Wang
..Organized by ...
Coastal and Ocean ographic Engineering Department University of Florida
Gainesville, Florida 32611


Beach Width Gained vs. Sediment Quality
Effects of Sea Level Rise on Beach Nourishment
Case I Nourishment Quantities for the Case of No Onshore Sediment Transport Case II Nourishment Quantities for the Case of Onshore Sediment Transport
The Linearized Equation of Beach Planform Evolution
Governing Equations
Transport Equation
Equation of Sediment Conservation
Combined Equation for Beach Planform Evolution
Analytical Solutions for Beach Planform Evolution
(1). A Narrow Strip of Sand Extending into the
(2). Initial Shoreline of Rectangular Planform
Effect of Retention on Setting Back the Fill Ends from
Project Boundaries
Effect of Ends on a Beach Fill
A Case Example Bethune Beach
Project Downdrift of a Partial or Complete Littoral

A. Estimation of closure depth
B. Errors induced by survey inaccuracy
C. Seasonal variations
A. Summary of Synoptic Meteorological
Observations (SSMO)
B. Measured Wave Data
C. Wave Hindcasting Information
Natural Bypassing
Artificial Bypassing
Selected Inlets and Physical Environment
Volumetric Calculation


Summary of Results

Florida Inlets Georgia Inlets
Ebb Shoal and Nearshore Environment
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 I
Hsiang Wang
Coastal & Oceanographic Engineering Department University of Florida, Gainesville
At present, there axe only three alternatives to shoreline recession; retreat as shoreline regresses, haxden 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 perceive 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 haxsh environment, it 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.
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 miles beach at Coney Island through hydraulic dredging, at a cost of about 21 cents per cubic yard. Numerous projects were carried out afterwards.
Hall (1951) complied 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 southeast 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 than 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

Number of
Locations 5 17 1 1 2 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 expenditures of each individual beach nourishment

Division of Beaches and Shores
Funds Spent for Restoration/Renourlshment Projects

1965 1984
In Five Year Intervals

- State Cost

[ Federal/Local Cost




1965-1970 No. Projects 3 Miles Restored/ Nourished 6.45

1971-1975 I
No. Projects- 12 Miles Restored/ Nourished 17.12

1975-1980 1
No. Projects 6 Miles Restored/ Nourished -13.35

No. Projects -7 Mies Restored/ Nourished 30.38

1abb-1Vu4I Total
No. Projects -28 Miles Restored/ Nourished 67.30

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



6 0-

40 -



Total Cost
Name of Project Of Project
Mexico Beach Restoration $ 40,625
Mexico Bch Renourishment --Pompano/Lauderdale fy-The-Sea
Restoration 1,873,437
Pompano Beach Renoturishment --Virgina Key/Key Biscayne Rest. 577,075
Virginia Key Renourishment --Cape Canaveral Beach Restoration 1,050,000 Hallandale Beach Restoration 779,977
Delray Beach Restoration 3,015,383
Delray Beach Nourishment --Delray Beach Renourishment --St. Petersburg Beach Restoration 682,716 Venice Beach Restoration 49,700
Ft. Pierce Beach Restoration 621,288
Ft. Pierce Renourishment --Bal Harbour Restoration 4,962,420
Indialantic/Melbourne Restoration 3,582,000 John U. Lloyd Restoration 2,945,262
Ilollywood/Itallandale Restoration 7,743,376 Lido Key Restoration 360,000
Ln Miami Beach Restoration 49,892,000
North Redington Beach Restoration 369,000 Jacksonville Beach Restoration 9,757,900 Mullet Key Restoration 649,878
Jupiter Island Restoration 3,574,221
Treasure Island Restoration 216,000
Treasure Island Renourishmont --Treasure Island Renourishment --Total Restoration Projects 92,742,258
Total Renourishment Projects ---

State Share Length Of Cost (miles)
$ 20,312 .65

241,055 292,491 976,044
305,109 36, 668 150,041
14,530,114 247,125
97,483 716,332
44, 650

2.80 .78 2. 67
.50 .17 1.30
.85 2.10 1.50
. 62
.30 10.50
1.20 4. 60
--- ~

Total Cost Of Project
$ 41,155 10,273,340

State Share Of Cost
20,000 3,549.,453
564,423 1,408,713
314,500 573,750

$22,890,339 $7,186,614

Note: Total Restoration
Ronourishment $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
Table 1.2. Expenditure on Individual Beach Restoratlon/Renourishment Projects, 1965-1984
(DNR, 1984).

Project Length
.55 5.20
1.70 .80 16.18

project during this period. As you can see, Miami 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 compiled 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 ideal of equilibrium beach profile (Bruun, 1954; Dean, 1977; Moore, 1982) was applied to beach nourishment to determine the shape of original and nourished beaches. Since the 1970's 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 ( 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 nour-

ishment projects were carried out at numerous locations covering the entire coast of the country. Roelse (1986) compiled a list of 32 projects completed between 1952-1985. Figure 1.2 shows the locations of artificial beach nourishment along the Dutch Coast. Of these projects, the Hoek Van Holland project was the largest. During the years of 1971- 72, 18.94 million m' (24.92 million yd') 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 Netherlands is about half that of a comparable job in the United States.
Since land reclamation and shore protection is a national priority in the Netherlands, considerable advances have been made there in beach nourishment technology even though they are a late corner 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 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.

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

Since the first project in the early 1920's, 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 coast over a period is politically more palatable than one-time large
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 Kin) 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 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. 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.

Reon I
Miles Completed 1.20

Reason II
Miles Completed

Federal/Local Percent of Total Cost
* 67% 77% 73% 71% 71%

State Percent
Of Total Cost
49% 33% 23% 27%

Regional Percent of
Air Cost
4.9% 8.0% 9.0% 78% 100.9%

Region III
Miles Completed 10.50
"_ Region IV
Miles Completed 12.10
Reaion V
Miles Completed


Total 103.7

(Southeast) V

(East Central)


Critical Erosion Non-Critical Erosion Stable or Accreting Shoreline

Total 137.0

Total 137.6
777I Total 177.4

(Northeast) III (Southwest) II (Panhandle) I

Total 219.2



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

V Total

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, Depaxtment 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 coast shared by the Federal dollars, a feasibility study must be conducted to show justifiable cost/benefit from the Federal level for project authorization. Projects needing State and Federal findings 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 findings. 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 step are given as follows:
1. Problem 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
Alternative 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
13). Environmental Impact Study
C). Cost Estimation
D). Financing E). Permitting
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 sometimes 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. Am 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 presents a flow chart for beach nourishment engineering.

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

o Storm Protection o Recreation o Beach Access o Envirmrvent o"Ec =y

Coastal and Sediment Process

o Sand Sources o Nourishment Method o Cost


o Longevity o Updrift-Downdrift Impact o Interactions (Inlet, Existing Engr. Works) o Effectiveness o Environmental Impact
implementation 0 Cost
o Delivering System o Time

Beach Nourishment Design Flow Chart.

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

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

o Geometry o Volumetric Requirement o Material Specification o Auxiliary Structures

Figure 1.4.


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 Coasts, 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 Artificial 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 & 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 Sediments 77,
ASCE, Charleston, S.C.
James, W. R. (1975) Techniques in Evaluating Suitability of Borrow Material for Beach
Nourishment, U.S. Army Coast al 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. (1975) 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, DE.
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 Netherlands.
Wang, W. C. (1988) List of Literature Related to the Beach Restoration Projects in the
State of Florida. Technical Rep., Coastal Engr. 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-77/081, Coastal and Oceano. Engr. Dept., Univ. of
Florida, Gainesville, FL.
Tonya, C. and Pilkey, O. (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
Robert G. Dean
Coastal & Oceanographic Engineering Department University of Florida, Gainesville
It is convenient to discuss the physical performance of beach nourishment projects in terms of the cross-shore response (or profile adjustment) and longshore response, i.e. transport of sand out of the area placed. it is also convenient in exploring performance at the conceptual level to utilize idealized considerations and simplified (linearized) equations in some cases. This allows one to obtain a grasp or overview of the importance of the different variables without the problem of 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) = Ay213 (2.1)
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 Consider6 ay ay
= a2y (2.2)
where x is the longshore distance, t is time, G is a "longshore diffusivity" which depends strongly on the wave height mobilizing the sediment and Eq. (2.2) is recognized as the "heat conduction equation".
Beach Width Gained vs. Sediment Quality
From Fig. 2.1, it is seen that the scale parameter, A, in Eq. (2.1) increases with increasing sediment size. Thus, as presented in Fig. 2.2, 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 Ap, 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", "non-intersecting", and "submerged" profiles. Figure 2.3 presents examples of these. Referring to the top panel in this figure of intersecting profiles, a necessary but not sufficient requirement for intersecting profiles is that the fill material be coarser than the native material. One can see that an advantage of such a profile is that the nourished profile "toes in" to the native profile thereby negating the need for material to extend out to the closure depth. The second type of profile is one that would usually occur in most beach nourishment projects. Nonintersecting profiles occur if the nourished material grain size is equal to or less than the native grain size. Additionally, this profile always extends out to the closure depth, h.. The third type of profile that can occur is the submerged profile (Fig. 2.3c) the characteristics of which are shown in greater detail in Fig. 2.4. This profile type requires the nourished material to be finer than the native. It can be shown that if only a small amount of material is used then all of this material will be mobilized by the breaking waves and moved offshore to form a

CI 1.01 w Suggested Empirical
I- Relationship
< From Hughes'
Field Results From Indlvdui Field Prol
CL Where a Range of Sand S
Q" Was Given
E 0.10
I- From Swart's
W Laboratory Results
LI 0.01
0.01 0.1 1.0 10.0 100.0
Figure 2.1. Beach Profile Factor, A, vs. Sediment Diameter, D, in Relationship h = Ay2'3(Modlfled from Moore, 1982).



Figure 2.2 Equilibrium Beach Profiles for Sand Sizes of 0.3 mm and 0.6 mm
A(D = 0.3 mm) = 0.12 m113 A(D = 0.6 mm) = 0.20 mi.


Added Sand

Intersecting Profile AF>AN

Added Sand
b) Non-Intersecting Profile

;;u Or 0N.
Virtual Origin of
Nourished Profile

Added Sand

C) Submerged Profile AF
Figure 2.3. Three Generic Types of Nourished Profiles.






B = 1.5m

b) Added Volume 490 m3 /M

c) Added Volume

d) Added Volume = 1660 m3 /M
Case of Incipient Dry Beach
Figure 2.4 Effect of Increasing Volume of Sand Added on Resulting
Beach Profile. A = 0.1 m1/3 A = 0.2 m1/3 h,= 6 m, B = 1.5 m.


Z 0
Uj, 10


small portion of the equilibrium profile associated with this grain size as shown in the upper panel. With increasing amounts of fill material, the intersection between the nourished and the original profile moves landward until the intersection point is at the water line. For greater quantities of material, there will be an increase in the dry beach width, Ay, resulting in a profile of the second type described.
Figure 2.5 illustrates the effect of placing the same volume of four different sized sands. In Fig. 2.5a, sand coarser than the native is used and a relatively wide beach Ay is obtained. In Fig. 2.5b, 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. 2.5c, 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. 2.5d, no dry beach is yielded with all the sand being used to satisfy the underwater requirements.
We can quantify the results presented in Fig. 2.5 for beach widening through nourishment by utilizing equilibrium profile concepts. It is necessary to distinguish two cases. The first is with intersecting profiles such as indicated in Fig. 2.3a and requires Ap > AN. For this case, the volume placed per unit shoreline length, .V, associated with a shoreline advancement, Ay, is presented in non-dimensional form as
__ K +y __3 (2.3)
BW, W, 5 B W, [1_ (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.
W*= (*)3/2 (2.4)
and the breaking depth, h,, and breaking wave height, Hb are related by h,= IbI
with ,c(;t 0.78), the spilling breaking wave proportionality factor. Figure 2.6 presents an estimate of h,, around the Florida shoreline.


a) Intersecting Profiles, AN= 0.1mlA F = 0.14m1/3

- ~i -

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

c) Non-Intersecting Profiles AN= 0.1m1/3AF = 0.09m1/3

d) Limiting Case Non-Intersecting


h,= 6m

of Nourishment Advancement. Profiles, AN= 0.1m"/3,AF = 0.088m113







Figure 2.5. Effect of Nourishment Material Scale Parameter, AF, on Width of
Resulting Dry Beach. Four Examples of Decreasing AF.

16 16

Mi 12 16 20 24 h, (Feet) ,

Figure 2.6 Recommended Distribtuion of h.Along the Sandy Shoreline
of Florida.

h, (Feet) 12 16 20 24

For non-intersecting profiles, Figures 2.3b and 2.5b,c and d, the corresponding volume V2 in non-dimensional form is
~+g (2.5)
W~B ( )~~( ) {[~+( )3/2 5/3 (AN)3/2} 25
It can be shown that the critical value (Ay/W,), for intersection/non-intersection of profiles is given by
(**)= (AN )3/2 (2.6)
with intersection occurring if Ay/W* is less than the critical value.
The critical volume associated with intersecting/non- intersecting profiles is
(IV )'c=(I + 3h*) [1-_ (AN)3/2] (2.7)
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
___h (AN~~ )3/ AN -(2.8)
B_,):2 W B p),21A
Figure 2.7 presents these two critical volumes versus the scale parameter ratio AF/AN for the special case h,/B = 4.0.
The results from Eqs. (2.3), (2.5) and (2.6) are presented in graphical form in Figs. 2.8 and 2.9 for cases of (h,/B) = 2 and 4 respectively. 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' (WB per unit length of beach. It is (= V )e ntlnt fbah ti
interesting that the shoreline advancement remains more or less constant for AF/AN > 1; for smaller values the additional shoreline width decreases rapidly. For AF/AN values slightly smaller than plotted, there is no beach width gain, i.e. as in Fig. 2.5d. 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

15 1 1 3
OO 10 LL
- / Oo 1o/ 20z /
C0 0 1 2 3
Fn- > 7) >
z/(2) z
Figure 2.7. (1) Volumetric Requirement for Finite Shoreline Advancement
(Eq. 2.8); (2) Volumetric Criterion for Intersecting Profiles
(Eq. 2.7). Variation with AF/AN. Results Presented for h, /B = 4.0
IC = I a)
0 I 0
z Z
0 0
0 1 2 3
Figure 2.7. (1) Volumetric Requirement for Finite Shoreline Advancement
(Eq. 2.8); (2) Volumetric Criterion for Intersecting Profiles
(Eq. 2.7). Variation with A 'AN. Results Presented for h, /B = 4.0


1.0 -. te ,e
i__m _~.. r ,i- .
0.10 0.5
1 etso \ VY 0.2
0.10 1.0 0.1
AV' = 0.05
I i f
-Asymptotes V' = 0.02
for Ay = 0
0.01 V [ 9' = 0.01
-Ayr Y' =0.005
AF' = V/BW, = 0.002
t- - ;h -
0.001 Definition Sketch
0 1.0 2.0 2.8
A' = AF /AN
Figure 2.8. Variation of Non-Dimensional Shoreline Advancement Ay/W, With A' and V'. Results Shown for h. /B = 2.0


0 .1 1
I11 I = 0.05
* Asymptotes I
for Ay =0
0.01 V' = 0.01I V' = 0.0051
V' = 0.0021
0.001 V B. = 0.01
Definition Sketch
=f( )
0 1.0 2.0 2.8
Figure 2.9. Variation of Non-Dimensional Shoreline Advancement Ay/W, With A' and V'. Results Shown for h, /B = 4.0

nourishment option. First, in the interest of objectivity, it must be said that the most extreme of the scenarios published 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 (2.9)
and, from Bruun's Rule
A = -S (2.10)
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)

AYN -h--B h,, +B
and V is the beach nourishment volume per unit length of beach. Therefore
AyN=- (h. +B) [V-SW.]

(2.11) (2.12)

The above equation can be expressed in rates by,

dy 1 F dV dS 1
dt ( h, -- B) [-T- Wt- I213 where aSnow represents the rate of sea level rise and H is the rate at which nourishment material is provided. It is seen from Eq. (2.13) that in order to maintain the shoreline stable due to the effect of sea level rise the nourishment rate 1 is related to the rate of sea level rise dS by
dv dS
-i = W(2.14) 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. 2.1. Using the spilling breaking wave approximation
h, _A W;,/
W Hb 3/2 (2.15)
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 Tfransport
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 2.10 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 8Q h
- + sources sinks (2.16)
ay at
in which h is the water depth referenced to a fixed vertical datum and the sources could include natural contributions such as hydrogenous or biogenous components, and suspended deposition or human related contributions, i.e. beach nourishment. Sinks could include removal of sediment through suspension processes. Eq. (2.16) can be integrated seaward from a landward limit of no transport to any location, y Q() o (sources sinks)dy-= 0 h (2.17)
If only natural processes are involved and there are no gradients of longshore sediment transport, the terms on the left hand side of Eq. (2.17) represent the net rate of increase of sediment deficit as a function of offshore distance, y. For y values greater than the normal width, W., of the zone of active motion, the left hand side can be considered as representing the "ambient" deficit rate due to cross-shore sediment transport resulting from long-term disequilibrium of the profile and source and sink terms.
In attempting to apply Eq. (2.17) to the prediction of profile change and/or nourishment needs under a scenario of increased sea level rise, it is reasonable to assume that over the next several decades the ambient deficit rate (or surplus) of sediment within the active zone will remain constant. However, an increased rate of sea level rise will cause an augmented demand which can be quantified as W. [(!) (dS)] in which (- ) is the reference
sea level change rate during which time the ambient demand rate is established. Thus the

i Increased Sea Level
O-g OrIgni-l Sea Level
Sediment .
"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

Figure 2.10. Possible Mechanism of Sedimentary Equilibrium (After Dean, 1987).

active zone sediment deficit rate will be r w. ahd + -d o d
New Deficit Rate = idyl r 0[jw. Y] 0 dS WS dW
in which ff represents the nourishment rate and the subscript "0" on the bracket represents the reference period before increased sea level rise. In order to decrease the deficit rate to zero, the required nourishment rate is dv [fow-ah ] [(dS) (dS) ] (2.19)
These models may assist in evaluating the vulnerability of various shoreline systems to increased rates of sea level rise. For Florida, long-term trend estimates of s 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 of 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 Q = K H I2v-g/7 sin 20b (2.20)
8 (1- p)(s --1) 2

in which p is the sediment porosity (a 0.35-0.40) and s is the sediment specific gravity (= 2.65). Equation (2.20) will later be linearized by considering the deviation of the shoreline planform from the general shoreline alignment to be small. Referring to Fig. 2.11, denoting p as the azimuth of the general alignment of the shoreline as defined by a baseline, / 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 H 12 sin 2(p ab)
2 =(2.21) Q= 8(1- p)(s 1) 2 (2.21)
where = p tanEquation of Sediment Conservation The one-dimensional equation of sediment conservation is
By 1 8Q
+ = 0 (2.22)
at (h + B) 8x
Combined Equation of Beach Planform Evolution
Differentiating with respect to x, the equation of longshore sediment transport, Eq. (2.21), we find
8Q K 5/2
Q= cos 2( a) (2.23)
a 8(1 p)(s 1) aRecalling the definition of 4 and linearizing X 1 ay r ay
= tan- ; (2.24)
2 8z2 ax
and considering the wave approach angle (/ abb) to be small such that cos 2(/ ab) 1, the final result is
_Q K H/2V 8f82y
S = (- .a(2.25) 5x 8(1-p)(s -1)aX2
Combining Eqs. (2.22) and (2.25), a single equation describing the planform evolution for a shoreline which is initially out of equilibrium is obtained as ay _y
= = G (2.26)
at ax2
G K v- /, (2.27)
8(s 1)(1 p) (h. + B)



Reference Base Line


Figure 2.11. Definition Sketch.

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. 2.12. A more detailed evaluation demonstrates that a more appropriate expression for G can be developed and expressed in terms of deep water conditions G K H Gog COS ao) cos 2(flo a.) (2.28)
G 1)(1 p)C. 04(h. + B) cos(fo a.) where the subscript "0" denotes deep water conditions and C. is the wave celerity in water depth, h.. Figure 2.13 presents estimates of G around the Florida peninsula and Figs. 2.14 and 2.15 present estimates of effective deep water wave height and period.
It is recognized that the form of Eq. (2.26) 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 n. Table 2.1 presents values of G for various wave heights in several unit systems where it is noted that the reference wave height is the breaking wave height.
Table 2.1: Values of G for Representative Wave Heights Hb Value of G in
(ft.) ft2/s miz/yr m 2/s km"/yr 1 0.0214 0.0242 0.00199 0.0626 2 0.121 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,
--- 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

20I I I F

Result From This Study,
Santa Barbara
Relationship Suggested




Plot of K vs. D. Results of Present and Previous Studies (Modified From Dean, 1978).


Figure 2.12.


0.02 0.06 0.10 0.14

G(ft2/s) 0.02 .0 0.10

Figure 2.13. Approximate Estimates of G(ft2/s) Around the Sandy
Beach Shoreline of the State of Florida. Based on
the Following Values: K = 0.77, g = 32.2 ft/sec2,
S = 2.65, p = 0.35, = 0.78, h, From Fig. 8., B Estimates Ranging from 6 to 9 ft, Ho from Fig. 23, T from Fig. 24.

1 35
H eff2(feet)

H eff2(feet)
1 3 5 8

1 .

Figure 2.14. Recommeneded Values of Effective Deep Water Wave Height,
Ho, Along Florida's Sandy Shoreline.

5 c3

. 14 i
d 10

2 6 10 14
Wave Period, T(sec)

Figure 2.15. Recommended Values of Effective Wave Period, T, Along
Florida's Sandy Shoreline.

Wave Period, T(sec)
2 6 10 14
I +

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. 2.16. The total area of the sand is designated m and the solution for this initial condition and the differential equation described by Eq. (2.26) is the following
y(x, t) exp (2.29)
which is recognized as a normal distribution with increasing standard deviation or "spread" as a function of time. Figure 2.17 shows the evolution originating from the initial strip configuration. Examining Eq. (2.29), it is seen that the important time parameter is Gt. The quantity, G, which is the constant in Eq. (2.27) serves to hasten the evolution toward an unperturbed shoreline. In Eq. (2.29) 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. 2.17 applies only 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. (2.23) and (2.26)
C : 8(s 1)(1 p)(h, + B) cos2(IJ- ab) (2.30)
and 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,


- m = YAx

I ~L

Figure 2.16. Initial Beach Planform. Narrow Strip of Sand
Extending From Unperturbed Shoreline.

Gt = 0.1
m -x2 /4G 0y(x,t) m e-x4Gt
' ). 4 "-nG t
2.0 I ..
5.0 ...
II 1 -4
-10 -5 0 5
x/ T
Figure 2.17. Evolution of an Initially Narrow Shoreline Protuberence.

it is clear that if this should occur then it is equivalent to "running the equation backwards" in time. 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 (cos 2(,6 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. 2.18 with a longshore length, e, 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. (2.26) 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) = -Yy {erf [ '% (21 + 1)] erf [ (2x 1)] }(2.31) where the error function "erf{}" is defined as erf(z) = 2fZe-U2du (2.32)
and here u is a dummy variable of integration. This solution is examined in Fig. 2.18 where it is seen that initially the two ends of the planform commence spreading out and as the effects from the ends move towards the center, the planform distribution becomes more like a normal distribution. There are a number of interesting and valuable results that can be

1.0 L' U 16Gt
t' t t' 0.04 .p 2
t' = 1.0 0
0.6- t' = 4.0
0.4 Shoreline Positions
01Symmetric About x/(f/2) = 0
0.2 ,
0.- -" ,," - -""****r-l
0 ~-
0 2 3 4
x/(1 /2)
Figure 2.18. Evolution of an Initally Rectangular Beach Planform on an Otherwise Straight Beach. Only One-Half of Project is Shown.

obtained by examining Eq. (2.31). First, it is seen that the important parameter is t (2.33)
where t 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 different situations, then ( 7Gt )
it is clear that the platform evolutions are also the same. Examining this requirement somewhat further, if two nourishment projects are exposed to the same wave climate but have different lengths, then the project with the greater length would tend to last longer. In fact, the longevity of a project varies as the square of the length, thus if Project A with a shoreline length of one mile "losses" 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 axe of the same length but located in different wave climates, it is seen that the G factor 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 platform located where the wave height is I foot would be expected to lose 50 percent of its material in 64 years.
Figure 2.19 presents a specific example of beach evolution and Fig. 2.20 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. 2.20, 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 a second project in a location where the wave height is 2 ft and the project length is 16 miles would lose only 10 percent of its material in a period of 40 years. Figure 2.20 was developed based on the solution presented in Eq. (2.31).
It is possible to develop an analytical expression for the proportion of sand, M(t),


Nourished Beach Planform


7 Years

30 Years

Pre-Nourished Shoreline

6 4 2 0 2 4 6 8


Figure 2.19.

Example of Evolution of Initially rectangular Nourished Beach Planform. Example for Project Length, J, of 4 Miles and Effective Wave Height, H, of 2 feet and Initial Nourished Beach Width of 100 Feet.

-_ H = 1.0, = 16 miles
*"- .o =--6 . ... ..-" .. .
.= 2.0, 0 = 16 miles
H = 1.0, = 4 Miles
H 4.o,,e 16 miles
- H- 2.0, -e
H - ie
. ................................................................

(fw ZO )
<. U

10 20 30

Figure 2.20.

Fraction of Material Remaining in Front of Location Placed for Several Wave Height, H, and Project Lengths, A Effect of Longshore Transport.

- --mles
H = 2.0, -= 1 mile
" "----- --..- -.....,_ H = 4 0 = 1 m i le

1.0 0.8 0.6


remaining in the location placed, as defined by

M(t) 1 t/(x,t)dx (2.34)
to yield
M(t) = 2'/- (e-(/2v ')2 1) + erf (2- ) (2.35)
which is plotted in Fig. 2.21 along with the asymptote for small times M(2 1 (2.36)
which appears to fit reasonably well for Vft/f < 0.5 (2.37)
A useful approximation for estimating the "half-life" of a project is obtained by noting that M = 0.5 for VxG-t/t t- 0.46. Thus the half-life, t50, is i 2
t50 = (0.46)2 G = 0.21- (2.38)
in which all variables are in consistent units. A more readily applied form is developed from Eq. (2.27) as
t50 = 8.7 (2.39)
where t5o is in years, in miles and Hb is the breaking wave height in ft. Effect on Retention of Setting Back the Fill Ends from Project Boundaries
As noted earlier, there is an understandable interest by a community or other entity which is funding a project in retaining the sand within their boundaries as long as practical. One approach to this concern would be to install retaining or stabilization structures near the ends of the fill. A second would be to simply set-back the limits of the fill from the project boundaries with the understanding that the sand would soon "spread out". Omitting the details, Fig. 2.22 presents results for relative end set-backs A/ = 0, 0.2 and 0.5. It is seen that the effects are greatest early in the project life (say V/G-tl = 0.6 or 0.8) where a set back A/f = 0.5 would increase the percent material retained from 42% to 73%.

NG tle
0 1.0 0.5 1.0
Z. w t = Time After Placement
-1 0 C. G= Alongshore Diffusivity Initial
U. LL- Asymptote Planform
O-Z O .5- M.1
C n -10 .0
O LLI 0 1 2 3 4 5 6
FIgure 2.21. Percentage of Material Remaining In Region Placed vs. the Parameter 4 .

Figure 2.22.

LUcc a mm L

Percentage of Material Remaining in Designated Area of Length, I + 2A. Rectangular Beach Fill of Length,.

1.0 2.0 3.0 4.0 5.0

Effect of Ends on a Beach Fill
It is somewhat interesting to evaluate the effect on longevity of providing a fillet at the two ends of a fill which is otherwise rectangular in planform. Basing the longevity on the retention of sand within the placed planform, it is interesting that tapered- end planforms have a substantially greater longevity than rectangular planforms. The reasons is apparent by examining Fig. 2.19. The loss rates of a rectangular planform fill are higher over the first increment of time than over the same increment of time but later in the project history. It is seen from Fig. 2.19 that the evolution of the planform occurs with the early changes occurring where the planform changes are the most extreme. This is not surprising when one recalls that the governing equation (Eq. (2.26)) is the heat conduction equation and that the fill planform is equivalent to a temperature distribution above background of the same form in an infinitely long rod. Returning again to the tapered end planform, which approximates the evolved rectangular planform at a later stage, the evolution of the tapered end fill at an early stage approximates that of a rectangular fill at a later stage.
Figures 2.23 and 2.24 present calculated evolutions for rectangular and tapered end planforms, respectively and Table 2.2 summarizes the cumulative losses from the region placed over the first five years. It is seen that the tapered end fills have reduced the end losses by about 33%.
Table 2.2: Comparison of Cumulative Percentage Losses from Rectangular and Tapered Fill Planforms (G = 0.02 ft2/sec; f = 3 miles; Y = 55 ft)

Cumulative Percentage Losses With Years After Rectangular Rectangular Planform Placement Planform With Triangular Fillets
1 5.7 2.4
2 9.5 4.6
3 11.8 6.6
4 13.8 8.3
5 15.5 9.8

A Case Example Bethune Beach
In 1985, shorefront property owners in Bethune Beach, Volusia County, FL applied


-2.0 -1.0 0 1.0 2.0


Figure 2.23.

Calculated Evolution of a Rectangular Planform Beach Nourishment Project. Planforms Presented for Initial Conditions and 1,2 and 5 Years After Placement.

Figure 2.24.

(D0 (D (D (D (D 700"0

-2.0 -1.0 0 1.0 2.0

Calculated Evolution of a Rectangular Planform with Triangular End Fillets. Planforms Presented for Initial Conditions and 1,2 and 5 Years After Placement.

for a permit to construct two segments of armoring. The Governor and Cabinet initially deferred a decision requesting that consideration be given to utilizing the same funds for beach nourishment. The two segment lengths were 925 ft and 3,850 ft, as presented in Fig. 2.25. The designation beside each segment (e.g. VO 353) is the identifier given by the Division of Beaches and Shores to the permit application. The cost of the revetments was about $200 per foot which at a nourishment cost of $6 per cubic yard would purchase approximately 33 cubic yards per front foot or a total of 160,000 cubic yards for the two segments combined.
Rather simple numerical modeling was carried out using Eqs. (2.26) and (2.27) with monthly averaged wave heights as determined by the University of Florida's wave gage at nearby Marineland, FL. The results of this numerical modeling are presented in Figs. 2.25 and 2.26. Figure 2.25 presents the planform evolution after one month and one year. It is seen in accordance with earlier discussions, that due to the relative short lengths of these segments, the sand spreads out rapidly in an alongshore direction. Figure 2.26 presents, as a function of time, the volume of sand remaining in front of the two segments where the nourishment would have been placed.
Project Downdrift of a Partial or Complete Littoral Barrier
In this case the project is located downdrift of a partial or complete littoral barrier, such as a jettied inlet. We will denote the net longshore transport as Qo and the bypassed quantities as FQo(O < F < 1), see Fig. 2.27. In this case, the fraction remaining, M2(t), is M2( t V(x't)dx
fVtx= t VV (2.40)
and can be shown to be
(*)~ ~~~ ~~ e( --,-1) (1 F)Qot (.1
M2(t) = erf (j + -1v'GT (e-(e/v)- ((-41)
in which V is the volume placed. Eq. (2.41) is presented vs .\/Ai/e in Fig. 2.27 for various values of (1 F)Qoe/VoG. This latter parameter presents the ratio of longshore

V0353 (925') 7000 6000 5000
4000 3000
V0370 (3850')
2000 1000

0 50
Nourished Shoreline
Shoreline After Two Months
I Initial
- .,----Nourished
After I "' One Year

Figure 2.25. Initial and Subsequent Planforms of Nourished
Beach. Bethune Beach, Florida, Example.

u* 8O0
LL 80
zO 0 44 60
I4 0+4
u.. 40 LLO
o I,- V0370
U 20 V0353
0I I I I
0 5 10 15 20 25
TIME (Months After Fill Placement)
Figure 2.26. "Loss" of Beach Fill From Infront of Area Placed as a Result of Longshore Transport. Bethune Beach, Florida, Example.

Oz 0 0
Oo .LL J
0 0

Figure 2.27.

1.0 2.0 3.0 4.0 5.0

Proportional Volumes of Beach Nourishment Remaining After Placement vs, G/7 and (1-F)Q o/Vo G.

transport losses due to a bypassing deficit to those losses resulting from the anomalous platform.
The concept of reduction in storm damage by beach nourishment will be illustrated by two approaches. First, data collected and summarized by Shows (1978) documented the relationship between average damage costs suffered by a structure as a function of the proximity of that structure to the shoreline set-back line in Bay County. The set-back
line is approximately parallel to the shoreline. Figure 2.28 presents these results for 540 structures in Bay County following Hurricane Eloise in 1975. The horizontal axis is the structure location relative to the set-back line which is more or less parallel to the shoreline. Relative to beach nourishment, the two most significant features of Fig. 2.28 are: (1) the steeply rising damage function with proximity to the set-back line (or shoreline), and (2) the possibility of displacing the damage function seaward by beach nourishment which would translate the curve in Fig. 2.28 horizontally to the left by the width of beach added. As a second illustration consider the situation in Fig. 2.28 which corresponds to a profile off Sand Key, Florida. A peak storm tide of 11 ft and an offshore breaking wave height of 20 ft will be assumed for purposes of this example. These conditions axe believed to be reasonably representative of a 100 year return period. Considering the pre-nourishment condition and utilizing the breaking wave model reported by Dally, Dean and Dalrymple (1985), the wave height distribution is presented in Fig. 2.29. Considering now a beach nourishment project which advances the shoreline gulfward a distance of 40 ft, the wave height distribution is as presented in Fig. 2.29. Table 2.3 summarizes the wave height at the seawall for the original and nourished conditions and also presents a measure of the damage potential for the two cases with and without nourishment. In these results the damage potential is considered to be proportional to the cube of the wave height. The presence of the nourishment project reduces the damage potential by nearly a factor of four!


-50 0 50 100 150

Seaward I Landward

Damage to Structure in Relation to its Location with Control Line (Resulting From Study of 540 Structures in Bay County After Hurricane Eloise, by Shows, 1978).

200 00 I-0
LLI V" 160
< ~ 120 LU
41- 80 cc 0 LU
>1- 40




Figure 2.28.


1 -Wave Height,
Original Profile CS~ 1 010 '*-wave Height,
Nourished Profile
0 I I I
0 100 200 300

-100 Year Storm Surge Z 12 ft nP
- ;4 0f ft
--- Nourished Beach,
Displaced 40 ft Gulfward
Original Beach ...

Figure 2.29. Wave Height Reduction at Seawall Due to Presence
of a Beach Nourishment Project.

- +10
2O 0
>I..-a -10

Table 2.3: Summary of Wave Height and Damage Potential Reduction at Seawall with Beach Nourishment Project*

*Refer to Fig. 2.29.

Table 2.4 Present Worth Damage Factor, F(w, I) as a Function of Interval Considered and Beach Width
Interest Present Worth Damage Factor, F(w, 1), for Various Beach Widths, w
Rate, W =O0ft W = 50ft W =l100ft W =150Oft
I1 _______ ______6% 1.84 0.89 0.59 0.37
8% 1.39 0.56 0.44 0.27
10% 1.07 0.49 0.44 0.27

There are various general approaches to developing estimates of damage reduction due to beach nourishment. One approach is to attempt to carry out a structure-by-structure damage analysis due to a storm of a certain severity as characterized by a storm tide, wave height and duration. The damage due to many such storms weighted by their probability of occurrence can then be combined to yield the total expected damage. A second approach and that which will be employed here is to recognize that during a particular storm, it is appropriate to consider (1) relative alongshore uniformity of wave attack, and (2) a representative proportional damage as a function of storm severity and beach width, W.
Having demonstrated qualitatively the damage reduction due to beach nourishment, we will proceed to a formalized procedure, making assumptions and simplifying as necessary.
The methodology will assume that a proportional structural damage curve is available as a function of storm return period, TR, and additional beach width, wo. Curves of this type would be site specific depending on the location of the existing structure relative to the shoreline, and the design and quality of the structures. Figure 2.29 presents one example of such a set of relationships. The cumulative probability, P(TR) of encountering a storm of return period TR in any given year is
P(TR) =(2.42) TR
The information presented in Fig. 2.30 can be developed with varying degrees of realism through Monte Carlo simulation methodology such that the result is applied directly and easily. One approach is to assume that the damage from one storm is repaired prior to the occurrence of a succeeding storm. The present worth damage factor, F(w, I, J) in a period of J years, depends on the interest rate, I, the maintained beach width, wo, and represents the ratio of present worth of all damage values over the J year to the present structure value.
This method obviously embodies many approximations, but does provide a rational framework for a very complex problem. One realization of the present worth damage factor for storms over the next J years if the beach width is maintained constant can be shown to


0 0.8
0 0.6 43 b
z C
O 0.2
0.0 I I
1 10 100 1000
Figure 2.30. Assumed Damage Function, D, for Various Beach Widths, w, and Storm Return Periods, TR.

FK(tuI,J) = E D(w,TR) (1 + I) (2.43)
Hear the superscript K denotes the Kth realization and the selection of the J storms is carried out through Monte Carlo simulation in accordance with the cumulative probability distribution, P (= -I). Thus, in addition to the most probable damage, it is possible to develop probability distributions of the present worth damage factor.
Table 2.4 presents the values of the average present worth damage factor P(w, I, o) for all future damages and constant beach width, w. As expected, for the higher interest rates, the present worth values are less. Of relevance is that the greatest incremental benefits occur for the beaches that are initially the most narrow, i.e. for the situation in which the structures are in greatest jeopardy. This reinforces the earlier statement that sand transported from a nourishment project that widens adjacent beaches should be recognized as a financial benefit of not loss to that project.
A somewhat more realistic approach would be to recognize that due to erosional processes, it would be necessary to renourish every j". years during which the beach would narrow from w, to wt at an annual recession rate, r, r = o (2.44)
For this case, one realization of the present worth damage function, F(wo,j*,r,I,J), is determined as
Z~o Dow r n J+(n +T R
FK(wD",rI,,, 21 (2.45)
n=o i+nj*+l o R ( ~
Each of the inner summations represents the contributions to the present worth damage factor during one nourishment interval. Damage reductions employing Eq. (2.42) can assist in identifying the optimal renourishment interval, .,. REFERENCES
Bruun, P. (1962) "Sea Level Rise as a Cause of Shore Erosion", ASCE Journal of Waterways and Harbors Division, Vol. 1, p. 116-130.

Dally, W.R., R.G. Dean and R.A. Dalrymple (1985) "Wave Height Variation Across
Beaches of Arbitrary Profile", Journal of Geophysical Research, Vol. 90, No. C6,
pp. 11917-11927.
Dean, R.G. (1987) "Additional Sediment Input to the Nearshore Region", Shore and Beach,
Vol. 55, Nos. 3- 4, p. 76-81.
Shows, E.W. (1978) "Florida's Coastal Setback Line An Effort to Regulate Beachfront
Development", Vol. 4, Nos. 1/2, Coastal Zone Management Journal, p. 151-164.

Chapter 3

Hsiang Wang
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 1970's only. These maps were rectified for both the horizontal and vertical distortions and the shorelines 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 1:24000. c. Composite historical offshore depth-contour change maps at a 1:24000 scale.
Figure 3.1 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.

R-IT 1877-u79 14 0G906.50 63110.50 9C 56.38 IHW 14t 6.50 63134.98 @0 U.S.CESS.
R-IT 1929 1480906.50 631100.50 90 160.81 MHMW IU4 8 60 63186 .AO U.S.CSiS.
194 18096.5 0088~f 1~R~* tlh~lil
01 19 l" l8'Pft:1 8 66t.h8:0 98 I:11 Pi :::
T 196 1971 400906. 631 00.5 90 315.44 NM 4 6U *
T 1974 5 480906. 3 63 08.50 90 417.38 KHM A-IT96 0O59 61181:1 90 JS122:1~:i
'-' 1" 143 6 Iit'' "i ;i '"'"!!?:! Zill: t! 400
R_ 1790114803 63 9C ;1 jj:f jj
R-985 8 ., 6 6 9 72. 8B 8 040 H
:1 "i" ltWil:ISo : 811 8 ttl 'S t:W jjjj[ : ji
R-2 194 194 68.0 6105.50 90 448.06 1 U.
8': 11 Si: 2 M ill 8 : ,.,,,:. 1 ms
R-: 1Iil I8.3 N8 ll~t 4,0,3,
1-Z 196-;e9 06. 63 N 91U 90 6.7 wN 'Lit:
l-2 197-1 5 14800680 63 051.5 90 65. H 0 6 2 0
91 0 1 ..a1 1 : 1 8 3 U S I s$
A-2 1976 1 480068.00 63051.0 90 01.69 MW 4 68.06 6 2400 US
A- 19 5 48006.00 .5 9 145. I* 2400 MR 0
R- 1077- 879 4 0P 661? 98 -20.8 MIW 11116 6 1 :t 000 U. o
R_3 390.8 HH0 6 0 U. $0
R-3 194- 948 19 6. 90 364.6 NH 60 U. *
::3 1966 479006. 0 63067 .00 90 117.88 MHW e50 6 0 U6 *
R:3 4 IllS't:Io tll:88 i90 I44t Njj8 ji
R-3 1'76 49006.5 63067 30 0 93 22.94 MHM 3 U.S *.
R-3 1q80 5 479006.5C 630673.00 90 468.63 NHM 60 DNA FO)
R- 1 s :ltl88:l t i 3 8 l Iit:It i i ltS8t:8 1tlt:It n61 ,Too t
R-3 1981t 1161:0 90YT
R-4T 1877-1879 1478094.09 630366.50 93 -20.75 NHW 1 00 630 2 0 U. (CS.
1416_ 4.6' .l.. -,l Il ill U S4. ,,:
R-47 1969-1971 1478094.13 63366.5C 90 169.38 1wHM 00 6 000 U.S N.0.
-Ed 1978 418094.03 63,366010 98 ONEIJ. 6010)
I! i 1s I lifi!!!!!0 !!itilu,66.jil i ll il! lll E Eito
- 4T 1r S 48094.03 630366.5'J 9 0 66
R-4i 19 8 .478094.0" 630366.5 90 311 1 MHW 4 094.00 6306 DNR SURVEY)
R-4T 1IC5 10 14780 94..,0 630366.50 90 270.38 MW 14 09 00 6306 2400 DNR PHOTO)
R 1- II:7-187 iT Ilt: E'lOO 3: H:18 t77:7? 888 ,:.6I: .
?1 1 t 76 5'. 16301C3. 93 169:1 MW 14 111 I : 1888 6 U Iit
9:1 194 471 T11:1 630l,1 :30 9o i: : 288 B i: lli
-S 71 776.'lit 6il :.00 90 19: th!:8 ti I: e1o g~i
P-5 194 +8 14762 90 6 0
R-5 19497 14776. 6 8 90 1459:U Ut it9 WI AS
5976 143.ll0ll l l t :0 9 6
R-5 9 M47 0q n 199o
- 935 4 ,o76.:53 6 0 7.0 0 o6.
R1905 1, 7 76.5 630 0 9 224. 8 6. P2400M
-6 91476239.01 629838.12 90 12.93 HHM 416 39.0 6314 3.1 00 U.S..S
R-iT 1469 629138319 90 15.69 "Ht! 6 39 630 053.
R-T 1941-10 58 1476239.01 629638.12 90 39.63 M 46239 0 630235 2400 NR(PHOTO)
P-h 182-669 1461. 61911:1 90 212.6: 141 W 4,6 39. 6'.1 ::CO
T 16 9146 9. 6 98 *HW 1 0# 1f 99
A-6T 19-1 12901 6983 *H to IW 3:41 00 U.S
R-67 .976 176239.01 629838.12 90 6201 101W 144;.1 24
R-T 1980 5 1416239.01 629538.12 90 397.63 14)W 1476239.01 630235.75 2400 ON(POO)
Figure 3.1. Example of Data File of the Digitized Shoreline Information
Stored in DNR.

For beach nourishment design, two kinds of information are useful-shoreline changes and volumetric changes. The problems associated with the computations of shoreline and volumetric changes are discussed in the following sections. COMPUTATION OF SHORELINE CHANGES
For beach nourishment design shoreline change information are useful to assess background erosion or accretion rate and the effects of structure on updrift and downdrift shorelines. An example is used here to illustrate the procedures.
The example used here is the stretch of shoreline centered around Sebastian Inlet which is located at the Brevard/Indian River County line on the east coast of Florida (Fig.3.2). Attempts to open the inlet by hand labor started in 1886 but the inlet was never remained open for any extended period until 1948 when the inlet was stabilized by the construction of permanent jetties. Therefore, it serves as an good example as how the structure effects the shoreline change through examining historical data.
Figure 3.3 plots the historical shoreline changes for three different period from 1929 to 1947, prior to inlet stabilization, from 1947-70, the initial stage of inlet stabilization and from 1970-1986, the later stage of inlet stabilization. As can be seen, prior to inlet stabilization by jetty structure, the shoreline overall advanced during this period. During the period of 194770, the effects of the post stabilized inlet was quite pronounced with updrift accretion and downdrift erosion of approximately 5 miles on each side. The estimated updrift accretion was about 3 ft/yr. whereas the downdrift erosion was about 5 ft/yr. Clearly, the littoral drift was not only impounded on the updrift side but also on the ebb tidal shoal and transported into the inlet. From 1970-86, the rate of shoreline changes slowed down considerably to approximately 1.5 ft/yr. erosional on the south side and 1.0 ft/yr. accretional on the north side. This was probably due to the fact that ebb tidal shoal became more matured during the later stage, thus, impounded less material.

Fig. 3.2. Location of Sebastian Inlet, FL., and the watershed of Indian River




' v Y w .1 -# T




I v~r TV



Fig. 3.3. Historical shoreline changes near Sebastian. Inlet
during three different periods (Inlet stabilized in

300 200 100

-.1uL I






uJ 200
Z < 100
- -100
O -200 C)

.~Ut L



By examining historical data, one can also identify the locations of critical erosion. In the present case, the most severe erosion occurs immediately on the downdrift of the downdrift jetty and at three miles downdrift of the inlet.
The data of shoreline change is often quite noisy. Usually some form of smoothing is required such as running average or harmonic analysis. To separately identify the background shoreline change and the change due to shore-perpendicular structures, two techniques can be used; the so-called odd-even analysis proposed recently by Douglas and Dean (1990) and the well known harmonic analysis.
The odd-even analysis was based on the reasoning that in the absence of structure, the shoreline change should be more or less spatially uniform, therefore, manifests even function change. The presence of shore-perpendicular structure, on the other hand, would cause opposite effects on the updrift and the downdrift shorelines; therefore, the resulting shoreline change should appear as odd function. Mathematically, the even and odd components of the shoreline changes can be established by the following equations: AVe(X) = I [AV(+x) + AV0x)] (3.1)
AVo(x) = 1[AV(+x) + AV(V4)] (3.2)
where V can be shoreline position change or volumetric change; the subscripts e and o refer to even and odd, respectively. The net change is then: AV = V + V (3.3)
The results of odd and even analysis for the period of 1947-70 for the Sebastian Inlet region while the effects of the inlet was most pronounced was illustrated in Fig 3.4.
The harmonic analysis serves similar purpose. The shoreline is expressed as a series of harmonic functions which contain even and odd functions as follows:
n n
V(x) =ao+ Zan cosknx + b sinknX (3.4)
1 1


....... EVEN
.............. ODD0



Fig. 3.4.

Even-odd function analysis near Sebastian Inlet for shoreline changes between 1947-1970 (Inlet location at origin).

200.0 150.0 100.0
50.0 0.0

U -LJ 0U-I

-250.0 -






where ko 21~j with L being the length of the shoreline, and k,, = irk. The coefficients a's and b's can be determined by conventional Fourier analysis. The coefficient ao represents the mean shoreline movement. All the cosine terms are even functions representing background shoreline changes whereas all the sine terms are odd functions representing shoreline changes due to structure effects. This harmonic analysis tends to smooth the data and also brings out the rhythmic feature, if any, of the shoreline change. This method is, however, not suitable for short shoreline length.
Other data analysis techniques such as Eigen function analysis are also used to bring out various features of shoreline changes such as shoreline rotations, etc.
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, a number of problems are involved which are discussed here:
A. Estimation of offshore depth limit
There are a number of conventional offshore control depths as defined in Fig. 3.5.: the breaking depth, db, is where the wave breaks, the depth of active profile, de, is defined as the seaward depth of littoral zone, the shoaling zone depth, d8, also known as the buffer zone depth, is the offshore depth of a zone within which the sediment motion is mainly onshore due to wave induced bottom drift and the closure depth, d~, is defined as the limiting water depth beyond which the sediment motion can be considered to be minimal in a time scale of engineering interest.
These depths are functions of many variables including, among other, wave and current environment, tidal range, offshore slope and topography, presence of structures and sediment characteristics. As just which depth we should select as depth of computation depends on the purpose.

d d de db Limit
c Active Area
Fig. 3.5. Definitions of offshore control depths.

To determine long term volumetric changes the closure depth is the logical choice. For the Atlantic coast, a depth of 27 ft (9m) measured from the berm elevation has been suggested as the 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 of offshore rock crops or reefs exist). At such a distance accurate profile data 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).
Using Indian River County as an example, Figure 3.6 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 3.7.
The effects of choosing different offshore closure depths are further illustrated in Figure 3.8. 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
Therefore, depending upon the selection of offshore boundary, this coast could appear to be accretional down to -15 NGVD. But this coast is erosional if the closure depth was used as the offshore boundary by losing about 4.7 x 106 yd 3 of sand during 1972-86.

G= Reef

Figure 3. 6.

Offshore Depth Contour of Indian River County (1972 DNR Survey).

40.0 ................. ... ........... .................... .-.....-.-.............- R-1 .-..-.-................................................................... N ov. 72
2-.Junie 86
m 20.0
S ----------.-....... ---.- .- *..*... ..
O 40.0
- 20.0
-2 -.- -- -.- -- -..
0 0.0
-40.0 .
Z 40.0
0 R-18
CL 20.0 > 0.0
LLJ -20.0 ---------..... .
w 420.0
-400 0 400 800 1200 1600 2000 2400 2800 3200 3600
(A) Profiles at North End
40.0 R-90
m 20.0 m, 0.0 L -20.0
O 40.0 --- ------------- -- - -
.. -40.0
O 40.0 .........................................................
0.0 R99
0.. 20.0
- 0.0
- -20.0 ;";"O
1 40.0
> o.o
- 40.0 ............................... .. ............ ...
I. -20.0 ~
-400 0 400 800 1200 1600 2000 2400 2800 3200 3600
(B) Profiles at South End
Figure 3. 7. Representative Survey Profiles Along Indian River County Shoreline
(R1, R18, R39 In North) (R90, R99, R114 In South)

q 150.0
Go O)
1- 50.0
u 0.0
Eg -50.0
CL i..1
u. -150.0
O u
L- -200.0
z 4
m -300.0


40000 50000 60000 70000 80000

Figure 3.8.

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

The selection of beach nourishment offshore depth limit is another important task as this depth greatly affects the nourishment volumetric requirement computation which, in turn, affects the project evolution and the performance of the project.
Clearly, it is impractical to use the closure depth as the nourishment limit for it will require too large a nourishment volume. Furthermore, at such a distance accurate profile data may not exist as mentioned earlier.
The depth of the active profile can be argued, and certainly is more practical, as a reasonable choice. This depth can be computed on the concept of critical shear stress, or as a solution of
U2 = Kc(S 1)gd (3.5)
where U, is the critical near-bed velocity, S is the ratio of sediment to fluid density, g is gravitational acceleration and d is the water depth. The coefficient K, is in the order of
0.03 for median sand. Hallermeier (1983) proposed the following empirical equation de = 2.9H(S 1)-'s- 110 (S 1T2 (3.6)
For field application it was also suggested that an annual value of de can be established by using H value exceeded 12 hrs per year, or,the local significant wave height with frequency of exceedance of 0.137%. Birkermier(1988) found the value from Eq.(3.6) to be too high and suggested the following modified equation: (Hs'137)2(3.7)
d, = 1.75(h8)0.137 57.9 gT2
For random waves with P-M spectrum and with JONSWAP spectrum, the values of Hs are 0.004 and 0.005, respectively. When these values are used, Eq.(3.6) gives de = 1.95 to 2.00(H.,)0.137 (3.8)
and from Eq.(3.7)
de = 1.45 to 1.51(H8)0.137 (3.9)
A value of de equal to 1.5 to 1.75 (hs)0.137 has been recommended as a practical range.

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 3.9 would be helpful to establish the confidence level of the results. From this figure, it can be seen that if the volumetric change is small (mild erosion or accretion), the survey induced error (relative) could be very large. On the other hand, if the volumetric change is large (strong erosion or accretion) the survey induced error, relatively speaking, is usually small. The other source of error which by its nature is less serious is due to the motion of the survey vessel. Over a long distance the errors of this type tend to compensate each other as oppose to cumulative.
C. Seasonal variations
The shape of the beach is known to vary seasonally. Therefore, comparisons of beach profiles surveyed at two different seasons could lead to wrong conclusions. Figure 3.10 shows that from 1972 (winter profile) to 1986 (summer profile), Indian River County had an apparent shoreline advance. 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 3.9, 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. These two counties are adjacent to each other; yet, during the same period the shoreline in one county advanced while the other retreated. Thus, the possibility of false signals due to seasonal variations must be examined.

" -4 ,-J

15 20

-20 -15 -10 -5 0 5 10 15 20 25

Figure 3.9.

Errors Induced by Shifting of Datum (1972 Is used as reference; Positive Value means 1986 Profile Shifted Seaward).

-20 -15 -10 -5 0 5 10

o0 o CD

Z, z

200.0 180.0 160.0
140.0 120.0 100.0 80.0 60.0
40.0 20.0 0.0

ST. LUCIE COUNTY (1972 to 1987)



Ft. Pierce

? 3!2 !!

0 20000
O 20000

40000 60000

- .&

80000 100000 120000 140000 160000


Figure 3.10. Total Shoreline Change of St. Lucle County.


. A, vv v

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 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 deep water 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 3.11. They are all in deep water with

100 0







100 0

800 600

Figure 3.11.

North Atlantic and Gulf of Mexico Buoys.

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 3.12. 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 3.1 illustrates the format of the monthly wave information summary and Figure 3.13 shows the graphic display of the monthly wave information.
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 3.2. 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




MIAMI 1977


Figure 3.12. COE Wave Stations.



Time: Day/Er

/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
/12 /18

Depth: Es: Ta:
(a) (m) (eeo)

10.8 12.3 10.8 11.8
12.2 11.0
12.4 11.3 11.9
12.0 11.3 11.6
11.0 11.7 11.5
11.3 11.5 11.6 11.3
11.4 11.9

1.43 1.16 1.18 1.09
0.84 0.77 1.23
1.47 1.64 1.54 1.68
1.12 0.82 0.89
0.74 1.45 1.23
0.93 1.25 1.28
1.12 1.24 1.38

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

Monthly Wave Data Analysis Report
% Wave Energy Distribution
(Period Bandvidth Limit -in seo)

2.4 1.3 1.85
1.6 1.6 1.6
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 5.8-4 21-16 13-10.7 9.1-8 7.1-5.8

2.6 6.8
2.5 1.6
1.6 1.5
2.2 1.1
0.5 0.7 1.1 0.6
1.4 1.6 1.6
1.6 0.5 0.5 0.6
1.4 1.3 0.8 1.0
0.9 0.5 0.6 0.3

19.8 16.6 11.1
12.6 5.6 6.2 1.8
0.9 0.8 6.3
3.0 1.7
2.6 2.4
*2.6 0.7 1.0 1.0
2.6 1.6
2.2 2.3
2.5 1.7
2.0 0.9

9.5 8.0 6.4
8.2 6.3 8.8 2.8
2.4 13.8
12.8 10.8
15.6 8.8
14.6 2.1 3.4 3.9
4.9 6.3

6.9 9.5 6.9 7.0
5.3 6.8 7.8
4.5 8.5
12.1 11.7
24.2 16.9 20.5
18.0 8.5 7.7 12.8
9.2 9.8 7.6 7.8

11.2 6.7 6.3 5.0 7.6 6.1 3.9 8.1

5.7 6.3 8.9 8.6
9.4 10.0 15.6
6.7 15.8 12.5
14.8 15.9 17.3 17.7
15.4 7.8
8.4 9.5
9.2 6.4 7.2
6.1 3.6
6.4 18.6

4.9 16. 8.3 24. 13.1 33. 14.4 32.
14.5 21. 16.4 29. 11.5 22. 11.7 34.
10.2 36. 14.7 29. 15.1 19. 12.5 30.
10.2 24. 10.8 20. 8.3 19. 9.8 16.

5.6 8.3 8.2 7.68
9.9 7.6 6.9 7.7
7.4 12.4 25.7

12. 44. 38. 32.
20. 31. 31. 36.
31. 35.
41. 24.

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

cDN.FORXAT A/Version 1987.1
COEL.University of Florida.Gainesville.Florida 32611
Table 3.1. Format for monthly Wave Data Analysis from Coastal Data Network,
COE, University of Florida.

."- 1 0......i...........
01 5 10 15 20 25 30


Graphic Display of Monthly Wave Information.

Figure 3.13.

Table 3.2 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 I t1 yes
#4 8/87- 1/88 i 11 yes
11/83- 5/84 30040'N, 81016'W 17.5 yes
St. Mary's 7/84-12/84 It it yes
entrance 3/85- 4/85 It it yes
#5 7/85- 9/85 11 it yes
8/87- 1/88 t if yes
Jacksonville 6/84-12/87 30018'N, 81-22'W 10.1 no
Marineland 1/81- 4/86 29040'N, 81-12'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 I t it 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 it yes
6/87-12/87 tI it no
Clearwater 3/82-12/87 27059'N, 82o51'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, 72o18'W 4000 no
41002 11/75- 4/86 32o18'N, 75012'W 3900 no
41006 5/82- 4/86 29018'N, 77o18'W 1200 no
44003 3/79- 4/86 40-48'N, 68030'W 150 no
44004 9/75- 4/86 39000'N, 70000'W 1300 no
44005 1/79- 4/86 42o42'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, 86o18'W 3250 no

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 (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 3.14 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
01 (H,) = exp [- exp (- c ) exp[-exp(-y)], c > 0, d > 0 (3.10)