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Development of methodology for thirty-year shoreline projections in the vicinity of beach nourishment projects

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Title:
Development of methodology for thirty-year shoreline projections in the vicinity of beach nourishment projects
Series Title:
UFLCOEL
Creator:
Dean, Robert G ( Robert George ), 1930-
Grant, Jonathan
University of Florida -- Coastal and Oceanographic Engineering Dept
Florida -- Dept. of Natural Resources. -- Division of Beaches and Shores
Place of Publication:
Gainesville Fla
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Coastal & Oceanographic Engineering Dept., University of Florida
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English
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1 v. (various foliations) : ill. ; 28 cm.

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Subjects / Keywords:
Shore protection -- Florida ( lcsh )
Beaches -- Florida ( lcsh )
Beach erosion -- Florida ( lcsh )
Coastal and Oceanographic Engineering thesis M.S
Coastal and Oceangraphic Engineering -- Dissertations, Academic -- UF
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government publication (state, provincial, terriorial, dependent) ( marcgt )
bibliography ( marcgt )
non-fiction ( marcgt )

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Bibliography:
Includes bibliographical references.
General Note:
"December 15, 1989."
Funding:
This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
Statement of Responsibility:
by Robert G. Dean and Jonathan Grant ; prepared for Division of Beaches and Shores, Florida Dept. of Natural Resources.

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University of Florida
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University of Florida
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All rights reserved, Board of Trustees of the University of Florida
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Full Text
Development of Methodology for Thirty-Year Shoreline Projections in the Vicinity of Beach Nourishment Projects
December 15, 1989
Prepared for:
Division of Beaches and Shores
Florida Department of Natural Resources
3900 Commonwealth Boulevard Tallahassee, FL 32399
Prepared by:
R. G. Dean and
Jonathan Grant
Coastal and Oceanographic Engineering Department University of Florida 336 Well Hall Gainesville, FL 32611




UFL/COEL-89/026

DEVELOPMENT OF METHODOLOGY FOR THIRTY-YEAR SHORELINE PROJECTIONS IN THE VICINITY OF BEACH NOURISHMENT PROJECTS
by
Robert G. Dean and
Jonathan Grant

Prepared for:
Division of Beaches and Shores Florida Department of Natural Resources 3900 Commonwealth Boulevard Tallahassee, FL 32399

December 15, 1989




TABLE OF CONTENTS
INTRODUCTION 1
BACKGROUND 1
General Description of Sediment Transport Processes in the Vicinity of A Beach Nourishment Project.......................................1I
Profile Equilibration.........................................2
"Spreading Out" Losses......................... ..............2
Background Erosion.........................................5
Role of Retention Structures................................... 5
Role of Sediment Size on Transport Rates .. .. .. .. ... ... .... ......5
Significance of Wave Height .. .. .. .. ... .... ... ... ... ... ....10
Wave Direction .. .. .. .. ... ... ... .... ... ... ... ... .....10
General Characteristics of Equilibrium Beach Profiles .. .. .. ... ... ...10
METHODOLOGY 12
Profile Equilibration .. .. .. .. ... .... ... ... ... ... ... .....12
Longshore Sediment Transport .. .. .. ... ... ... ... ... ... .....20
Combined Linearized Equations. .. .. .. .. ... ... ... .... ... ....22
Rectangular Beach Nourishment Project .. .. .. .. ... ... ... .... ..25
Erosion Adjacent to a Littoral Barrier .. .. .. .. .... ... ... ... ....30
Numerical Solution. .. .. .. .. ... ... .... ... ... ... ... .....33
Boundary Conditions. .. .. .. .. ... ... ... ... .... ... ... ....36
Wave and Other Parameters of Use in Applying the Methodology. .. .. .. ...38
STEP-BY-STEP DISCUSSION OF METHODOLOGY 38
Graphical Procedure. .. .. .. ... ... ... ... ... ... .... ... ..38
CASE A NOURISHMENT ALONG AN UNINTERRUPTED SHORELINE 41
Step 1 Specify Beach Nourishment Project Characteristics. .. .. .. .. ....41
Step 2 Determine the Equilibrated Project Width, Ayo .. .. .. .. ... ....41
Step 3 Calculate Effective Alongshore Diffusivity, G .. .. .. .... ... ..41
Step 4 Calculate Shoreline Position Due to Spreading Out Losses .. .. .. ...43 Step 5 Calculate Background Erosion Losses .. .. .. .. ... ... ... ....43
Step 6 Calculate Resulting Shoreline Position. .. .. .. ... ... ... ...43




CASE B NOURISHMENT DOWNDR.IFT OF A LITTORAL BARR.IER 43
Step 1 Specify Beach Nourishment Characteristics................... 44
Step 2 Determine the Equilibrated Project Width, Ayo................ 44
Step 3 -Calculate Effective Alongshore Diffusivity, G................... 44
Step 4 Calculate Shoreline Position Due to Spreading Out Losses .. .. .. ...46 Step 5 Calculate Background Erosion Losses .. .. .. .. ... ... ... ....46
Step 6 Calculate Resulting Shoreline Position. .. .. .. ... ... ... ...46
NUMERICAL PROCEDURE 47
CASE A NOURISHMENT ALONG AN UNINTERRUPTED SHORELINE 47
STEP 1 Specify Beach Nourishment Project Characteristics............. 47
STEP 2 Determine Equilibration Project Width, Ayo................. 47
STEP 3 Develop Background Erosion Data as Piecewise Linear Segments 47 STEP 4 Develop Input File.................................. 47
STEP 5 Run Program.......................................51
STEP 6 Examine Output in File DNRBS.OUT .. .. .. .. .... ... ....51
CASE B NOURISHMENT WITH STRUCTURES PRESENT 57
STEP 4B Specify a Reference Background Transport..................57
STEP 5B Specify Structure Location(s) and Length(s) in Program..........57
EXAMPLES ILLUSTRATING APPLICATION OF METHODOLOGY 59 Graphical Examples.........................................59
Numerical Examples........................................ 59
REFERENCES 65
APPENDIX A 66
APPENDIX B 72
APPENDIX C 84
APPENDIX D 94
APPENDIX E 104




APPENDIX F 114
APPENDIX G 125
APPENDIX H 134
APPENDIX I 144




LIST OF FIGURES

1 Effect of Nourishment Material Scale Parameter, AF, on Width of Resulting Dry
Beach. Four Examples of Decreasing AF ......................... 3
2 "Spreading Out" Losses Occurring Due to Mobilization of Sediments by Waves. 4 3a Variation of Shoreline Position with Time at Various Locations Relative to a
Nourishment Project. No Background Erosion ...................... 6
3b Variation of Shoreline Positions with Time at Various Locations Relative to a
Nourishment Project. Uniform Background Erosion of 2 ft/yr ............ 7
4 Illustration of Nourishment Stabilization by Terminal Structure ............. 8
5 Plot of K vs D. Results of Present and Previous Studies (modified from Dean,
1978) ........ ......................................... 9
6 Shoreline Orientation Downdrift of a Complete Littoral Barrier .......... ... 11
7 Beach Profile Factor, A, vs Sediment Diameter, D, in Relationship h = Ay2I3
(modified from Moore, 1982). Note: A(ftl/3) = 1.5 A(m'/3) ............. 13
8 Recommended Distribution of h. Along the Sandy Shoreline of Florida..... ...14 9 Three Generic Types of Nourished Profiles .......................... 15
10 Effect of Increasing Volume of Sand Added on Resulting Beach Profile, AF =
0.1 m1/3, AN = 0.2 m1/3, h. = 6m, B = lm ......................... 17
11 Variation of Non-Dimensional Shoreline Advancement Ayo/W. with A' and V'.
Results Shown for h./B 2.0 ................................. 18
12 Variation of Non-Dimensional Shoreline Advancement Ayo/W, with A' and V.
Results Shown for h./B = 4.0 ................................. 19
13 Definition Sketch .......... .................................. 21
14 Variation of Ratio C,/Co vs h/Lo ......... .......................... 23
15 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, r. = 0.78, h. From Fig. 8, B Estimates Ranging from 6
to 9 ft, H0 from Figure 23, T From Figure 24 ....................... 24
16 Example of Evolution of Initially Rectangular Nourished Beach Planform. Example for Project Length, f, of 4 Miles and Effective Wave Height, H, of 2
Feet and Initial Nourished Beach Width of 100 Feet ................... 26
17a Evolution of an Initially Rectangular Beach Planform on an Otherwise Straight
Shoreline. Results for t' = 0, 0.1, 0.2, 0.5 and 1.0 ................... 27a
17b Evolution of an Initially Rectangular Beach Planform on an Otherwise Straight
Beach. Results for t' = 0, 2.0, 4.0, 6.0 and 8.0 ...................... 27b




17c Evolution of an Initially Rectangular Beach Planform on an Otherwise Straight
Beach. Results for t' = 0, 10.0, 15.0, 20.0 and 30.0 ................... 27c
18 Percentage of Material Remaining in Region Placed vs. the Parameter V/Ut7t. 29 19 Example of Shoreline Evolution in Response to Littoral Barrier. Based on
Method of Pelnard-Considere. Longshore Sediment Transport Rate Used
in Example = 180,000 cubic yards per year. Littoral Barrier Length = 160 ft. 31 20 Pelnard- Considere Solution for Shoreline Recession Downdrift of a Complete
Littoral Barrier ........ ................................... 32
21 Two Alternative Methods for Predicting Beach Nourishment Performance Downdrift of a Littoral Barrier ....... ............................. 34
22 Computational Scheme Used in Numerical Method ..................... 35
23 Recommended Values of Effective Deep Water Wave Height, H0, Along Florida's
Sandy Shoreline .......................................... 39
24 Recommended Values of Effective Deep Water Wave Period, T, Along Florida's
Sandy Shoreline .......................................... 40
25 Form for Computation of Performance Along Uninterrupted Shoreline ..... .. 42 26 Form for Computations of Performance Downdrift of a Littoral Barrier . . 45 27 Data Input Preparation Form for Numerical Procedure .... ............. 48
28 Input File DNRBS.INP for Example 2 .............................. 49
29 Example of Output File DNRBS.OUT for Input File in Figure 27. Example No.
1. (Total of 11 Pages of Output ................................ 52
30 Estimates of Net Annual Longshore Sediment Transport Along Florida's East
Coast ........ ......................................... 58
C-1 Numerical Example 1, Ayo = 112 ft, Nourishment Length = 2 miles, Zero Background Erosion .......... .................................. 86
C-2 Numerical Example 2, Shoreline Position Variation with Time at Locations Indicated and Shown in Figure C-1 ...... ......................... 87
D-1 Numerical Example 2, Ayo = 112 ft, Nourishment Length = 2 miles, Uniform
Background Erosion = 2 ft/yr ................................. 96
D-2 Numerical Example 2, Shoreline Position Variation with Time at Locations Indicated and Shown in Figure D-1 ...... ......................... 97
E-1 Numerical Example 3, Ayo = 112 ft, Nourishment Length = 2 miles, Variable
Background Erosion ....................................... 106
E-2 Numerical Example 2, Shoreline Position Variation with Time at Locations Indicated and Shown in Figure E-1 ............................... 107




F-1 Numerical Example 4, Ayo = 112 ft, Nourishment Length = 1,000 ft, No Background Erosion . 116
F-2 Numerical Example 2, Shoreline Position Variation with Time at Locations Indicated and Shown in Figure F-1 . . . . .. . . . . . . . . 117
G-1 Numerical Example 5, 112 ft Long Structure at North End of Project, Nourishment Length = 2 miles, No Background Erosion . . . . . . . . 126
G-2 Numerical Example 2, Shoreline Position Variation with Time at Locations Indicated and Shown in Figure G-1 . . . . . . . . . . . . 127
H-1 Numerical Example 6, 112 ft Long Structure at South End of Project, Nourishment Length = 2 miles, Uniform Background Erosion . . . . . . . 136
H-2 Numerical Example 2, Shoreline Position Variation with Time at Locations Indicated and Shown in Figure H-1 . . . . . . . . . . . . 137
I-1 Numerical Example 7, 112 ft Long Structure at South End of Project, Nourishment Length = 2 miles, Variable Background Erosion . . . . . . . 146
1-2 Numerical Example 2, Shoreline Position Variation with Time at Locations Indicated and Shown in Figure I-1 . . . . . . . . . . . . . 147




DEVELOPMENT OF METHODOLOGY FOR
THIRTY-YEAR SHORELINE PROJECTIONS IN THE
VICINITY OF BEACH NOURISHMENT PROJECTS INTRODUCTION
The purpose of this report is to develop and illustrate with examples readily applied methodologies for calculating the response of shorelines in the vicinity of beach nourishment projects. The need for such methodology is a result of Florida Statutes 161.053(G) and Rule 16B-33.024(3)(e) which require, with minor exceptions, coastal structures to be located landward of a thirty- year projection of the Seasonal High Water Shoreline (SHWL).
The conceptual interpretation of these Statutes and Rule is that the performance of the beach nourishment project should be considered in projecting the Seasonal High Water Line (SHWL) position to a time thirty years into the future. This requires consideration of both the background erosion rate which is the normal rate in areas that have not been nourished and the shoreline retreat component due to "spreading out" losses from the beach nourishment project.
BACKGROUND
General Description of Sediment Transport Processes in the Vicinity of a Beach Nourishment Project
In general, when sand is placed in conjunction with a beach nourishment project, this project represents an "~anomaly" to the shoreline planform and the natural processes will tend to smooth out this anomaly. In addition, many times the placed profile will be steeper than the natural profile and the profile will tend to equilibrate over time. The sections below describe the individual processes and characteristics of the response of a beach nourishment project.




Profile Equilibration

As noted, beach nourishment projects are generally placed with profiles which are steeper than the natural profile for the size of sediment that is used in the beach nourishment project. Thus over the years this profile will tend to equilibrate to its natural shape. In addition, if the sediment size used in the beach nourishment is fine, the profile will tend to be rather mild in slope and the shoreline advancement will be small for a given volume of beach nourishment per unit length of beach. Figure I shows the qualitative effect of grain size in terms of the dry beach width for the same added volume per unit length of beach. The upper panel presents the profile that would result for a beach nourishment grain size which is larger than the native sand resulting in a fairly wide dry beach width. The three lower panels illustrate the effect of decreasing grain size maintaining the volume per unit beach length the same. It is seen that with decreasing grain size the dry beach width progressively decreases to a point where in the lower panel the dry beach width is zero. For this condition all of the sand that has been placed has been moved offshore in a profile which is consistent with the grain size used in the nourishment.
"Spreading Out" Losses
The placement of a beach nourishment project results in a platform anomaly which interacts with the waves to result in sediment transport away from this anomaly. This process is illustrated in Figure 2 and shows the transport occurring away from the anomaly in a manner that will result in a smoothing or spreading out of the sediment. The term "spreading out" losses actually refers to a redistribution of the sediment and not a total loss to the system but rather a loss from the region in which the sediment is placed. As will become evident later, this loss from the nourished axea is manifested as a gain of sediment volume in the nourishment-adjacent areas.




92.4m
7 B = 1.5M

45.3m

b) Non-intersecting Profiles AN= AF= 0.1mI /3

15.9m

c) Non-Intersecting Profiles:AN = 0.1m113AF = 0.09m1/3

d) Limiting Case of Nourishment Advancement, 1/3 Non-Intersecting Profiies, AN= 0.1m1 /3AFI = 0.085m I I I I I

100

200

300

400

500

h, = 6m

= 6m

600

OFFSHORE DISTANCE (i)
Figure 1. Effect of Nourishment Material Scale Parameter, AF,on Width of
Resulting Dry Beach. Four Examples of Decreasing AF.




* **"Spreading Out"
Losses
Waves
Planform Anomaly Due to
* Beach Nourishment
* Spreading Out"
Losses
*(From Region Placed)

Figure 2. "Spreading Out" Losses Occurring Due to Mobilization
of Sediments by Waves.




Background Erosion

Usually the need for a beach nourishment project is due to a background erosion which, for an ideal project, is relatively slow. With the placement of the beach nourishment project, there will be two components of shoreline retreat. It will be assumed that the two components of shoreline recession, i.e. background erosion and the component due to spreading out losses, can be added linearly. The background erosion which was present prior to the placement of the beach nourishment project will continue. Figure 3 illustrates qualitatively the superposition of these two components for several locations within and adjacent to a beach nourishment project. Figure 3a presents the case for no background erosion and Figure 3b for a uniform background erosion of 2 ft/yr. Role of Retention Structures
In some cases, especially short beach nourishment projects, it may be worthwhile to consider the use of retention structures to extend the life of the projects. Figure 4 illustrates qualitatively one such application. Structures must be used with great care, especially in areas where there is a substantial longshore transport magnitude. An additional situation in which retention structures have been used effectively to prevent loss of sediment in Florida has been at the ends of littoral systems such as at the termini of barrier islands. Two such locations are the north jetty at John's Inlet in Pinellas County and the two small terminal structures at the south end of Gasparilla Island in Lee County. Role of Sediment Size on Transport Rates
It has been noted that the dominant losses due to a beach nourishment project are due to spreading out losses or transport away from the region where the sediment is placed. The sediment transport is proportional to a coefficient, K, which has been found to depend on sediment size as shown in Figure 5; thus with the use of coarser grained material, the project will perform much more effectively. Although there has not been any substantial documentation to illustrate adverse effects of using material which is substantially coarser




Ow = 100
OO
OOZ wiz
-CC< 50 IUl 0 00 = CC U) U.

Figure 3a.

5 10 15 20 25
TIME (Years) AFTER NOURISHMENT

Variation of Shoreline Position with Time at Various Locations Relative to a Nourishment Project. No Background Erosion.




100

a
z0
LJI--

-50

0 5 10 15 20 25 30

TIME (Years) AFTER

NOURISHMENT

Figure 3b. Variation of Shoreline Positions with Time at Various Locations Relative to a
Nourishment Project. Uniform Background Erosion of 2 ft/yr.




Figure 4. Illustration of Nourishment Stabilization
by Terminal Structure.




2.0

Res
1.0-R

0.5

1.0

DIAMETER, D (mm)
Figure 5. Plot of K vs. D. Results of Present and Previous Studies (modified
from Dean, 1978).

ult From This Study, Santa Barbara
elationship Suggested
Previously




than the native material, it has been hypothesized that if such material is used it may effectively armor the beach in the nourishment area thereby resulting in less transport from the area nourished and a deficit and associated erosion on the area dowudrift of the project. Significance of Wave Height
After placement of a beach nourishment project, it is evident intuitively that the mobilizing effects of wave height cause profile equilibration and the spreading out losses mentioned earlier. Thus the determination of reliable, effective wave heights is important to the prediction of the performance of any beach nourishment projects.I
As will be described later, for two identical projects which are placed in areas where the wave height differs by a factor of two, the longevity of these projects would differ by a factor of 5.3.
Wave Direction
It is somewhat surprising that on a long, uninterrupted shoreline the effect of wave direction is relatively unimportant to the performance of a beach nourish ment project. The interpretation of this insensitivity will be discussed in a later portion of this report. However, wave direction is extremely important in the case of a beach nourishment project located adjacent to a structure which interferes with the longshore sediment transport. Figure 6 illustrates such a situation where sand is placed immediately downdrift of a jetty and the orientation of the beach planform immediately adjacent to the jetty is parallel to the incident wave crests. Thus, it will be necessary to provide estimates of wave direction or to develop alternative methodologies which do not require accurate estimates of wave direction.
General Characteristics of Equilibrium Beach Profiles
In general, equilibrium beach profiles tend to be concave upward and the profiles tend to be milder in slope for the finer sediment and steeper for coarser sediment. Equilibrium beach profiles have been found by Bruun (1954) and Dean (1977) to be reasonably well




Inlet

N.
Shoreline Orientation Downdrift of a Complete Littoral Barrier.

Figure 6.




represented by the form

h(V) = Ay2/3 (1)
in which h is the depth at a distance y seaward of the shoreline and A is a scale parameter.
A significant contribution to the objectives of this report was developed by Moore (1982) in the form of a plot of the sediment scale parameter, A, in terms of the sediment size, Figure 7.
A second important relationship to the objectives of this study is that of closure depth, h,,. Closure depth is a concept which describes the maximum depth to which sediments will be mobilized by the waves. Although in general this closure depth is expected to be dependent on wave height and wave period, for purposes of this study, the closure depth will be regarded as a value dependent on position around the state of Florida. The recommended closure depth versus location around the state is presented in Figure 8. METHOD OLO GY
Profile Equilibration
In considering the profiles resulting from beach nourishment, generically there are three types of nourished, equilibrated profiles. These are presented in Figure 9. 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..




"E
LU ILl
0r Cl)

1.0) 0.10

0.01
0

Relationship
From Hughes'
Field Res-ults From Individual Field Profiles where a
Range of Sand Sizes was given SLabr t- ----A From Swart's
6AA Laboratory Results

.U1

10.0

100.0

SEDIMENT SIZE D (mm)
Figure 7. Beach Profile Factor, A, vs Sediment Diameter, D, in Relationship
h = Ay2/3 (modified from Moore, 1982). Note: A(ft1l/3) = 1.5 A(ml/3).




12 16 20 24 h, (Feet)

h. (Feet) 12 16 20 24

Figure 8. Recommended Distribution of h. Along the Sandy Shoreline
of Florida.

- I U .




a) Intersecting Profile AF>AN

Added Sand
b) Non-Intersecting Profile

Virtual Origin of Nourished Profile

Added Sand

c) Submerged Profile AF
Figure 9. Three Generic Types of Nourished Profiles.




The third type of profile that can occur is the submerged profile (Figure 9c) the characteristics of which axe shown in greater detail in Figure 10. 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 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, Ayo, resulting in a profile of the second type described.
The next major section describes the methodology for calculating planform response to a beach nourishment project. It is assumed that profile equilibration occurs when the material is placed. This assumption is not important to the final thirty year projection. Actually, of course the profile equilibration will occur gradually, but will probably be near completion within a few years. This assumption merely allows the overall response calculations to be carried out in two steps. Following the discussion of profile equilibration, graphical and numerical methods are presented for predicting the shoreline (planform) evolution. As might be expected the numerical method provides greater flexibility for representing realistically the actual situation.
It can be shown that the initial additional dry beach width, Ayo, is related to the placed and native sediment characteristics and the closure depth, h", and berm height, B. To render the results more compact, the results are cast in the following non- dimensional form
___ f (AF/IAN, V / BW,, (2)
in which W,, is the width of the active surf zone on the native profile, i.e.
W.= (h./AN)311 (3)
Figures 11 and 12 present results of AyO/W. for h, /B values of 2 and 4, respectively.




OFFSHORE DISTANCE (m)

100

200

300

400

500

a AB = 1.5m
"': : ..;. h ,. = 6m": .......
a) Added Volume =120 M 3 /M I

b) Added Volume =490 M3 /M

Case of Incipient Dry Beach

Figure 10. Effect of Increasing Volume of Sand Added on Resulting
Beach Profile. AF= 0.1m1/3, AN= 0.2m113, h. = 6m, B = 1m.

,4
zo
0
WU 10
-JI

I




10.

1.0
lVesil V =0.
Ay V' =0.05
"B __ I'_ __ _ _-_ _0 AF' he
I I
0.10 ---- 0 .10.01efnto SkthI
S V' = 0.01
0.01/
- .*---W
FV' = 0.005
A 4F w A V/BW = .002
h W -- - --'-
0.001 -Deflinition Sketch
0 1.0 2.0 2.8
A' = AF/AN
Figure 11. Variation of Non-Dimensional Shoreline Advancement
Ayo/W with A' and -V'. Results Shown for h, /B = 2.0.




1.0
1.0 Non-Intersecting
Profile j*
V'V /BW. =5.0 .
0.11
,Intersecting
2 Profiles
f0 l
0.10
A Yo I I o.0o
Aw
W Asymptotes
* for Ayo= 0
I I
0.02
0.01 i
0t 10 20.005
WA V' = 0.002
Fgr12Vaiino No-imesina Shrln Adaceet, 0/i wt
s V' = 4.0 0
IV =001....
-Definition Sketch '
y f( h AF V
W "B-' AN' BW
0.00010
1.0 2.0 2.8
A' = AF/AN
Figure 12. Variation of Non-dimensional Shoreline Advancement AYo/W., with
A' and -'. Results shown for h, /B = 4.0.




It is seen that for each non- dimensional volume, the non-dimensional additional beach width increases with increase in ratio of sediment scale parameters; however, the increase is relatively small for ratios greater than 1.2. Additionally, there is some lower ratio of scale parameters for each non-dimensional volume below which there will be no additional dry beach width. This corresponds to the case presented in Figure 1d. As noted previously, the profile equilibrations will be assumed to occur instantaneously. The stage is now set for consideration of the longshore sediment transport and planform evolution. Longshore Sediment Transport
The equations available for representing planform evolution are a sediment transport equation and a sand conservation (or continuity) equation. The transport equation is empirically based and describes the total transport in the longshore direction due to waves arriving at a breaking angle, ab to the shoreline. The continuity equation is fundamental and simply balances sediment volume changes with transports into and out of the region under consideration. These equations are:
K H5/2 Vgig sin(P CYb) cos(f# ab) (4)
Transport: Q = b 8(s 1)(1 p)
Continuity: O-V Q(5)
at- ax()
in which V is sediment volume per unit length of beach, g is gravity, /C is the ratio of breaking wave height to water depth (usually taken as 0.78), Pl represents the azimuth of the outward normal to the shoreline, ab represents the azimuth of the direction from which the breaking waves originate, s is the specific gravity of the sediment (approximately 2.65), p is the inplace porosity of the sediment (usually taken as 0.35) and t is time. Figure 13 presents a definition sketch for ab and fl. The sign convention used in this report is that the positive x (and Q) direction are to the right as an observer looks offshore.
For most shoreline evolution models and those that will be presented here, the model predicts the position of one contour, such as the NGVD contour or the SHWL contour.




0
U
0
4
0

Reference Base Line

Figure 13. Definition Sketch.




These models assume that as beaches erode or accrete the profile moves without change of form in a landward or seaward direction, respectively. Thus after equilibration occurs, the shoreline change, Ay, associated with a volumetric change, A, can be shown to be given by
Ay- =(h, + B) (6)
The two governing equations, namely the transport and conservation equations, can be applied directly to predict the evolution of a beach nourishment project or they can be combined in a linearized manner. Both of these approaches will be described in the following sections.
Combined Linearized Equations
Eq. (4) describes the sediment transport in terms of the difference between the shoreline orientation and wave direction. Foregoing the algebra, it can be shown that the combined and linearized equation governing the evolution of a beach system is y 82y ()
at aX2
in which the parameter, G, can be interpreted as the "alongshore diffusivity" and is expressed as
GK H '4C' g94 cos'2(Po ceo) cos 2(flo c,) (8)
8 8(s 1)(1 p)C, 0.4(h. + B) cos(3o a,,) where the subscript "o" denotes deep water conditions, C, is the wave celerity in the water depth h, and Eq. (8) is derived in Appendix A. The ratio C,/Co is C,/Co = tanh (2rh) (9)
in which Co = gT/27r, CG, = gT/47r and C./Co is presented vs h,/Lo in Figure 14.
Figure 15 presents approximate values of G along the sandy beach shorelines of the state of Florida.
Equation (7) is the so-called heat conduction or diffusion equation which is well-known in classical physics and has many known solutions. Two solutions which are of interest




c 0.05 1 ------21
o/ r
L
0
0 0.05 0.10 0.15 0.20
h*/Lo

Figure 14. Variation of Ratio C,/Co vs. h/Lo




0.02 0.06 0.10 0.14
G(ft2/s)

G(ft2/s) 0.02 .0.10
/eo0

Figure 15. 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.




here will be discussed below; these solutions pertain to the graphical methodology thereby allowing a first estimate of the performance of a beach nourishment project. These solutions and the development of the combined and linearized equation concepts are due to PelnardConsidere (1956).
Rectangular Beach Nourishment Project
The first solution of interest is for the evolution of an initially rectangular beach nourishment project of length, , which projects a distance Ayo from the original shoreline. The solution is
Y(X,t) = A- {erf [_ ( -ef [, (T 1)]1} (10)
in which the term "erf" refers to the error function described mathematically as erf(z)= e-2 du (11)
in which u is a dummy variable.
Figure 16 illustrates an example of the performance of such a beach nourishment project and Figures 17a, b and c present the results in non-dimensional form. It can be seen from Eq. (9) that if the term e is the same for two beach nourishment projects the nonVt
dimensional performance of the two beach nourishment projects will be the same. Thus, for two projects constructed with the same wave characteristics but with one project twice the length of the second project, the first project will lose the same percentage of sediment as the second project in a duration that is four times as long as that for the second project. Similarly if two projects have the same length but the first project has a wave height onehalf that of the second wave height then the first project will have a longevity which is in excess of five times the longevity of the second project. In general this relationship may be stated as
t2= 1 ()2 ( )24 (12)




DISTANCE FROM ORIGINAL
SHORELINE, y (ft)

Nourished Beach Planform

6 4 2 0 2 4 6 8

ALONGSHORE DISTANCE, X (miles)

Figure 16.

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.




1.0 0.9
0.8

0.5 0.4
0.3 0.2 0.1
0.0

Figure 17a.

t' = 16 Gt
912

- Initial Planform, t' = 0.0 I I I I I I I I I

\
~1
\ \~,
~~~1;~~~~~ - -
I'
''
\ \

2.0
2.0

II 1 1
3.0 3.5 4.0 4.5
x/ (Z/2)

I I
5.0 5.5

Evolution of an Initially Rectangular Beach Planform on an Otherwise Straight Shoreline. Results for t' = 0, 0.1, 0.2, 0.5 and 1.0.

I I I I
6.0 6.5 7.n 7.5
.t 0.0
......................s = 0 0. 1
- -----------t'=0.2
----------t'=0.5
--t =1 .0

-




-7 0.6
>1
0.5
N
0 .4 . . .. . .
0.3
0.1
0.0 I I
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.
x/(k/2) t' =0.0
t =2.0
Figure 17b. Evolution of an Initially Rectangular Beach Planform on an t'=.0
Otherwise Straight Shoreline. Results for t' = 0,2.0,4.0,
6.0 and 8.0. =.
-' =8.0




0.7
0.6
0.5- - --.. . ...
0.3 -..
0.0
0.0 --- -----------0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5
x/(k/2) t1'=0.0
Figure 17c. Evolution on an Initially Rectangular Beach Planform ...................... t0.0
on an Otherwise Straight Shoreline. Results for -----------' =15.0
t' = 0,10.0, 15.0, 20.0 and 30.0. -t' =20.0
-t =30. 0




in which t, and t2 represent the times required for projects 1 and 2 to lose the same percentage of sand from the region placed. Thus, the longevity of a project in terms of the time required to lose a certain percentage of the sediment from the project area varies directly as the square of the length of the project and inversely as the 2.4 power of the wave height.
Equation (10) may be integrated to determine the fraction of material, M, remaining within the area placed. This is shown formally as M(t) = 1 y(x,t)dx (13)
and upon carrying out the integration the result is M (t) = 2 N$- [e-(/2vr-)2 1] + erf (~ )(14) which is plotted in Figure 18 where the horizontal axis is the parameter encountered previously in the solution for the evolution of this particular planform.
If we are interested in the time required for 50% of the nourished material to be transported out of the area placed, then from Figure 17 we see that the appropriate value of VG-/ is 0.46. Thus the time required to lose 50% of the sediment from the region placed is
t5o= 0.21- (15)
in which all variables are in consistent units. A more readily applied form is = 8 (16)
HbH1
where tso is in years, t is in miles and Hb is the breaking wave height in feet. As an example a project 2 miles in length with an effective breaking wave height of 2 ft would "lose" 50% of the volume placed due to spreading out losses in 22
t50 = 8.7- = 6.15 years (17)
It is emphasized that this solution is for a long unobstructed shoreline and includes only spreading out losses, i.e. no background erosion.




JGtI/e
.0
20 1.0 0.5 1.0
- inI I I I |I I I I I I I I I I I I I I I I I I I I I II
-- U ~ t = Time After Placement
- ) G= Alongshore Diffusivity Initial Y
c 4;CFillU.L Asymptote Planform
OZz 0.5- NM=1
zo0
ORu0
2F O 7... ..
C-L-'I0.0
O L 0 1 2 3 4 5 6
Figure 18. Percentage of Material Remaining In Region Placed vs. the Parameter V-Gt~i?




Erosion Adjacent to a Littoral Barrier

The second analytical solution of relevance to this study is that of the downdrift erosion adjacent to a littoral barrier as shown in Figure 19. The solution for this situation is applicable for an initial condition of a straight and uniform shoreline and a wave arriving at a constant direction. The solution is presented as Y(Xt) [V4tex X' xvr~erfc x(18)
yC ,t) -)] t < t,
y(x,t) = Yerfc (-r) t > tc (19)
where
erfc(z) = 1 erf(z) (20)
y2 r
tc 4Gtan20 (21)
in which Y is the length of the structure, 0 represents the angle of the approach wave and t, is the time at which bypassing commences. Because we are interested primarily in the beach response downdrift of a barrier and there is usually no bypassing, Eq. (18) would be the solution of primary interest. Figure 20 presents the non- dimensional solution, y/(.\/4iU tan 0), versus non- dimensional distance, x/V-Gt, from the downdrift jetty.
There are two approaches to predicting shoreline changes downdrift of a littoral barrier, such as a jetty. One method, that just described, requires knowledge and specification of an effective wave direction. Available information to define wave directions is quite limited, especially on the west coast of Florida. Fortunately a second method, which will be recommended here, requires data which are more readily available along the Florida coastline.
The recommended procedure utilizes background erosion data rather than an effective wave direction. The justification for the use of background erosion data rather than wave




3
w
2
0

DISTANCE
LANDWARD (ft)

YEARS

Littoral

100
DISTANCE
SEAWARD (ft)
Initial Shoreline

0
cc
U
U.
2
z 0
3 0
z I
Co
a

Example of Shoreline Evolution in Response to Littoral Barrier. Based on Method of Pelnard-Considere. Longshore Sediment Transport Rate Used in Example =180,000 cubic yards per year. Littoral Barrier Length = 160 ft.

Figure 19.




NON-DIMENSIONAL DISTANCE DOWNDRIFT OF COMPLETE LITTORAL BARRIER
x/44G0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1
O. Littoral Barrier Waves
) -0.2
(,j -Y
Oz
Z U) -0.4
C.) Ijw
Z x x
0
Z -0.6'

Figure 20. Pelnard Considere Solution For Shoreline Recession Downdrift of a Complete Littoral Barrier.




direction is that the local background erosion rates in the vicinity of a littoral barrier axe due to and a manifestation of waves arriving at the shoreline. This alternate recommended method would not be possible in the case where an inlet is to be cut because at that time there are no a priori background erosion data. Fortunately, in Florida, quite reliable background erosion data exist in the vicinity of most inlets.
For the recommended approach, the modifications to the graphical method described previously for an uninterrupted shoreline are small and are illustrated diagrammatically in Figure 21. The only changes are that (a) the effective length of the project, e, is twice the physical length of the project, f, and (b) the waves are considered as advancing normal to shore. This accomplishes the desired effect of a zero transport at the littoral barrier, since the transport at the center of a project for normally incident waves is zero.
The methods described here will be illustrated by later examples. Numerical Solution
The numerical solution that will be presented here is a so- called explicit scheme in which the equations for sediment transport and continuity are solved sequentially. In particular referring to Figure 22, the shoreline positions are held constant for a time step, At, while the sediment transport is computed. Following this operation, the sediment transport is held constant for a time step and the equation of continuity is applied to these transport values to update the shoreline positions.
This type of explicit model referred to here has a stability criterion which limits the maximum time step, At, that can be utilized. The maximum time step is given approximately by
(At)max 1 AX2 (22)
2 G
and G is defined in Equation (8) and approximate values presented in Figure 15. For most purposes in Florida, a time step of 86,400 seconds (I Day) and a grid size (Ax) of 500 feet are reasonable. From Eqs. (8) and (22) it is seen that the larger the wave height, the smaller the allowable time step. Also, the smaller the grid size, the smaller the allowable time step.




LittoralS Barrier
* ~ Nourishment
a) Method With Waves Approaching
at a Specific Angle. Background Erosion Without Effect of Littoral
Barrier

Littoral Barrier

Waves (3 ) = 0

Nourishment

b) Recommended Method With Waves
Approaching Normal to Shoreline.
Background Erosion Includes Effect
of Littoral Barrier.

Figure 21. Two Alternative Methods For Predicting Beach Nourishment
Performance Downdrift of a Littoral Barrier




Figure 22. Computational Scheme Used In Numerical Method.




As noted previously, one of the primary advantages of the numerical solution is the much greater flexibility of specifying initial conditions and input to the model. Additionally, with minor modifications to the program, renourishments could be represented.
To effectively utilize the greater flexibility inherent in the numerical procedure and in particular to include structures where desired, the background erosion rates are translated into background transport rates. Formally the background transport rates, QB(x), are determined from the continuity equation
QB (X) = QB (XO) (h. + B)j Y dt (23)
in which 2YDis the background shoreline change rate and xO is a reference shoreline location at which a reference transport QB(XO) is specified. Boundary Conditions
The application of the sediment transport and continuity equations with initial planform conditions require specification of boundary conditions at the two ends of the grid system in order to complete the problem formulation. In general, there are two types of boundary conditions. The first that will be discussed is a specified shoreline position at one or both of the ends of the computational domain. A simple example of the specified shoreline positions would be that the shoreline is fixed at its initial value or the value could be prescribed over the computational time period. A second boundary condition that could be applied is a specified discharge at one or both ends of the computational domain. Examples of situations in which each of these boundary conditions would be applied are discussed below.
The fixed boundary condition could be applied at the ends of a computational domain for the case of a beach nourishment project on an uninterrupted shoreline; however, if the ends of the computational domain are too close to the changes that would occur due to the nourishment, then these conditions can adversely affect the accuracy of the results. A useful and direct approach to evaluating whether the fixed boundary conditions are sufficiently distant from the point of interest is to simply double the extent of the computational domain




and to evaluate the effects on the shoreline changes in the region of interest over the period for which the computations are carried out.
The second type of boundary condition of interest is the specified transport boundary condition. Examples where a specified transport boundary condition would be appropriate are immediately downdrift of a partial or complete littoral barrier. If the barrier were a complete obstruction to the longshore sediment transport, then a specified discharge of zero would be appropriate; however, if there was some bypassing around the littoral barrier, then the volume per unit time of the bypassing would be the appropriate input transport boundary condition. Obviously in this case since the discharge values are centered at the grid lines, it would be appropriate to locate a grid line at the littoral barrier. The transport boundary condition could also be applied at the ends of the computational grid. If this were done, the shoreline displacement would be free to vary with time. If the transport boundary condition is specified as zero at the ends of the computational grid, there would be no change of volume within the computational domain., This could be the case in which complete littoral barriers existed at the two ends of the system of interest. In the model developed for this project, the boundary condition imposed at the two ends of the computational domain is the transport condition with the background transport as the imposed values.
A situation in which the boundary condition will change within the computational period might be a case where a groin of specified length was included somewhere within the computational domain. As the shoreline advances seaward toward the groin tip, the boundary condition would be a zero transport condition. However after the shoreline reached the end of the groin then the shoreline would remain fixed at that position which would in effect then be a fixed shoreline position boundary condition. In a case where the longshore sediment transport direction changed with time, the boundary condition at a structure could alternate between a fixed transport boundary condition and a specified shoreline position.




Wave and Other Parameters of Use in Applying the Methodology
Four parameters will be presented and recommended for applying the methodology developed in conjunction with this study.
The first parameter of interest is the limiting depth of motion, h.. Although this quantity is not known precisely, recommended values for h. have been presented in Figure 8. The berm height, B, is also required and appropriate values can be determined from profiles at the site of interest. Generally, berm heights range between 6 and 9 ft (above NGVD) in Florida.
A third parameter of interest is the effective wave height. The recommended distribution of wave heights around the Florida peninsula is shown in Figure 23. These wave heights were based primarily on the Coastal Data Network results where available. It is seen that, on the Florida east coast, the wave heights vary from the largest near the Florida/Georgia border and decrease toward the southern portions of the state. On the Florida west coast, the heights decrease toward the north with very low values along the Big Bend area, then increase toward the Florida/Alabama border. Finally, estimates of effective wave period are presented for the coast of Florida in Figure 24. Approximate. values of the longshore diffusivity parameter, G, have been presented in Figure 15 and may be used as a reasonable approximation.
STEP-BY-STEP DISCUSSION OF METHODOLOGY
In this section the limitations and the step-by-step application of the graphical and numerical procedures will be presented.
Graphical Procedure
The graphical procedure as presented here pertains to (1) a rectangular nourishment on an uninterrupted shoreline, and (2) a rectangular beach nourishment immediately downdrift of a complete littoral barrier such as a jetty. In both of these cases it is considered that the shoreline change is the linear sum of the result of the spreading out losses and the background erosion rate as determined by historical data.-




H eff2(feet) .q3
1 3 5 8 JAx
MA
SST
cc x x CL VB x
VE N WP
MI
1 3 5 8
H ef 2(f eet)
Figure 23. Recommended Values of Effective Deep Water Wave Height, Ho, Along Florida's Sandy Shoreline.




2 6 10 14
Wave Period, T(sec)

0
S14 10
0
.- 6
S2

Figure 24. Recommended Values of Effective Wave Period, T, Along
Florida's Sandy Shoreline.
40

Wave Period, T(sec)
2 6 10 14




CASE A NOURISHMENT ALONG AN UNINTERRUPTED
SHORELINE
The computation sheet presented as Figure 25 has been developed and should be referenced when reviewing the step-by-step procedure described below. Step 1 Specify Beach Nourishment Project Characteristics
These include
Project Length, t Sediment Size, D
Volume Added Per Unit Length, V
Step 2 Determine the Equilibrated Project Width, Ayo
To accomplish this h, from Figure 8
" Estimate B from local profile data berm height
" Determine AF and AN from Figure 7 from sediment sizes and local profile data,
respectively
" Calculate Ayo/W. from Figures 11 and 12, interpolating if necessary. Step 3 Calculate Effective Alongshore Diffusivity, G
The alongshore diffusivity, G, is obtained as expressed by Eq. (8) and is calculated from the wave, sediment and other local factors (G can also be estimated from Figure 15).
" Determine Ho from Figure 23
* Determine T from Figure 24 Determine C.~ from Figure 14




BEACH NOURISHMENT PROJECTION
(Graphical Computations, Uninterrupted Shoreline) General Location:

Wave Height, H0 Wave Period, T Wave Direction, ao:

(Fig. 23): ft, Closure Depth, h. (Fig. 8): ft
(Fig. 24): sec, Sediment Size, D: mm
0, Transport Factor, K (Fig. 5): Berm Height, B: __ ft

Alongshore Diffusivity, G (From Equation below or Figure 15).
2.4C1.2g0.4 op
K H C~g4 cos(3o ao) cos 2(3o a,)
8 (s 1)=(1 p)C 0 (h + B) cos(o )
8 (s 1)(1 -p)Cno.4(h, + B) cos(fo0- a,)

Background Erosion

= ft2 /s
Equilibrated Beach Width, Ayo

AN (Fig. 7) or From Profile: Ap (Fig. 7):
Volume Per Unit Length: Ayo (Figs. 11 and 12): Project Length, , = __ miles =

ftl/3 ftl/3 ft3/ft
ft
ft

For 30 years

(1) (2) (3) (4) (5) (6)
Distance y ) /Ayo Ys YB (ft) = YN =
From Center, x(ft) (Fig. 17) (ft) 30 x ER Ys Yb (ft)
Figure 25. Form for Computation of Performance Along Uninterrupted Shoreline.

x Erosion Rate (ER)
ft/yr




* Other Recommended Values:

=0. 78
8=2.65
p = 0.35
g = 32.2
Step 4 Calculate Shoreline Position Due to Spreading Out Losses
" Calculate non-dimensional time for t = 30 years or other time of interest
where all variables are in consistent units
" Calculate x/(e/2) at locations of interest (Column 2, Bottom Table in Figure 25)
" Determine y/Ayo from Figure 17 (Column 3, Bottom Table in Figure 25) Step 5 Calculate Background Erosion Losses
" Estimate background erosion rate from DNR data base
" Multiply rate by time (30 years) to obtain background erosion component (Column
5, Bottom Table in Figure 25)
Step 6 Calculate Resulting Shoreline Position
Add linearly the changes due to spreading out losses and background erosion to obtain the total changes. If the area of interest is not within the project area, apply the same methodology, however, here the spreading out losses (from the project area) will result in a shoreline advancement (see Figure 3). CASE B NOURISHMENT DOWNDRIFT OF A LITTORAL BARRIER
As discussed previously, there are two methods for calculating response downdrift of a littoral barrier. It is recommended that the method utilizing background erosion data be




applied rather than the method requiring the wave approach angle. The recommended method is described below.
The computation sheet presented as Figure 26 for this case has been developed and should be referenced along with the step-by-step procedure described. Step I Specify Beach Nourishment Characteristics
These include (same as for Case A)
Project Length, f (Effective Length, t' = 2f)
Sediment Size, D
Volume Added Per Unit Length, V
Step 2 Determine the Equilibrated Project Width, AyO
(Same procedure as for Case A)
" h. from Figure 8
" Estimate B from local profile data berm height
" Determine AF and AN from Figure 7 and local profile data, respectively
" Calculate Ayo/W. from Figures 11 and 12, interpolating if necessary. Step 3 Calculate Effective Alongshore Diffusivity, G
(Same as for Case A)
The alongshore diffusivity, G, is obtained as expressed by Eq. (8) and is calculated from the wave, sediment and other local factors (G can also be estimated from Figure 15).
" Determine HO from Figure 23
" Determine T from Figure 24 Determine C. from Figure 14




BEACH NOURISHMENT PROJECTION
(Graphical Computations, Downdrift of a Littoral Barrier) General Location:
Wave Height, H0 (Fig. 23): ft, Closure Depth, h. (Fig. 8): __ ft
Wave Period, T (Fig. 24): see, Sediment Size, D: mm
Wave Direction, ao: 0, Transport Factor, K (Fig. 5):
Berm Height, B: __ ft
Alongshore Diffusivity, G(From Equation Below or Figure 15)
K H CO2 G04 cos(0 ao) cos2(8o a,)
8 (G 1)(1 p)C (h + B) cos=(o )
8 (s 1)(1 -p)Cco.4(h, + B) cos(lo a.)

Background Erosion

x Erosion Rate (ER)
ft/yr
For 30 years

= ft2/s
Equilibrated Beach Width, Ayo
AN (Fig. 7) or From Profile: ftl/3
AF (Fig. 7): ft1/3
Volume Per Unit Length: ft3/ft
Ayo (Figs. 11 and 12): ft
Project Length, , = __ miles = ft
Effective Project
Length, t! = 2f = __ miles = ft

1Gt =16G(30x365x24x3600)
16 =t) 16 = =)
(1) (2) (3) (4) (5) (6)
Distance y -) /Ayo Us YB(ft) = YN =
From Littoral Barrier, x(ft) (Fig. 17) (ft) 30 x ER y, Yb (ft)
Figure 26. Form for Computation of Performance Downdrift of a Littoral Barrier.




e Other Recommended Values:

= 0.78
s = 2.65
p = 0.35
g = 32.2
Step 4 Calculate Shoreline Position Due to Spreading Out Losses
" Calculate non-dimensional time for t = 30 years or other time of interest 16 Gt 4 Gt
where all variables are in consistent units.
(Note: Different coefficient from Case A)
" Calculate x/(e'/2) at locations of interest where the origin of x is at the littoral barrier Calculate y/Ayo from Figure 17 (Note in this case, the horizontal axis in Figure 17
is to be interpreted as x/(e'/2) or equivalently, x/e.) Step 5 Calculate Background Erosion Losses
" Estimate background erosion rate from DNR data base
" Multiply rate by time to obtain background erosion component Step 6 Calculate Resulting Shoreline Position
Add linearly the changes due to spreading out losses and background erosion to obtain the total changes. If the area of interest is not within the project area, apply the same methodology, however, here the spreading out losses (from the project area) will result in a shoreline advancement (see Figure 3).




NUMERICAL PROCEDURE

As noted previously, the numerical procedure provides greater flexibility for representing shoreline and beach nourishment conditions. Prior to using the program, there is a certain amount of data preparation that is required. Some of this preparation is similar to that for the graphical procedure as described earlier. The numerical procedure also allows input of structures of arbitrary lengths at any location within the computational domain. At this stage, the program is straightforward, but not overly "user friendly".
As for the case of the "Graphical Procedure", the methodology will be illustrated below for the case of nourishment along an uninterrupted shoreline and for the case of structures present. The preparation sheet presented as Figure 27 has been developed to assist in data preparation and should be referenced along with the step-by-step procedure described below.
CASE A NOURISHMENT ALONG AN UNINTERRUPTED SHORELINE
STEP I Specify Beach Nourishment Project Characteristics
This is the same as described previously for the Graphical Procedure. The only difference is that now greater flexibility is available with the numerical procedure allowing varying volumes of nourishment along the shoreline including any number of nourishment segments. STEP 2 Determine Equilibration Project Width, AyO
Utilize same method as described for Graphical Procedure
STEP 3 Develop Background Erosion Data, as Plecewise, Linear Segments STEP 4 Develop Input File
A description of the input file (DNRBS.INP) is given below and Figure 28 presents an example input file.




BEACH NOURISHMENT PROJECTION
(Numerical Procedure)

General Location:
Wave Height, Ho (Fig. 23):
Wave Period, T (Fig. 24):
Wave Direction, co:
Deep Water Contour Orientation, flo:
Longshore Axis Orientation, M:
Grid Dimension, Ax: Time Increment, At:

_____ft.,
sec.,
0 0 0
______ft
_____sec

Closure Depth, h, (Fig. 8): Berm Height, B: Sand Diameter, D: Transport Factor, K (Fig. 5): VFACT:
Background Transport, QREF: IREF:
IMAX:
NTIMES: No. of Structures, NS:

mm ft3/s

Structure Specificiation
Structure Structure Structure
Number Location, I Length (ft)

Equilibrated Beach Width Ayo

Background Erosion

X

Erosion Rate, ER, (ft/yr)

Nourishment Specification

I Range

Ayo

AN (Fig. 7) or From Profile: AF (Fig. 7): Volume Per Unit Length: Ayo (Figs. 11 and 12):

ftl/3 ft1/3
_t3/ft
ft

to to to to to

Figure 27. Data Input Preparation Form for Numerical Procedure.
48




EXAMPLE OF INPUT FILE: DNRBS.INP (Example No. 2)
EXAMPLE NO. 2 UNIF. BACK. EROS. NO STRUC. 2 MILE PROJ. ~d cre o
r wasve peri +j 1A ~ p))r4 D.J e d-j~
eJA*4 C pj A-Vbt. &
2.00 6.0 90.0 90.0 180.0 500.0 86400.0
17.0 6.0 0.77 1.0 0.0 1 180 10950 0 r -5ec Ast
VFr- i-Jo o4err~ 17.0 6.0 0.77 1.0 0.0 1 180 10950 0

0.0 2.
90000. 3.
- Frrs H
80 100
80 112.0 81 112.0 82 112.0 83 112.0 84 112.0 85 112.0 86 112.0 87 112.0 88 112.0 89 112.0 90 112.0 91 112.0 92 112.0 93 112.0 94 112.0 95 112.0 96 112.0 97 112.0 98 112.0 99 112.0 100 112.0

0 90000. 2.0 49500.
0 100000. 3.0 140000.
orB a Cail le-o rtsfej tiour

D
/ a-inS

iVofe1 ;-h.
- e

2.0 2.0

60000.

t,4 (r I' Ce /I/ No:.) A V0 Q,

L/Oe. Prv~lc

-6_ L. e1 1.C Sc

Figure 28. Input File DNRBS.INP For Example 2

.1
3.0] P"trs OF(DstemS,
J nr a s)

vfqur, 44s

aw r- L -, vi s ;r- Anno't /-ov%




Card 1 (Format: 20A4): Identification Card with 80 Characters of Alphanumeric
Input
Card 2 Format: 8F8.2): Contains the Following Input Parameters
First Parameter: Deep Water Effective Wave Height in Feet, H0 (From
Figure 23)
Second Parameter: Wave Period in Seconds, T (From Figure 24)
Third Parameter: Deep Water Wave Direction, ao, in Degrees
Fourth Parameter: Deep Water Contour Orientation, Po, in Degrees
Fifth Parameter: Longshore Axis Orientation, p, in Degrees
Sixth Parameter: Grid Dimension, Ax, in Feet
Seventh Parameter: Time Increment, At, in Seconds
Card 3 Format: 5F8.2,416): Contains the Following Input Parameters
First Parameter: Depth of Limiting Motion, h,, in Feet (From Figure 8)
Second Parameter: Berm Height, B, in Feet
Third Parameter: Sediment Transport Parameter, K (From Figure 5)
Fourth Parameter: Factor to Increase or Decrease Proportionally All Input
Beach Widths, AyO
Fifth Parameter: Background Transport, QBKREF (cubic feet/sec) (See
Eq. (23))
Sixth Parameter: Grid Line Index, IREF, at Which QBKREF is to Apply
Seventh Parameter: Number of Grids, IMAX
Eighth Parameter: Number of Time Steps, NTIMES
Ninth Parameter: Number of Structures, NS
Card 4 Format: 5(I6,F8.3)): Note this Card (and Possibly a Subsequent Card if NS
> 5) is only Present if NS > 0 and Contains NS Pairs of Grid Lines and Structure Lengths. At Present the Program is Dimensioned to Accommodate Up To 10 Structures
Cards 5 and 6 Format (8F8.2): These Two Cards Contain Pairs of (x, EB(x)) where x is
in Feet and EB is the Location Background Erosion in Feet/Year. The Program is Presently Configured for Seven Pairs; However, it is Possible to Specify Background Erosion Conditions with as Little as Two Pairs. For Example, if the Background Erosion is Uniform at Two Feet/Year and the Computational Domain is 60,000 ft in Length, the Two Active Pairs Could
be: 0.0 2.0 80000.0 2.0
The Remaining Five Pairs Entered Would be Immaterial. Note it is necessary to provide two cards here, even if all the meaningful information is
contained in the first card.
Card 7 This Card Specified the First, NNOUS, and Last, NNOUE, Grid Indices for
the Nourished Segment
Cards 8 and Following (Format: 16, 3F8.2): Each of These Cards Specifies the Grid Index, I, and the Associated Shoreline Advancement, Ayo (I)
This completes specification of the input File DNRBS.INP




STEP 5 Run Program
STEP 6 Examine Output in File DNRBS.OUT
A description of the output file DNRBS.OUT is presented below and Figure 29 presents an example of this output with annotations. This output is for the input file presented in Figure 28.
Card 1: This card is an image of the first input card which is an identification card
Cards 2,3,4,5,6: These cards simply repeat input values
Cards 7 and 8: These two cards are pairs of (x, EB(x)) specified in Input Cards 5 and 6
Next Block of Data: Presents pairs of (I, QBI) in which QBI is the background erosion transport across the Ith grid line. The units of QBI are in ft3/sec Next Card: This card repeats the first nourished grid index, NNOUS, and the last
nourishment grid index, NNOUE, as provided by Input Card 7
Next Block of Data: Presents three entries per grid: (I,X(I), DYO(I)), in which I is the grid block index, x(I) is the x coordinate of the grid block and DYO(I) is the initial nourished width at the grid block. In the example presented, because there are 450 sets of entries, one for each grid block.
Next Block of Data: Provides pairs of I, Y(I) for one year after nourishment for all grid blocks
Next Card: Presents the proportion of the additional dry beach area relative to the
initial area that remains within the project area after one year. This
proportion is denoted PCT(LCUR)
Remaining Output: The remaining output consists of detailed shoreline output for 5, 10, 20 and 30 years and the proportional surface area remaining for each of the thirty years.
This completes the description of the information in the output file DNRBS.OUT




'/3-

Figure 29. Example of Output File DNRBS.OUT for Input File in
Figure 28. Example No. 2. (Total of 5 Pages of
Output).
EXAMPLE OF OUTPUT FILE: DNRBS.OUT (Example No. 2)
EXAMPLE NO. 2 UNIF. BACK. EROS. NO STRUC. 2 MILE PROJ.

HO = 2.00 FT., T = 6.00 SEC., ALPO = 90.00 DEG., BTAO = XMU = 180.00 DEG., DX = 500.00 FT., DT = 86400.00 SEC. HSTR = 17.00 FT., B = 6.00 FT., XK = .77 VFACT =
QBKREF = .00 FT.**3/SEC.
IREF = 1, IMAX = 180, NTIMES = 10950, NS =

90.00 DEG.,
1.00

2.00 .90E+05 3.00 .10E+06

2.00 .50E+05 3.00 .14E+06

2.00 .60E+05
2.00

BACKGROUND EROSION TRANSPORT RATES

.001 4
.005 9
.009 14 .012 19 .016 24 .020 29 .023 34 .027 39 .031 44 .034 49 .038 54 .042 59 .045 64 .049 69 .053 74 .056 79 .060 84 .063 89 .067 94 .071 99 .074 104 .078 109 .082 114 .085 119 .089 124 nfo- 129
52 134
139
.104 144 .107 149

. OOE+00
.90E+05

3.00

1 6
11
16 21 26 31 36 41 46 51
56 61 66 71 76 81 86 91 96 101
106 ill
116 121 126 131 136
141 146

.000
.004 .007 .011 .015
.018 .022 .026 .029 .033 .036 .040 .044 .047 .051 .055 .058 .062 .066 .069 073 .077 .080
.084 .088 .091 .095 .098 .102 .106

2 7
12 17 22 27 32 37 42 47 52 57 62 67 72 77 82 87 92 97 102 107 112 117 122 127
132 137 142 147

.001
.004 .008 .012
.015 .019
.023 .026 030
034 037 041 044
.048 052 055 .059 .063 .066 .070 .074 .077 .081
.085 088 .092 .096 .099 .103
.106

3 8
13 18
23 28 33 38 43 48 53 58 63 68 73 78 83 88 93 98 103 108 113 118 123 128 133 138 143
148

.002 .006 .009 .013 .017 .020 .024 .028 .031 .035 .039 .042 .046 .050 .053 .057 .061 .064 .068 .071 .075 .079 .082 .086 .090 .093 .097
.101
.104 .108

5
10
15 20 25 30
35 40 45 50
55 60
65 70 75 80
85 90
95 100
105 110
115 120 125 130 135 140 145 150

.003 .007 .010 .014 .018 .021 .025
.028 032 036 039 .043 .047 .050 .054 .058 .061 .065 .069 .072 .076 .079 .083 .087 .090 .094 .098 .101
.105 .109




156 161 166
171 176 181

.113 .117 .120
.124 .128
.131

157 162 167
172 177

80 100
INITIAL SHORELINE

1
3
5
7
9
11
13 15 17 19
21 23 25
27 29 31 33 35 37 39 41 43 45 47
49 51
53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97
99 101
103 105

0.
1000. 2000. 3000. 4000. 5000. 6000. 7000. 8000. 9000. 10000. 11000. 12000. 13000. 14000. 15000. 16000. 17000. 18000. 19000. 20000. 21000. 22000. 23000. 24000. 25000. 26000. 27000. 28000. 29000. 30000. 31000. 32000. 33000. 34000. 35000. 36000. 37000. 38000. 39000. 40000. 41000. 42000. 43000. 44000. 45000. 46000. 47000. 48000. 49000. 50000. 51000. 52000.

.114 .117 .121 .125 .128

158 163 168 173
178

. 115
.122 .125 .129

159
164 169 174 179

(INCL. NOURISHMENT) POSITION

.00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00
.00 .00 .00 .00
.00 .00
.00 .00 .00 .00 .00
.00 .00 00
00 .00 .00
00 .00
00 00 00 .00 .00 00
.00 112.00 112.00 112.00 112.00 112.00 112.00 112.00 112.00 112.00 112.00
.00 .,00 .00

2
4
6
8
10
12 14 16 18
20 22 24 26 28 30 32
34 36 38
40 42 44 46 48 50
52 54
56
58 60
62 64 66 68 70
72 74 76 78 8o
82 84 86 88 90
92 94 96 98 100
102 104 106

500. 1500. 2500. 3500. 4500. 5500. 6500. 7500. 8500. 9500. 10500. 11500. 12500. 13500. 14500. 15500. 16500. 17500. 18500. 19500. 20500. 21500. 22500. 23500. 24500. 25500. 26500. 27500. 28500. 29500. 30500.
31500. 32500. 33500. 34500.
35500. 36500. 37500. 38500. 39500. 40500. 41500. 42500. 43500. 44500. 45500. 46500.
A -7r- t
53
50500. 51500. 52500.

.00
.00 .00 .00 .00 .00
.00 .00 .00 .00 .00 .00
.00 .00 .00
.00 .00 .00
.00 .00 .00 .00 .00
.00 .00 .00 .00 .00
.00 .00 .00 .00 .00 .00
.00 .00 .00 .00 .00
112.00 112.00 112.00 112.00 112.00 112.00 112.00 112.00
112.00 112.00 112.00
.00
.00 .00

115 .119 .123 .126
130

160 165
170 175 180

.116 .120
.123 .127
.131




113 115 117 119
121 123 125 127 129 131 133 135 137 139
141 143 145 147 149 151 153 155 157 159 161 163 165 167 169 171 173 175 177 179 100
1
7
13 19 25 31 37
43
49 55 61 67 73 79,
85 91 97
103 109
115
1211 127 133 139
145 151 157 163

55000. 56000. 57000. 58000. 59000. 60000. 61000. 62000. 63000.
64000. 65000. 66000. 67000. 68000. 69000. 70000. 71000. 72000. 73000.
74000. 75000. 76000. 77000. 78000. 79000. 80000. 81000. 82000. 83000.
84000. 85000. 86000. 87000. 88000. 89000. 116

.00
.00 .00 .00 .00
.00 .00
.00 .00 .00 .00 .00
.00 .00 .00
.00 .00
.00 .00
.00 .00
.00 .00
.00 .00
.00 .00 .00
.00 .00 .00 .00 .00
.00 .00 000
TIME -2.00
-2.00
-2.00
-2.00
-2.00
-2.00
-2 .00
-2.00
-2 .00 -2.00
-1.93
-.18
15.06 58.16 96.98 102.52
74 .10 26.75
2.31
-1.77
-2 .00 -2.00
-2 .00
-2.00
-2 .00 -2.00
-2 .00 -2.00

112 114 116 118
120 122 124 126 128 130 132
134 136 138
140 142 144 146 148 150 152
154 156 158 160 162
164 166 168 170 172
174 176 178 180
.084
3
9
15
21 27
33 39
45 51
57 63 69
75 81 87
93 99 105 III 117 123 129 135
141 147 153 159 165

55500.
56500.
57500.
58500.
59500.
60500.
61500.
62500.
63500.
64500.
65500.
66500.
67500.
* 68500.
69500.
* 70500.
71500.
72500.
73500.
74500.
75500.
76500.
77500.
78500.
79500.
80500.
81500.
82500.
83500.
84500.
85500.
86500.
87500.
88500.
89500.
.000 -.542
1 YEARS
-2.00 4
-2.00 10
-2.00 16
-2.00 22
-2.00 28
-2.00 34
-2.00 40
-2.00 46
-2.00 52
-2.00 58
-1.87 64 .84 70
20.45 76 2 66.34 82 7 100.24 88 10 100.24 94 9 66.34 100 5 20.45 106 1 .84 112
-1.87 118
-2.00 124
-2.00 130
-2.00 136
-2. 5
-2.
-2.uv iD4
-2.00 160
-2.00 166 -

.00 .00
.00 .00 .00 .00 .00 .00 .00 .00 .00
.00 .00
.00 .00 .00
.00 .00 .00 .00
.00 .00
.00 .00
.00 .00 .00 .00 .00 .00 .00
.00 .00
.00 .00
- 542

084

.000

-2.00
-2.00
-2.00
-2.00
-2.00
-2.00
-2.00
-2 .00
-2 .00
-2.00
-1.96
- .87
10.62
49 .83 92.71 103 .87 81 .19 33.87
4 .34
-1 .60
-1.99
-2 .00
-2.00
-2 .00
-2 .00
-2 .00
-2.00
-2.00

2
8
14 20 26
32 38
44 50 56 62 68
74 80 86 92
98
104 110 116
122 128
134 140 146 152 158
164

2 .00 2 .00
2.00 2 .00
2.00 2 .00 2 .00
2.00 2 .00
2.00 1.77 2.31 6.75
4.10 2.52 6.98 8.16 5 .06
-.18
1.93
2 .00 2 .00 2 .00
2.00 2.00 2 .00 2.00 2.00

5
11 17 23 29
35
41
47 53 59 65 71
77 83 89
95 101 107 113
119 125 131 137
143 149 155 161 167

-2 .00
-2.00
-2.00
-2 .00
-2.00
-2.00
-2 .00
-2.00
-2.00
-1.99
-1.60
4 .34 33 .87 81.19 103 .87 92.71 49 .83 10.62
- .87
-1.96
-2.00
-2.00
-2.00
-2.00
-2 .00
-2.00
-2 .00
-2.00

6
12
18
24 30 36
42
48 54 60 66 72
78
84 90 96
102 108
114 120 126 132 138
144 150 156 162 168

-2 .00
-2.00
-2.00
-2.00
-2.00
-2.00
-2 .00
-2.00
-2.00
-1.98
-1.31
7 .07
41.64 87 .43
104.31 87 .43 41.64 7 .07
-1.31
-1.98
-2 .00
-2.00
-2.00
-2.00
-2.00
-2.00
-2 .00
-2.00




1 7
13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103 109 115 121 127 133 139 145 151 157 163

175

-2.00 176 LCUR = LCUR = LCUR = LCUR =
-10.00 2
-10.00 8
-10.00 14
-10.00 20
-10.00 26
-10.00 32
-9.98 38 -9.86 44
-9.37 50 -7.68 56 -3.12 62
6.41 68
21.71 74 40.01 80
54.71 86 59.00 92 50.69 98
33.93 104 16.05 110
2.57 116
-5.09 122 -8.46 128 -9.61 134
-9.92 140 -9.99 146
-10.00 152
-10.00 158
-10.00 164

169 -10.00
175 -10.00
LCUR = LCUR = LCUR = LCUR = LCUR =

-20.00 2
-20.00 8
-19.99 14
-19.98 20
-19.92 26
-19.76 32
-19.31 38
-18.25 44
-16.05 50
-12.04 56
-5.64 62 3-.15 68 13.40 74 23.14 80 29.93 86
31.79 92 28.14 98 20.10 104 9.92 110 -.01 116
-8.06 122
-13.62 128
-16.96 134

-2.00 177
* PCT(LCUR)
PCT ( LCUR) I PCT(LCUR)
PCT(LCUR)
TIME =
-10.00 3
-10.00 9
-10.00 15
-10.00 21
-10.00 27
-10.00 33
-9.97 39
-9.82 45
-9.21 51
-7.17 57
-1.93 63 8.58 69 24.70 75 42.92 81
56.29 87 58.45 93 48.29 99
30.84 105 13.41 111 .91 117
-5.89 123
-8.76 129
-9.70 135
-9.94 141
-9.99 147
-10.00 153
-10.00 159
-10.00 165
-10.00 171
-10.00 177
PCT(LCUR) PCT(LCUR) PCT (LCUR) PCT(LCUR) PCT(LCUR)
TIME =
-20.00 3
-20.00 9
-19.99 15
-19.97 21
-19.91 27
-19.71 33
-19.19 39
-17 .98 45
-15.53 51
-11.15 57
-4.33 63 4.80 69 15.12 75 24.55 81
30.62 87 31.55 93 27.06 99 18.48 105 8.19 ill
-1.51 117
-9.16 123
-14.31 129
-17.34 135

-2.00 178
.78 .68 .60 .53

5
-10.00
-10.00
-10.00
-10.00
-10.00
-9.99
-9.96
-9.77
-9.00
-6.58
-.59
10.91 27.75 45.69 57.54 57.54 45.69 27.75 10.91
-.59
-6.58
-9.00
-9.77
-9.96
-9.99
-10.00
-10.00
-10.00
-10.00
-10.00
10

-20.00 4 -20.00
-20.00 10 -20.00
-19.99 16 -19.99
-19.97 22 -19.96
-19.89 28 -19.86
-19.65 34 -19.59
-19.05 40 -18.89
-17.68 46 -17.34
-14.95 52 -14.32
-10.19 58 -9.16
-2.96 64 -1.51 6.48 70 8.19 16.82 76 18.48 25.85 82 27.06 31.16 88 31.55 31.16 94 30.62 25.85 100 24.55 16.82 1I 15.12 6 4.80
-2 -4.33
-I0.i : i -11.15
-14.95 130 -15.53
-17.68 136 -17.98

YEARS

-2.00 179

4
10
16 22 28 34 40 46 52 58 64 70 76 82 88
94 100
106 112 118
124 130 136 142 148 154 160 166 172 178 .47 .42 .38 .33 .30

-10.00
-10.00
-10.00
-10.00
-10.00
-9.99
-9.94
-9.70
-8.76
-5.89
.91
13.41 30.84 48.29 58.45 56.29 42.92 24.70 8.58
-1.93
-7.17
-9.21
-9.82
-9.97
-10.00
-10.00
-10.00
-10.00
-10.00
-10.00

5
11
17 23 29
35 41
47 53
59 65
71 77 83 89
95 101 107
113 119 125 131 137 143 149 155
161
167 173 179
5
11
17 23 29
35 41 47 53 59 65 71 77 83 89 95 101 107
113 119 125 131 137

-10.00
-10.00
-10.00
-10.00
-10.00
-9.99
-9.92
-9.61
-8.46
-5 .09 2 .57
16.05 33.93 50.69 59 .00
54 .71
40.01 21.71
6.41
-3.12
-7.68
-9.37
-9 .86

170 176

6
12 18 24 30 36 42 48 54 60 66 72 78 84 90
96 102 108 114 120 126 132 138

-10.00
-10.00
-10.00
-10.00
-10.00
-9.98
-9.90
-9.50
-8.10
-4.17
4.40 18.82 37.00 52.84 59.18 52.84 37.00 18.82 4.40
-4.17
-8.10
-9.50
-9.90
-9.98
-10.00
-10.00
-10.00
-10.00
-10.00
-10.00
-20.00
-20.00
-19.98
-19.94
-19.80
-19.42
-18.49
-16.53
-12.86
-6.88
1.54 11.66 21.66 29.10 31.87 29.10 21.66 11.66 1.54
-6.88
-12.86
-16.53
-18.49

YEARS

1
7
13 19 25
31 37 43 49 55 61 67
73
79 85 91 97 103 109 115 121 127 133

-20.00
-20.00
-19.99
-19 .95
-19 .83
-19 .51
-18.70
-16.96
-13.62
-8.06
-.01
9.92 20.10 28.14 31.79 29 .93 23 .14 13 .40 3.15
-5.64
-12.04
-16.05
-18.25

6
12 18 24 30 36 42 48 54 60
66 72
78 84 90
96 102 108 114 120 126
132 138

-9.98 144
-10.00 150
-10.00 156
-10.00 162
-10.00 168
-10.00 174
-10.00 180

-2.00 180 -2.00 415




145 151 157
163 169 175
1
7
13 19
25 31 37 43
49 55 61 67
73 79 85 91 97
103 109
115 121 127
133 139
145 151
157 163
169 175

-19.51
-19.83
-19.95
-19.99
-20.00
-20.00
LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR =
-59.99
-59.52
-58.93
-58.13
-57.01
-55.45
-53.40
-50.80
-47.68
-44.15
-40.40
-36.71
-33.41
-30.83
-29.24
-28.83
-29.64
-31.59
-34.45
-37.92
-41.66
-45.36
-48.77
-51.72
-54.14
-56.02
-57.42
-58.41
-59.12
-59.63 LCUR =

TIME
-59.92
-59.43
-58.82
-57.97
-56.78
-55.15
-53.00
-50.31
-47.11
-43.53
-39.77
-36.13
-32.92
-30.49
-29.08
-28.88
-29.89
-32.01
-34.99
-38.53
-42.28
-45.95
-49.30
-52.16
-54.49
-56.28
-57.61
-58.55
-59.21
-59.71

3
9
15 21 27 33 39
45 51 57 63 69
75 81 87 93 99 105 111i 117 123 129 135 141 147 153 159 165 171 177

30 PCT(LCUR)

146 -19.59 147 152 -19.86 153 158 -19.96 159 164 -19.99 165 170 -20.00 171 176 -20.00 177
10 PCT(LCUR) 11 PCT(LCUR) 12 PCT(LCUR) 13 PCT(LCUR) 14 PCT(LCUR) 15 PCT(LCUR) 16 PCT(LCUR) 17 PCT(LCUR) 18 PCT(LCUR) 19 PCT(LCUR) 20 PCT(LCUR) 21 PCT(LCUR) 22 PCT(LCUR) 23 PCT(LCUR) 24 PCT(LCUR) 25 PCT(LCUR) 26 PCT(LCUR) 27 PCT(LCUR) 28 PCT(LCUR) 29 PCT(LCUR)

2
8
14 20 26 32 38
44 50
56 62
68 74 80
86 92 98 104 110
116 122 128 134 140 146 152
158 164 170 176

-19.65
-19.89
-19.97
-19.99
-20. OC
-20.0 C
30
-59.84
-59.34
-58.6S
-57.8C
-56.54
-54.83
-52.5S
-49.81
-46.54
-42.91
-39.1E
-35.55
-32 .4E
-30.17
-28.9)
-28.97
-30.17
-32.45
-35.5E
-39. 15
-42. 9
-46.54
-49.81
-52. 5
-54 .82
-56 .54
-57.7S
-58.6E
-59.31
-59.7E

148 154 160 166 172
178 .26 .23 .19
.16 .13 .10 .08 .05
.02 .00
-.03
-.05
-.08
-.10
-.13
-.15
-.17
-.20
-.22
-.24
YEARS
4
10
16
22 28
34 40 46 52
58 S64
70 76
82 88 94 100
106 S112
118 124 130 136 142 148 154 160 166 172 178

-19.71
-19.91
-19.97
-19.99
-20.00
-20.00

-59.76
-59.24
-58.56
-57.62
-56.29
-54.49
-52.17
-49.30
-45.95
-42.28
-38.53
-34.99
-32.01
-29.89
-28.88
-29.08
-30.49
-32.92
-36.13
-39.77
-43.53
-47.11
-50.31
-53.00
-55.15
-56.77
-57.96
-58.80
-59.39
-59.85

149 155 161 167 173
179

5
11
17 23 29 35
41 47 53 59
65
71 77
83 89 95 101
107 113
119 125 131 137 143 149 155 161 167 173 179

-19.76
-19.92
-19.98
-19.99
-20.00
-20.00
-59.68
-59.14
-58.43
-57.42
-56.02
-54.14
-51.72
-48.77
-45.36
-41.66
-37.92
-34.45
-31.59
-29.64
-28.83
-29.24
-30.83
-33.41
-36.71
-40.40
-44.15
-47.68
-50.80
-53.40
-55.45
-57.00
-58.12
-58.91
-59.48
-59.92

150 156 162 168 174
180
6
12 18
24 30 36 42 48 54 60 66 72 78
84 90 96 102
108 114 120 126
132 138 144 150 156 162
168 174 180

-19.80
-19.94
-19.98
-20.00
-20.00
-20.00
-59.60
-59.04
-58.28
-57.22
-55.75
-53.78
-51.27
-48.23
-44.76
-41.03
-37.31
-33.92
-31.19
-29.42
-28.81
-29.42
-31.19
-33.92
-37.31
-41.03
-44.76
-48.23
-51.27
-53.78
-55.74
-57.21
-58.27
-59.02
-59.56
-59.99

= -.26




CASE B NOURISHMENT WITH STRUCTURES PRESENT
In this case, all of the description presented for Case A is relevant with the exceptions noted below. Because Steps 1, 2, 3, and 4 are identical, they will not be repeated here. STEP 4B Specify a Reference Background Transport
As has been described earlier, in situations where structures are present, it is necessary to establish the net background longshore transport rate as this will interact with the structure. The net longshore background transport on the east coast of Florida could be estimated from Figure 30. Since background transport rates on the west coast are so variable spatially, no attempt will be made here to provide a recommendation. Rather, it is suggested that each rate should be developed on a case-by-case basis.
The background transport rate is specified to the program on Card 3 as QBKREF and the grid index value associated with the background transport rate QBKREF is specified as IREF on Card 3. Note that QREF must be specified in units of ft3/second and that the conversion factor from cubic yards per year to cubic feet per second is
Q(cubic feet per second) = 8.56 x 10-7 Q(cubic yards per year)
STEP 5B Specify Structure Location(s) and Length(s) in Program
In the current version of the program, up to 10 structures can be specified including the grid line and length. The structures interact with the background sediment transport and the transport induced by the beach nourishment project.
Specification of the structure number, location and length is by Card 4 (this card present only if structures are specified).




6 I 'HOLUES "___S/SANTA I u ;-K. ..0
"A ROSAI A t I .,"AL F RNANDINA
LBER WAKULLAWATO, BAKER
'WALTONDIXE ALAHU S 600,000 yd/yr
GG Op EV S. .HAMILTON- JACKSONVILLE
' EW' S MYN A ADISON
'I~ ~ ~ CITU WAUL I LAK BA..'
TAYLOR If., am, --S I ,GULFFRANKLIN *RA ST. AUGUSTINE
FORD T.
> G'6I- ON
D CHRIST J OMARINELAND AI S ALACHUA PUTN A' P(E
Gu~~i o I v" . ...
PO 10CEL 35,0 yd /yr
LE, I- DAYTONA 3
MAE H I VOLUSI 500,000 yd /yr
-.,, ---- CBE, EFiTPEREW SMYRNA
L CITUS)MR LAy
- -K SUMTE'R J UPI/TOER
HERNAN'b ,
ASO I I ORANGEJSQ
PASCO -'- -- APE CANAVERAL
G\\OSSCEOLA 230,000.y ly C OPOLK ROWA 2 350,000 yd3/yr
4ap IR
| N I \% "0I IO/
NN A D
L 4-__._ _.__ 1' RIU VER BEACH
BAKER HALOE Al MANATEE HARDEE OKEE 11230,000 yd Iyr
- L UCIHBEE ST. PIERC F49,5,-I' AREOTTLO' E H 3,00y'y
oI 8
. BAERS HULOVE
' LDo '230,000 y
***E
soOI I OI PALM / BEMIAM
Figure 30. Estimates of Net Annual Longshore Sediment Transport
Along Florida's East Coast.




EXAMPLES ILLUSTRATING APPLICATION OF METHODOLOGIES
In this section, a number of examples are presented illustrating application of the methodologies. The purpose of these examples is to familiarize the reader thoroughly with the methodologies and the anticipated results. As in preceding sections of this report, the examples will be organized by "Graphical Methodology" and "Numerical Methodology". Graphical Example
The following four examples illustrate application of the methodology to the following situations.
Graphical Example 1: Uninterrupted Shoreline, No Background Erosion Graphical Example 2: Uninterrupted Shoreline, Uniform Background Erosion Graphical Example 3: Uninterrupted Shoreline; Non-Uniform Background Erosion Graphical Example 4: Downdrift of a Littoral Barrieri Non-Uniform Background Erosion
The computations and results are presented on the following four worksheets. Numerical Examples
A number of examples were run with the numerical methodology and are described briefly on the following page. Because the documentation for each example is fairly extensive, each example is presented in an individual appendix.




Numerical Example 1: Numerical Example 2: Numerical Example 3: Numerical Example 4: Numerical Example 5: Numerical Example 6: Numerical Example 7:

Uninterrupted Shoreline, No Background Erosion, Nourishment Length = 2 Miles, Initial Added Width =112 ft, Wave Height = 2.0 ft, Waves Normally Incident, Results Presented in Appendix C.
Uninterrupted Shoreline, Uniform Background Erosion of 2 ft/yr, Nourishment Length = 2 Miles, Initial Added Width = 112 ft, Wave Height = 2.0 ft, Waves Normally Incident, Results Presented in Appendix D.
Uninterrupted Shoreline, Variable Background Erosion, Nourishment Length of 2 Miles, Initial Added Width = 112 ft, Wave Height = 2.0 ft, Waves Normally Incident, Results Presented in Appendix E.
Uninterrupted Shoreline, No Background Erosion, Nourishment Length = 3,500 ft, Wave Height = 2.0 ft, Waves Normally Incident, Results Presented in Appendix F.
One Structure 112 ft Long Located at North End of Nourishment Project, Nourishment Length = 2 Miles, Initial Added Width = 112 ft, Wave Height = 2.0 ft, Waves Normally Incident, No Background Erosion, Results Presented in Appendix G.
One Structure 112 ft Long Located at South End of Nourishment Project, Uniform Background Erosion of
2 ft/yr, Waves Normally Incident, Nourishment Length = 2 Miles, Initial Added Width = 112 ft, Wave Height = 2.0 ft, Results Presented in Appendix H.
One Structure 112 ft Long Located at South End of Nourishment Project, Waves Approaching at 100 Angle to Shoreline, Variable Background Erosion, Nourishment Length = 2 Miles, Initial Added Width = 112 ft, Wave Height = 2.0 ft, Results Presented in Appendix I.

For each numerical example, the input file, DNRBS.INP, and output file, DNRBS.OUT, are presented and the results are discussed and plotted.




,c5RAPHICA-L- E~)(*4 ?L4 'I
BEACH NOURISHMENT PROJECTION
(Graphical Computations, Uninterrupted Shoreline) General Location:
Wave Height, H0 (Fig. 23): a 0 ft, Closure Depth, h, (Fig. 8): /7 ft
Wave Period, T (Fig. 24): (P see, Sediment Size, D: mm
Wave Direction, ao: 0 Transport Factor, K (Fig. 5): 0,77
Berm Height, B: eo ft Alongshore Diffusivity, G (From Equation below or Figure 15).
K H"C g gO.4 cos(go ao) cos 2(o80 a.) G =8 (s 1)(1 p)C.r'.04(h. + B) cos(fo a.) 0,77 E roioEu)" rated. ) Bd ft2
Background Erosion Equilibrated Beach Width, Ayo

x Erosion Rate (ER)
- _. o ft/yr
For 30 years

Av (Fig. 7) or From Profile: Ap (Fig. 7):
Volume Per Unit Length: Ayo (Figs. 11 and 12): Project Length, e, = 2, 0 miles -=

O, ftl/3
0. Z 0 ftl/3 Fl/ ft3/ft //2 ft /0,l ft

(1) (2) (3) (4) (5) (6)
Distance Y ( z) Ayo Y, YB (ft) = YN =
From Center, x(ft) (Fig. 17) (ft) 30 x ER y. ye (ft)
_.0 __, OJZ, 311 0 31.1
___2s T o 2.1Z.1 0__




6p~p R ICA L -,rPLE a
BEACH NOURISHMENT PROJECTION
(Graphical Computations, Uninterrupted Shoreline) General Location:
Wave Height, Ho (Fig. 23): 2 0 ft, Closure Depth, h. (Fig. 8): 1 ft
Wave Period, T (Fig. 24): (~,o see, Sediment Size, D: mm
Wave Direction, ao: 0, a, Transport Factor, K (Fig. 5): O0'T7
Berm Height, B: & ft

Alongshore Diffusivity, G (From Equation below or Figure 15).
__ K Ho ""'go cos(Po ao) cos 2(flo a.)

Background Erosion

8 (a 1)(1 p)C.ic0.4(h. + B) cos(Jo a.) X= a/it -7 ft2/s
Equilibrated Beach Width, Ayo

x Erosion Rate (ER)
-i ,s ,40 ft/yr
For 30 years, For 30 years

AN (Fig. 7) or From Profile: AF (Fig. 7):
Volume Per Unit Length: Ayo (Figs. 11 and 12): Project Length, , = ., miles =

O. Z ft'/3 Of2C ft1/3 .S// 3 ft3/ft
// 2-ft /0, c' ft

1Gt = 16G(30x365x24x3600)
16-=16 = /2- =
2 J2
(1) (2) (3) (4) (5) (6)
Distance ) /Ayo Y UB(ft) YN= =
From Center, x(ft) (Fig. 17) (ft) 30 x ER y, yp (ft)
o ____ 0.7-8 31,4 &t >__5ZBO _o o. 2_ CO Z, I ,o
l___ __o_ ____ a (.b -_ s_




diRAPNICAL. EXAiPLE ,
BEACH NOURISHMENT PROJECTION
(Graphical Computations, Uninterrupted Shoreline) General Location:
Wave Height, Ho (Fig. 23): 0. ft, Closure Depth, h. (Fig. 8): o ,ft
Wave Period, T (Fig. 24): 6 sec, Sediment Size, D: mm
Wave Direction, ao: 0 0, Transport Factor, K (Fig. 5): 0,11
Berm Height, B: to ,o ft Alongshore Diffusivity, G (From Equation below or Figure 15).
2.4= K 2 go.4 (o
HO a~9csf oa)cos 2(8o0- a.)

8 (s 1)(1 p)C.r0.4(h. + B) cos(o a.) 5a.Y a-.t- i-4-1Q I 0-

,11q7 ft2/s

Background Erosion

Equilibrated Beach Width, Ayo

xz Erosion Rate (ER)
-__ o o ft/yr
For 30 years

AN (Fig. 7) or From Profile: AF (Fig. 7):
Volume Per Unit Length: Ayo (Figs. 11 and 12): Project Length, 1, = R, ) miles =

e 2* S ftl/3 O, 2 0 ftl/3
-.5// 3 ft3/ft 112. ft
/0 560 ft

(1) (2) (3) (4) (5) (6)
Distance Y 1AYO Y/, JB(ft) YN
From Center, x(ft) (Fig. 17) (ft) 30 x ER y, y. (ft)
-._t 524o 0CZ ,L 30.0 -_ __4
- o I o. z9, I 3 9. 4
0 0 o.2& 31,c1 45."o -13,o
+- 2 ,0~- b Wr, 465",- -)3._,__ i-i0 4247. (0 -35-_,




BEACH NOURISHMENT PROJECTION
(Graphical Computations, Downdrift of a Littoral Barrier) General Location:
Wave Height, Ho (Fig. 23): O ft, Closure Depth, h. (Fig. 8): 170 ft
Wave Period, T (Fig. 24): (, .' sec, Sediment Size, D: mm
Wave Direction, ao: V 0, Transport Factor, K (Fig. 5): 0-71
Berm Height, B: _,. ft
Alongshore Diffusivity, G(From Equation Below or Figure 15)
2.4CGI:0.4 2(#o p.
K HOCog4 cos(#o o) cos 2(#o a.)
8 (G 1)(1 p)C=04(h + B) cos(o .)
8 (C 1)(1i- p)cxo.4(h, + B) cos(#o a.)

Background Erosion

= 0.14"7 ft2/s
Equilibrated Beach Width, Ayo

x_ Erosion Rate (ER) 0 ,oD, ft/yr
f o -)_ __ Fors 3y.eO
"_I -1ZO
For 30 years

AN (Fig. 7) or From Profile: AF (Fig. 7):
Volume Per Unit Length: Ayo (Figs. 11 and 12): Project Length, f, = __ miles Effective Project Length, = 2 = __ miles =

0o2.aS ftl/3 0, 20 ftl/3 -11 ft3/ft
1/2 ft = /t, C ft
2.1, /20 ft

16Gt 16G(30x365x24x3600)
(e)2 (2)2
(1) (2) (3) (4) (5) (6)
Distance y eI /Ayo Us UB(ft) = UN =
From Littoral Barrier, z(ft) (Fig. 17) (ft) 30 x ER y, ya (ft)
Q 0 o,Sz. 5.-i. <,oo -6z
5z80 0.5 0.50 Soo 4 -4z.
1o66o 1.0 o.q. 47,0 240 -i2.
21)2o 2_0 0. ___ -15"




REFERENCES
Balsillie, J. (1987) "Offshore Profile Description Using the Power Curve Fit, Part II: Standard Florida Offshore Profile Tables", Beaches and Shores, Technical and Design Memorandum No. 82-1-IIa, Florida Department of Natural Resources, Tallahassee,
FL.
Bruun, P. (1954) "Coast Erosion and the Development of Beach Profiles", Beach Erosion Board, Technical Memorandum No. 44.
Dean, R. G. (1977) "Equilibrium Beach Profiles: U.S. Atlantic and Gulf Coasts", Department of Civil Engineering, Ocean Engineering Report no. 12, University of Delaware,
Newark, DE.
Dean, R. G. (1978) "Review of Sediment Transport Relationships and the Data Base", Proceedings of a Workshop on Coastal Sediment Transport with Emphasis on the National Sediment Transport Study", Report DEL-SG-15-78, University of Delaware,
Newark, DE.
Dean, R.G. (1987) "Additional Sediment Input to the Nearshore Region", Shore and Beach, Vol. 55, Nos. 3-4, p. 76-81.
Moore, B.D. (1982) "Beach Profile Evolution in Response to Changes in Water Level
and Wave Height", Masters Thesis, Department of Civil Engineering, University of
Delaware, Newark, DE.
Pelnard Considere, R. (1956) "Essai de Theorie de l'Evolution des Formes de Rivate en
Plages de Sable et de Galets", 4th Journees de l'Hydraulique, Les Engergies de la
Mar, Question III, Rapport No. 1.




APPENDIX A
DEEP WATER WAVE EQUIVALENTS
FOR SHORELINE MODELING




APPENDIX A
DEEP WATER WAVE EQUIVALENTS FOR SHORELINE MODELING
Consider the transport equation K EbCG6 cos(P8, azb) sin(#, ab) pg(s 1)(1 p)

I '
I
\I
I I
III I :11 I I I I I
II
I//I
1// / I I I / I I I

(A.1)

IL

Definition Sketch
The bathymetry of concern will be considered as straight and parallel bottom contours seaward of the effects of a beach nourishment project. This seaward depth limit is denoted as h,. For depths smaller than h., it is assumed that all contours are parallel to the shoreline. The azimuth, /9,, of the outward normal within the depth limit affected by the nourishment




project is related to the azimuth of the outward normal, 0o, outside the limit of the project by
P(sx) = fo + A# (x) (A.2)
in which A# is small.
Using conservation of energy and Snell's law to transform Eq. (A.1) from the breaker line to the depth contour h,, SKE*C. cos(W, a*)sin(, a.)Cb (A.3)
Spg ( 1)(1 p)C, and using Eq. (A.2)
K E, CG. sin 2(Po + Af a.) Cb (A.4)
2 pg(s 1)(1 p) C,
and expanding
E, CG. sin 2(fo a.) Ccos 2AC Q =K- cos 2A/2 pg(s 1)(1 p) C.
E. Co.cos 2(6o -ca.) O
+ KE, C cos(fl ,) sin2A -Cb (A.5)
2 pg(s-1)(1-p) C,
Since Ap is small, cos 2A/ m 1 and sin 2A,8 a 2Afl, and the first term is recognized as the transport without the project present (the background transport, QB) and the second term the transport induced by project placement, Qp.
The background transport will first be expressed in terms of deep water wave characteristics
.. E* CG cos(Po a.) sin(flo a.) Cb
QBACKGROUND = QB = K pg(s 1)(1 p) C,
= K EoCGo cos(Po ao) sin(flo so) Cb (A.6) pg(s-1)(1-p) Co
Eq. (A.6) contains Cb which we now wish to relate to deep water conditions. Using energy conservation,
EbCG, cos(,8 ab) = E*CG. cos(P, a,) = E*CG. cos(,6o + A8 a*)




Therefore

EbCGb cos(,8, ab) = E. CG. [cos(Po a.) cos A8 sin(,. a.) sin AP] and since A8 is small, the last term can be neglected and cos A,8 a 1. Finally EbCG, cos(fl, ab) : EoCGo cos(30 SCo) and employing the following shallow water approximations
CGb Cb -igb.
Hb M hb (i Fs 0.78)
g2 H2Cb cos(, ab) = g2 H2CGo cos(fo ao)
2 CK cos(a ab) =g2 GH oC Cos(Po O)
Cb= [g2Ho2CGo cos(o o)2 (A.7)2
Co =(A.7) in which cos(,8 ab) has been approximated by unity.
Returning now to the project transport and using conservation of energy considerations and Snell's law to transform to deep water K EoCaGo cos 2(o a.) cos(Po o) ACb (A.8)
pg(s- 1)(1-p)cos( o- a) CA,
Employing Eq. (A.7), the project related transport can now be written without reference to shallow water
K HjC1-g04 cos12 (o ao) 1
S0 = cos 2(0 a*) A# (A.9)
S8(s 1)(1 p) cos(o a*)o.4c s2C *,A
Using Snell's law,
Po a* = sin-1 C sin(Po ao) (A.10)
The shore planform direction anomaly A8 is
A#) tan- a(A.11)
a x 8x




Combining Eqs. (A.8) and (A.11) with the continuity equation ay 1 aQP
at (h. + B) 8ax
we find

ay K H4 C1'4g 0.4
at 8(s 1)(1 p)C .04(h. + B) Defining the longshore diffusivity,

cos 12(#o ao) cos 2(fo a.) a2y I cos(Po a.) Ix2

K H24 C1g2 o.4 cos1.2 (o ao) cos 2(fo a.)
G = 8(s 1)(1 p)C. XO.4 (h. + B) cos(0 a.) (A.13)
and it is noted that G is now expressed entirely in terms of deep water wave quantities (with the use of Eq. (A.10)). The diffusion equation for shoreline evolution is obtained in the usual form
ay Ga2y (A.14)
at aX2
We now consider the equations that will be used for numerical analysis. Commencing with Eq. (A.3) and inserting Eq. (A.2) in the cosine term
Q = K E. Ca. [cos(o a.) cos AP sin(flo a.) sinA/P] sin(fl cx,)Cb (A.15)
1 1 C-

S- AJ- P)(
and since A# is small and using conservation of energy = K EoCGo cos(Po ao) sin( ,)Cb pg(s 1)(1 p)C.
Combining Eq. (A.7) with the expression for deep water wave energy, Eo
Eo- pg
8
yields
KH Cgo0' 4cos2(o ao)
Q= 8(s 1)(1 p)C04 sin(#, -c.)
8(s 1)(1 p)CNo.4 snfs-o,

(A.16)
(A.17) (A.18)

and
C,
a. = o sin-1 [C sin(flo ao)] (A.19)
which completes the development. It is noted that with the exception of the trigonometric term involving (V, a.) and the term C., all quantities are expressed in terms of deep water conditions.

(A.12)




Representative Wave Conditions

To simplify input conditions it is desirable to define representative wave characteristics. In developments here, we will consider a constant wave direction, but time-varying wave height and period. At each time, the waves will be considered as represented by a single period and a Rayleigh wave height distribution with significant wave height H,. The effective height is thus
0' 2. 2.4
Hef = J H2"4p(H)dH] (A.20)
in which all wave heights are in deep water and p(H) is the Rayleigh distribution, 2H e(H/H,,,)2 A.1
p(H) = H2mae (A.21)
Eq. (A.20) can be solved numerically to yield Heff = Km, Hrms = KH (A.22)
where Krm. = 1.04 and K, = 0.735. Thus the long-term effective wave height He11 at a particular location is
Hef I = E (KH)2.4 (A.23)
A somewhat more appropriate but more cumbersome value of Hef$ is N I (K,H,)2.4 1"2 12.4
Heff2 =N 1 ( 1.2 ] -j (A.24)
C 1.2
and the effective value of to be used in Eq. (A.18) is the denominator of Eq. (A.24) C,
raised to the 2.4 power. The recommended values of effective deep water wave height around the state of Florida are plotted in Figure 23.

I




APPENDIX B
PROGRAM LISTING
AND
SAMPLE INPUT AND OUTPUT

Program: Input File: Output File:

DNRBS.FOR DNRBS.INP DNRBS.OUT

(Note: Input and Output Files Presented for Numerical Example 2)




PROGRAM LISTING: DNRBS.FOR
C
C THIS PROGRAM DEVELOPED FOR DIVISION OF BEACHES AND SHORES, C DEPARTMANT OF NATURAL RESOURCES FOR USE IN PREDICTING *
C THIRTY YEAR EROSION PROJECTIONS **
C *********************************************************************
C
DIMENSION YO(500),YN(500),X(500),Q(500),HB(500),ALP(500), 1 XER(40),EROSB(40),SUMA(50),VTOTA(50),YEARA(50),
2 ITNOUR(10),ISEG(10),IS(10,10),IE(10,10),DY(10,10),
3 WORD(20),YEAR(10),DV(10,10),NSEG(10),PCT(50),DYO(500)
4 ,QBACK(500),YSTRUC(10),ISTRUC(10)
OPEN(UNIT=6,FILE='DNRBS2.OUT',STATUS='NEW') OPEN(UNIT=5,FILE='DNRBS2.INP',STATUS='OLD') OPEN(UNIT=7,FILE='DNRBS2.DAT',STATUS='NEW')
55 FORMAT('***** IT = 1, I=1, EROSION RATE = ',E12.2)
120 FORMAT(6(I4,F8.2))
121 FORMAT(/,5X,'NTIME = ',16,' HB = ',F8.2,' ALP = 'F8.3,' SUM = '
1 F8.2,' STDEV = ',F8.2,/)
122 FORMAT(//)
123 FORMAT(5F8.2,416) 124 FORMAT(8F8.2) 125 FORMAT(4(E8.2,F8.2)) 126 FORMAT(20A4) 127 FORMAT(20A4,/) 160 FORMAT(816) 162 FORMAT(F8.2,316,2F8.2) 164 FORMAT(816) 165 FORMAT(/)
166 FORMAT(16,3F8.2) 167 FORMAT(' INITIAL SHORELINE (INCL. NOURISHMENT) POSITION',/) 168 FORMAT(I6,F8.1,2E12.4,F8.2) 170 FORMAT(' HO =',F6.2,' FT., T =',F6.2,' SEC., ALPO = ',F6.2,' DEG.
1, BTAO = ',F6.2,' DEG., '
2 ,5X,' XMU =',F8.2,' DEG., DX = ',F8.2,' FT., DT = ',F8.2,' SEC.') 172 FORMAT(' HSTR = ',F8.2,' FT., B = ',F8.2,' FT., XK = ',F8.2, 1' VFACT = ,F8.2,14X,'QBKREF = ',F8.2,' FT.**3/SEC.') 173 FORMAT(' IREF = 1,6,', IMAX = ',16,', NTIMES = ',18,
1 ', NS = ',16)
444 FORMAT(20X,'TIME = ',18,' YEARS') 446 FORMAT(' NYEARS = ',18,' DYSITE = ',F8.2) 447 FORMAT(' BACKGROUND EROSION TRANSPORT RATES',/) 448 FORMAT(5(I6,F8.3)) 449 FORMAT(216,8F8.3) GRAV=32.2
NER=7
SG=2.65
POR=0.35
PI=3.14159
PIO2=PI/2.0
ITNM=1
XKAP=0.78
QBACK(1)=0.0 73
LCUR=0
READ(5.126)(WORD(T.T=1,20)




WRITE(6,127)(WORD(I),I=1,20) WRITE(7,126)(WORD(I),I=1,15)
READ(5,124)HO,T,ALPO,BTAO,XMU,DX,DT
READ(5,123)HSTR,B,XK,VFACT,QBKREF,IREF,IMAX,NTIMES,NS
IF(NS.GT.0)READ(5,448)(ISTRUC(I),YSTRUC(I),I=1,NS)
WRITE(7,170)HO,T,ALPO,BTAO,XMU,DX,DT
WRITE(7,172)HSTR,B,XK,VFACT,QBKREF
WRITE(6,170)HO,T,ALPO,BTAO,XMU,DX,DT
WRITE(6,172)HSTR,B,XK,VFACT,QBKREF
WRITE(6,173)IREF,IMAX,NTIMES,NS
WRITE(6,165)
IF(NS.GT.0) WRITE(6,448)(ISTRUC(I),YSTRUC(I),I=1,NS)
ALPO=ALPO*PI/180.0 BTAO=BTAO*PI/180.0
XMU=XMU*PI/180.0
READ(5,124)(XER(I),EROSB(I),I=1,NER)
WRITE(6,165)
WRITE(6,125)(XER(I),EROSB(I),I=1,NER) WRITE(*,125)(XER(I),EROSB(I),I=1,NER)
READ(5,160)NNOUS,NNOUE
WRITE(*,160)NNOUS,NNOUE
DO 60 I=NNOUS,NNOUE
READ(5,166)I,DYO(I)
60 DYO(I)=DYO(I)*VFACT
TOTH=HSTR+B IMM1=IMAX-1 IMP1=IMAX+1
DO 30 I=1,IMP1
X(I)=(I-I)*DX
YN(I)=0.0
30 YO(I)=0.0
C**** FOLLOWING IS BACKGROUND EROSION AND ASSOCIATED TRANSPORT
DO 240 I=1,IMAX
CALL INTERP(EROSB,ERC,NER,X,XER,I,DT,QBACK,TOTH,DX,IREF)
240 CONTINUE
DQ=QBACK(IREF)-QBKREF
DO 241 I=1,IMP1,
241 QBACK(I)=QBACK(I)-DQ
CALL WVNUM(HSTR,T,CC)
CO=GRAV*T/(2.0*PI)
CGO=CO/2.0
ALPSTR=BTAO-ASIN(CC/CO*SIN(BTAO-ALPO))
C WRITE(6,124)HSTR,T,CC,CO,CGO,ALPO,BTAO,ALPSTR
CALP=COS(ALPO-ALPSTR) SALP=SIN(ALPO-ALPSTR)
WRITE(6,165) WRITE(6,447)
WRITE(6,448)(I,QBACK(I),I=I,IMP1)
WRITE(6,165)
WRITE(6,160)NNOUS,NNOUE
WRITE(6,167)
C ***** FOLLOWING IS TIME LOOP
DO 300 NT=1,NTIMES
IF(MOD(NT,10).EQ.0) WRITE(*,*) NT,NTIMES
BB=XK*HO**2.4*CGO**1.2*GRAV**0.4*COS(BTAO-ALPO)**1.2/
1 (8.0*(SG-1)*(1.0-POR)*CC*XKAP**0.4)
SUM=0.0 SUM2=0.0 NFLAG=0
IF(NFLAG.EQ.1) GO TO 302
IF(NT.EQ.1I.OR.NT.EQ.0) CALL NOUR(NT,ITNM,YO,IMAX,ITNOUR,
1 NSEG,IS,IE,DY,VTOT,IT,DV,X,NNOUS,NNOUE,DYO,DX,TOTH) C YO(1)=0.0
C YO(IMAX)=0.0 74
C*****FOLLOWING IS TRANSPORT LOOP




'J I~ .UA 'dJ ~ J. .~ 4 U"...~ i i ~. an4. I ".
HaNI'Z=UI2I aT Oa 0 00 0 9 C 9T /1a=NODD
(I)x=Dx
W( a9)lV-0o TOT (S'ota9'9I1)LVWOda o0 (00t)XD K '(00t)X'(0t)H3X'(0 )gSOH NOISNaKIU (JaUI'HXC'HLOL'MZDV 0'~IlHaX'Xl-'HIDH'gSOHdS)d a,&I aNI.Ll0dOH S
D
;D
aNa
dOlS
(L=LINn)asoqD (9=lINn) sOD (9=aLINn) asOD afINILNOD ZOE (TdWI'I=I' (I) iYI) (0ZT'9) aLIUM D (TrawI'1=1'(I)NA'I)(OZT'L)aLraM
aLis~clS-dVaa&N(9W'9)aLLIaM ZOE 01 Oi(o 'H 'D N ZN'HO'S'DZ'IO*I'aNZN)JI D
Sdv AN=DZN D
IE'Z*SH Ha.N-90"Z9-((LZ)NA+(9Z)NA)*s'0=a.!sAa
afINIINOD OOC O0009 STI/1U*(I-N)+0'066T=(H D')VaA (HnONN'SfONN' I X' H1O 1OLA'VqnS'nofl I unO A'.Ld'wns'XQ'NA) D1ad qqVD TOE (XVKI'I=I (I) NA'I) (0ZT'9) H.IUM SHoAN ( t t t 9 )IUM TOE OJ. 09(OE'aN'DZN'aNv'OI' N'DZN'aNV's'aN'DZN'aNv'T' N'DZN)aI SHUVAN=DZN
99E/1N=SdIVaAN~ TOE OLL 09 (0"HN'(0G9V'aN)aOK)aI D toC 01 Of (o"N'(G9V'1N)Ow)aI (Oa(.N=&(o'I)(OZT'9)awdM o
aHNILNOD O0Z
OOZ 01 OD(o"'aN'lNO'v'aN'I)aI
(I)N=(I)OA
HflNI1NOD 89Z O'Z/((I-I)X-(T+I)X)=XCI 99Z 89Z O1 OD
(T)x-(z)x=xa 99Z OLL Of(T*' 0'I)aI XNI'IT=I 00Z Oa NOI1VflZ AIIflNIINOD 'dOa SI !NIMO0qTo0a*D
(X-,iN)XDow-(XVKI)O+(Tda I)XDVw =(Ta :)O
(Z)XDVab-(Z)6+(T)xova?5=(l)6
(T)o L=(T)NA
anNIL&NOD 001
aAVSi'(I)XDVab'(I)OA'(1-I)OA'(I)DfldSA I
(U1SdSqV'DDHnSI I
(()b=aAVS
('dJSdqV-VJa) NIS *g= (1) (OdqV-V.L) NIS =NIS (Odqv-vla)S~O=DS~O Zoza- (T( -I) X- (I) X) (T I)o0A- (1)o020))ZUV-nKx=Vla




DX=XER(IER)-XER(IER-1)
DXX=XC-XER(IER-1)
AA=DXX/DX BB=1.0-AA
ERC=-CON*(BB*EROSB(IER-I)+AA*EROSB(IER))
QBACK(I+1)=QBACK(I)-DXB*TOTH*ERC/DT
IF(I.NE.2)GO TO 6
C WRITE(6,100)I,IER,ERC,DT,TOTH,DX,AA,BB
C WRITE(6,101)QBACK(I),QBACK(I-1),QBACK(I+1),CON,DXB
6 GO TO 20
10 CONTINUE
20 RETURN
END
C
C
C ********
c
C
SUBROUTINE NOUR(NT,ITNM,YN,IMAX,ITNOUR,NSEG,
1 IS,IE,DY,VTOT,ITC,DV,X,NNOUS,NNOUE,DYO,DX,TOTH)
DIMENSION YN(500),ITNOUR(10),NSEG(10),DY(10,10),
1 IS(10,10),IE(10,10),DV(10,10),YNT(500),
2 X(500),DYO(50)
24 FORMAT(' OUTPUT FROM SR NOUR ',16,' ISC = ',16,' IEC = ',I6)
26 FORMAT(' REACHED SR NOUR',216,F8.2)
28 FORMAT(' NOUR EVENT = ',16,' YEAR = ',F8.2,
1 VOL ADDED = ',F8.3,' MILL YDS**3',/)
30 FORMAT(2(I6,F10.0,F8.2))
32 FORMAT(' TOTAL VOLUME ADDED = ',F12.1 ,' CUBIC YARDS',/)
VTOTT=0.0 FACT=1.0
C IF(NT.NE.1)FACT=0.5
DO 6 I=NNOUS,NNOUE
6 YN(I)=YN(I)+DYO(I)*FACT
DO 12 I=NNOUS,NNOUE
12 VTOTT=VTOTT+(X(I+1)-X(I-1))/2.0*YN(I)
VTOT=VTOTT
C WRITE(6,32)VTOT
C WRITE(7,32)VTOT
WRITE(6,30)(I,X(I),YN(I),I=1,IMAX)
RETURN
END
C
C ************* THIS SUBROUTINE CALCULATES PERCENTAGES OF C TOTAL VOLUME REMAINING
SUBROUTINE PERCT(YN,DX,SUM,PCT,VTOT,LCUR,LCURM,SUMA,VTOTA,TOTH,X
1 ,NNOUS,NNOUE)
DIMENSION YN(400),PCT(50),SUMA(50),VTOTA(50),X(200)
24 FORMAT(5X,'LCUR = ',I6,' PCT(LCUR) = ',F8.2)
SUM=0.0
DO 20 I=NNOUS,NNOUE
20 SUM=SUM+(X(I+1)-X(I-1))/2.0*YN(I)
LCUR=LCUR+1 LCURM=LCUR
SUMA(LCUR)=SUM
VTOTA(LCUR)=VTOT
PCT(LCUR)=SUM/VTOT
WRITE(6,24)LCUR,PCT(LCUR) WRITE(*,24)LCUR,PCT(LCUR)
RETURN
END
C
C*********THIS SUBROUTINE CHECKS PnR Aun ACCOUNTS FOR THE TRANSPORT C AROUND STRUCTURES 76
C
SUBROUTINE STR(NS,YSTRUC,I,YO,Q,IMAX,DX,ALPC,XMU,QB,BB,PIO2,
1 ISTRUC,ALPSTR)




18 FORMAT(316,6F8.2)
C WRITE(*,18)NS,I,I,YSTRUC(1)
DO 20 IS=1,NS
IC=IS
20 IF(I.EQ.ISTRUC(IS))GO TO 40
GO TO 80
40 DYP=YO(I)-YSTRUC(IC)
DYM=YO(I-I)-YSTRUC(IC)
C WRITE(6,18)I,ISTRUC(IC),IC,DYP,DYM
DXC=DX/2.0
IF(DYP.GE.0.0.AND.DYM.GE.0.0)GO TO 80
IF(DYM.LT.0.0.AND.QB.GT.0.0)QB=0.0 IF(DYP.LT.0.0.AND.QB.LT.0.0)QB=0.0
IF(DYM.GE.0.0.OR.DYP.GE.0.0)GO TO 42
Q(I)=0.0
GO TO 80
42 IF(DYM.LT.0.0)GO TO 44
C TO HERE IF DYM.GT.0.0.AND DYP.LT.0.0
BTA=XMU-ATAN2(-DYM,DXC)-PI02
GO TO 46
C TO HERE IF DYP.GT.0.0.AND.DYM.LT.0.0
44 BTA=XMU-ATAN2(DYP,DXC)-PIO2
46 Q(I)=BB*SIN(BTA-ALPSTR)
80 RETURN
END
C
C ****** THIS SUBROUTINE CALCULATES WAVE LENGTH AND CELERITY
C
SUBROUTINE WVNUM(HSTR,T,CC)
20 FORMAT(I6,8F8.3)
G=32.17
EPS=0.001
TWOPI=6.283185
SIG=TWOPI/T
XK=TWOPI/(T*SQRT(G*HSTR))
DO 100 IT=1,20
ARG=XK*HSTR
EK=(G*XK*TANH(ARG))-SIG**2
SECHA=1.0/COSH(ARG)
EKPR=G*(ARG*(SECHA**2)+TANH(ARG))
XKNEW=XK-EK/EKPR
IF(ABS(XKNEW-XK).LT.ABS(EPS*XKNEW)) GO TO 120
XK=XKNEW
100 CONTINUE 120 XK=XKNEW
XL=TWOPI/XK
CC=XL/T
RETURN
END




INPUT FILE: DNRBS.INP
(Example No. 2)

EXAMPLE
2.00
17.0
0.0
90000.
80 10 80 11
81 11 82 11 83 11 84 11 85 11 86 11 87 11 88 II, 89 11 90 1i 91 11 92 II 93 11 94 II 95 11 96 II: 97 1i1 98 II 99 11 100 II:

NO. 2 UNIF. BACK. EROS. NO STRUC. 2 MILE PROJ.
6.0 90.0 90.0 180.0 500.0 86400.0
6.0 0.77 1.0 0.0 1 180 10950
2.0 90000. 2.0 49500. 2.0 60000.
3.0 100000. 3.0 140000. 2.0
0
2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0

0
3.0




OUTPUT FILE: DNRBS.OUT (Example No. 2) EXAMPLE NO. 2 UNIF. BACK. EROS. NO STRUC. 2 MILE PROJ.

HO = 2.00 FT., T = 6.00 SEC., ALPO = 90.00 DEG., BTAO = 90.00 DEG., XMU = 180.00 DEG., DX = 500.00 FT., DT = 86400.00 SEC. HSTR = 17.00 FT., B = 6.00 FT., XK = .77 VFACT = 1.00
QBKREF = .00 FT.**3/SEC.
IREF = 1, IMAX = 180, NTIMES = 10950, NS = 0

2.00 .90E+05 3.00 .10E+06

2.00 .50E+05 3.00 .14E+06

2.00 .60E+05
2.00

BACKGROUND EROSION TRANSPORT RATES

1 6
11
16 21 26 31
36 41 46 51 56
61 66 71 76 81 86 91 96 101
106 il1
116 121 126 131 136 141 146 .151 156 161 166 171 176 181

.000
.004 .007 .011
.015 .018
.022 .026 .029 .033
.036 .040 .044 .047 .051 .055 .058 .062 .066 .069 .073 077 080 084 .088
091 095
.098 .102 .106 .109 .113
.117 .120
.124 .128 .131

2 7
12 17 22 27 32 37 42 47 52 57 62 67 72
77 82 87 92 97 102
107 112 117
122 127 132 137 142
147 152
157 162 167
172 177

.001 .004 .008
.012 .015
.019 .023 .026 .030
-034 .037 .041 .044 .048 .052
.055 .059 .063 .066 .070 .074 .077 .081 .085 .088 .092 .096 .099 .103 .106 .110 .114 .117 .121 .125 .128

3
8
13 18 23
28 33 38
43 48 53 58
63 68
73 78
83 88 93 98
103 108 113
118 123 128
133 138 143
148 153 158 163 168 173 178

A) 1 nn

" OOE+00
.90E+05

3.00

.001 .005 .009 .012 .016 .020
.023 .027 .031 .034 .038 .042 .045 .049 053 .056 060
063
.067 .071 .074 .078
.082
.085 .089
.093 .096 .100
.104 .107 .111
.115 .118 .122 .125 .129

4 9
14 19 24 .29 34 39 44 49 54 59 64 69
74 79 84 89 94 99 104 109 114 119 124 129 134 139 144 149 154 159 164 169 174 179

.002 .006 .009 .013 .017 .020
.024 .028 .031 .035 .039 .042 .046 .050 .053 .057 .061 .064 .068 .071 .075 .079 .082 .086 .090 .093 .097 .101
.104 .108 .112 .115 119 .123 .126 .130

5
10
15 20 25
30 35
40 45 50
55 60
65 70
75 80
85 90
95 100
105 110
115 120 125 130
135 140 145 150 155 160 165 170 175 180

.003
.007 .010
.014 .018
.021 .025 .028 .032 .036 .039
.043 .047 .050 .054 .058 .061 .065 .069 .072 .076 .079 .083 .087 .090 .094 .098 101
.105 .109 .112 .116 .120 123 127 .131




00' 00' 00' 00* 00* 00' 00* 00* 00' 00* 00' 00' 00'
00"
00' zil
00* 1 IT
00* ZII 00' ZII
00. ZTI
00
00* 00* 00* 00* 00* 00' 00 oo0
00' 00' 00' 00, 00* 00* 00* O' OG* 00' 00* 00* 00* 00' 00* QO* 00' 00, 00' 00* 00* 00* 00, 00, 00* 00, 00' 00* 00* 00* 0*l

"00SE9 "OOGZ9 "0(
Oc
"OC
*OOGLG
"0099
"00999
* OOS 5
*005% "OOGzG
* oasis "00906
*0096f7
I 0098t, "O0SLt
*00997
"OOGTTT
" oosov
00S167
* 0099C 00S8
OOGT7C OOSVC
"OOGOC I OOSL
* 0090C
*0090
"0096Z
*OOGLZ
*0099
* oos17z
*'00SEZ
.00961 .00981
OOGLI
009
*0099I .00ST71
*00911
0096
009
* OOGS
* 00519
* 009
* 00st, 009Z
*OOST 089

ezi
9ZT
t7Z1 0Z1 OZI
81T
911
ZTI OTT 801
901 tIOI ZOT
001 86
96 176
Z6
06 88 98 t78 z 8
08 8L
9L V L OL
89 99 v 9 09 09
81 99
17 9
017 8V
9 tV
0T
81C 91
OT
8
9 T7 0 z 8 T 91
8I 9I
T7
zI

00' 00* 00* 00* 00* 00* 00*
00" 00"
00' 00* 00' 00* 00* 00 TT
00 1 Ti 00' ZIT 00 1lTT 00'* IT
00 *ZT 00' II O00. II
00* 00' 00*
00, 00* 00* 00' 00' 00' 00' 00' 00* 00' 00' 00* 00* 00' 00* 00* 00* 00* 00, 00* 00* 00* 00* 00* 00* 00* 00' 00* 00' 00* 00' 00' 00' 00* 00* 00*

*0009 "O0009
"00019 '00009 "00069 '00089
* 00OLS
"00095 "00055
"0001
000I5
"00005 00067
0008t,
* 0009t7
"O00171 "O0017 "O00E1
"O00T1 "O00007 0006 0008
* OOOL7
* 0009
*000
"O00 000 "000 "000i "000 '0006C "0008C
"O00L
*0009C
*O005 "0001C
*0006 "00zE "O00Ig
* 0008Z
00061 00081
*OOOLI
"00091 ooosi
"000 17 "O001 "00 I
"O00II O000 "0006 "0008
"OOOL "0009 "0005
* 001
* oooE
* 0006 "0001 "O0009
"0

I ~ n.,e-r~t rr~KT- I ap-rrrr nt-Tc rrw -r T rTTT

LZI
IZI
611 LIt
511 CII
TT 111 601 LOT GO CO TO
66 L6
96
6 16
68 LS
58 C8
18 6L LL SL IL
69 L9
99 C9
19 69
L9
99 Es
6Vb
L t
9 V
IS
617 L E
91C
6 LZ
6Z
6I
61 LI
9 T
1
6
L
G
C
I

I .,-, -,- -,,- -




-2.00 2 -2.00 8 -2.00 14 -2.00 20 -2.00 26 -2.00 32 -2.00 38 -2.00 44 -2.00 50 -2.00 56 -1.96 62
-.87 68 10.62 74 49.83 80 92.71 86 103.87 92 81.19 98 33.87 104
4.34 110
-1.60 116 -1.99 122 -2.00 128 -2.00 134 -2.00 140 -2.00 146 -2.00 152 -2.00 -158 -2.00 164 -2.00 170 -2.00 176 LCUR = LCUR = LCUR = LCUR =

131 133 135 137 139
141 143 145 147 149 151 153 155 157 159 161 163 165 167 169 171 173 175 177 179 100

TIME
-2.00 3
-2.00 9
-2.00 15
-2.00 21
-2.00 27
-2.00 33
-2.00 39
-2.00 45
-2.00 51
-2.00 57
-1.93 63 .18 69 15.06 75 58.16 81 96.98 87 102.52 93 74.10 99 26.75 105 2.31 111
-1.77 117
-2.00 123
-2.00 129
-2.00 135
-2.00 141
-2.00 147
-2.00 153
-2.-00 159
-2.00 165
-2.00 171
-2.00 177 PCT( LCUR) PCT (LCUR) PCT(LCUR) PCT(LCUR)
TIME =

1 -10.00 2 -10.00 3 7 -10.00 8 -10.00 9 13 -10.00 14 -10.00 15

U~vv .V 65000. 66000. 67000. 68000. 69000. 70000. 71000. 72000. 73000.
74000. 75000. 76000. 77000. 78000. 79000. 80000. 81000. 82000. 83000.
84000. 85000. 86000. 87000. 88000. 89000. 116

-2.00 4
-2.00 10
-2.00 16
-2. 00 22
-2.00 28
-2.00 34
-2.00 40
-2.00 46
-2.00 52
-2.00 58
-1.87 64 .84 70 20.45 76 66.34 82 100.24 88 100.24 94 66.34 100 20.45 106 .84 112
-1.87 118
-2.00 124
-2.00 130
-2.00 136
-2.00 142
-2.00 148
-2.00 154
-2.00 160
-2.00 166
-2.00 172
-2.00 178
* .78 =81 .68
- .60
- .53
5 YEARS

.UU .00 .00
.00 .00 .00 .00
.00 .00 .00 .00 .00 .00 .00 .00 00 .00 .00 .00 .00 .00 .00 00 .00 .00 .00

132
134 136 138
140 142 144 146 148 150 152
154 156 158 160 162
164 166 168 170 172
174 176 178 180
084

'O -z.jv j
65500.
66500.
67500.
68500.
69500.
70500.
71500.
72500.
73500.
74500.
75500.
76500. 77500. 78500. 79500. 80500. 81500. 82500. 83500.
84500. 85500. 86500. 87500. 88500. 89500. .000 -.5 1 YEARS

Jvv
. 00 .00 .00 .00 .00 .00 .00 .00 .00 .00
.00 .00
.00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00
42 -.542
-2.00 5
-2.00 11
-2.00 17
-2.00 23
-2.00 29
-2.00 35
-2.00 41
-2.00 47
-2.00 53
-2.00 59
-1.77 65
2.31 71 26.75 77 74.10 83 102.52 89 96.98 95 58.16 101 15.06 107
-.18 113
-1.93 119
-2.00 125
-2.00 131
-2.00 137
-2.00 143
-2.00 149
-2.00 155
-2.00 161
-2.00 167
-2.00 173
-2.00 179

-2.00 156
-2.00 162
-2.00 168
-2.00 174
-2.00 180

-10.00 4 -10.00 5 -10.00 6 -10.00
-10.00 10 -10.00 11 -10.00 12 -10.00
-10.00 16 -10.00 17 -10.00 18 -10.00

.000

1
7
13 19 25 31
37
43 49 55 61 67 73
79 85 91 97
103 109 115
121 127 133 139
145 151 157 163 16.9
175

-2 .00
-2.00
-2.00
-2.00
-2.00
-2 .00
-2.00
-2.00
-2 .00
-1.98
-1.31
7 .07
41 .64 87 .43
104.31 87 .43
41 .64 7 .07
-1.31
-1.98
-2 .00
-2 .00
-2.00
-2.00
-2 .00
-2.00
-2.00
-2.00
-2.00
-2.00

084

-2.00
-2.00
-2.00
-2 .00
-2. 00
-2.00
-2.00
-2.00
-2.00
-1.99
-1.60
4 .34 33.87 81 .19
103 .87 92.71 49.83 10.62
- .87
-1 .96
-2.00
-2 .00
-2.00
-2 .00
-2.00

000

6
12 18
24 30 36
42 48 54
60 66
72 78
84 90 96
102 108
114 120 126 132 138
144 150




25 31 37 43
49 55 61
67 73
79 85
91 97 103 109 115 121 127 133 139 145 151
157 163 169 175
1 7
13 19 25 31
37 43 49 55 61 67 73 79 85 91 97 103 109 115 121 127 133 13.9
145 151 157 163 169 175

158 164 170 176
2 8
14 20 26 32 38 44 50
56 62 68 74 80
86 92 98 104 110
116 122 128 134 140 146 152 158 164 170 176

-10.00
-10.00
-10.00
-10.00 LCUR =
LCUR = LCUR = LCUR = LCUR =
-20.00
-20.00
-19.99
-19.98
-19.92
-19.76
-19.31
-18.25
-16.05
-12 .04
-5 .64
3 .15
13 .40 23.14 29.93 31.79 28. 14 20. 10 9.92 -.01
-8 .06
-13.62
-16.96
-18.70
-19.51
-19. 83
-19.95
-19.99
-20.00
-20.00 LCUR = LCUR = LCUR =

3 9
15
21 27 33 39 45 51 57
63 69
75 81 87 93
99
105 il1
117 123 129 135 141 147 153 159 165 171 177

10 PCT(LCUR) 11 PCT(LCUR) 12 PCT(LCUR)

10 YEAR!
-20.00 4
-20.00 10
-19.99 16
-19.97 22
-19.89 28
-19.65 34
-19.05 40
-17.68 46
-14.95 52
-10.19 58
-2.96 64 6.48 70 16.82 76 25.85 82 31.16 88 31.16 94 25.85 100 16.82 106 6.48 112
-2.95 118
-10.19 124
-14.95 130
-17.68 136
-19.05 142
-19.65 148
-19.89 154
-19.97 1 ar
-19.9 82
-20.0
-20.0
- .26
= .23
.19

-10.00 26
-10.00 32
-9.98 38
-9.86 44
-9.37 50
-7.68 56
-3.12 62 6.41 68 21.71 74 40.01 80 54.71 86 59.00 92 50.69 98 33.,93 104 16.05 110 2.57 116
-5.09 122
-8.46 128
-9.61 134
-9.92 140
-9.99 146
-10.00 152

-10.00 27
-10.00 33
-9.97 39
-9.82 45
-9.21 51
-7.17 57
-1.93 63 8.58 69 24.70 75 42.92 81 56.29 87 58.45 93 48.29 99 30.84 105 13.41 111 .91 117
-5.89 123
-8.76 129
-9.70 135
-9.94 141
-9.99 147
-10.00 153
-10.00 159
-10.00 165
-10.00 171
-10.00 177 PCT(LCUR) PCT(LCUR) PCT(LCUR) PCT(LCUR) PCT(LCUR)

-10.00
-9.99
-9.96
-9.77
-9.00
-6.58
-.59
10.91 27.75 45.69 57.54 57.54 45.69 27.75 10.91
-.59
-6.58
-9.00
-9.77
-9.96
-9.99
-10.00
-10.00
-10.00
-10.00
-10.00

28 34 40 46 52 58 64 70 76 82 88
94 100
106 112 118 124 130 136 142 148 154 160 166 172 178 .47 .42 .38 .33 .30

-10.00 29
-9.99 35
-9.94 41
-9.70 47
-8.76 53
-5.89 59 .91 65 13.41 71 30.84 77 48.29 83 58.45 89 56.29 95 42.92 101 24.70 107 8.58 113
-1.93 119
-7.17 125
-9.21 131
-9.82 137
-9.97 143
-10.00 149
-10.00 155
-10.00 161
-10.00 167
-10.00 173
-10.00 179
-20.00 5
-20.00 11
-19.99 17
-19.96 23
-19.86 29
-19.59 35
-18.89 41
-17.34 47
-14.32 53
-9.16 59
-1.51 65 8.19 71 18.48 77 27.06 83 31.55 89 30.62 95 24.55 101 15.12 107 4.80 113
-4.33 119
-11.15 125
-15.53 131
-17.98 137
-19.19 143
-19.71 149
-19.91 155
-19.97 161
-19.99 167
-20.00 173
-20.00 179

-10.00
-9.99
-9.92
-9.61
-8.46
-5.09
2.57 16.05 33.93 50.69 59.00 54.71 40.01 21.71

30 36 42 48 54 60 66 72 78 84 90
96 102
108

6.41 114
-3.12 120
-7.68 126
-9.37 132
-9.86 138
-9.98 144
-10.00 150
-10.00 156
-10.00 162
-10.00 168
-10.00 174
-10.00 180

-10.00
-9.98
-9.90
-9.50
-8.10
-4.17
4.40 18.82 37.00 52.84 59.18 52.84 37.00 18.82 4.40
-4.17
-8.10
-9.50
-9.90
-9.98
-10.00
-10.00
-10.00
-10.00
-10.00
-10.00
-20.00
-20.00
-19.98
-19.94
-19.80
-19.42
-18.49
-16.53
-12.86
-6 .88 1.54 11.66
21.66 29.10
31.87 29.10
21.66 11.66 1.54
-6.88
-12.86
-16.53
-18.49
-19.42
-19.80
-19.94
-19.98
-20.00
-20.00
-20.00

-20.00
-20.00
-19.99
-19.95
-19.83
-19.51
-18.70
-16.96
-13.62
-8.06
-.01
9.92 20.10 28 .14 31.79 29 .93 23 .14 13 .40 3.15
-5 .64
-12.04
-16.05
-18.25
-19.31
-19.76
-19.92
-19.98
-19.99
-20.00
-20.00

TIME
-20.00
-20.00
-19.99
-19.97
-19.91
-19.71
-19.19
-17.98
-15.53
-11.15
-4.33
4.80 15.12 24.55 30.62 31.55 27.06 18.48 8.19
-1.51
-9.16
-14.31
-17.34
-18.89
-19.59
-19.86
-19.96
-19.99
-20.00
-20.00

6
12 18 24 30
36 42 48 54 60 66 72 78 84 90
96 102 108 114 120 126 132 138 144 150 156 162 168 174 180




LCUR LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR = LCUR =
LCUR =
-59.99
-59.52
-58.93
-58.13
-57.01
-55.45
-53.40
-50.80
-47.68
-44.15
-40.40
-36.71
-33.41
-30.83
-29.24
-28.83
-29.64
-31.59
-34.45
-37.92
-41.66
-45.36
-48.77
-51.72
-54.14
-56.02
-57.42
-58.41
-59.12
-59.63 LCUR =

P CTl( LCUR) 5 PCT(LCUR) i PCT(LCUR) SPCT(LCUR) SPCT(LCUR) I PCT(LCUR) ) PCT(LCUR) SPCT(LCUR) SPCT(LCUR) SPCT(LCUR) I PCT(LCUR) SPCT(LCUR) SPCT(LCUR) SPCT(LCUR) SPCT(LCUR) SPCT(LCUR) PPCT(LCUR) TIME =
-59.92 3
-59.43 9
-58.82 15
-57.97 21
-56.78 27
-55.15 33
-53.00 39
-50.31 45
-47.11 51
-43.53 57
-39.77 63
-36.13 69
-32.92 75
-30.49 81
-29.08 87
-28.88 93
-29.89 99
-32.01 105
-34.99 111
-38.53 117
-42.28 123
-45.95 129
-49.30 135
-52.16 141
-54.49 147
-56.28 153
-57.61 159
-58.55 165
-59.21 171
-59.71 177

-59.84
-59.34
-58.69
-57.80
-56.54
-54.83
-52.59
-49.81
-46.54
-42.91
-39.15
-35.55
-32.46
-30.17
-28.97
-28.97
-30.17
-32.45
-35.55
-39.15
-42.91
-46.54
-49.81
-52.59
-54.83
-56.54
-57.79
-58.68
-59.31
-59.78

30 PCT(LCUR)

4
10
16 22 28 34 40 46 52 58 64 70 76 82 88
94 100
106 112 118
124 130 136
142 148 154 160 166 172 178
-.26

= .13
= .10
= .08
= .05
= .02
= .00
= -.03
= -.05
= -.08
= -.10
= -.13
= -.15
= -.17
= -.20
= -.22
= -.24
30 YEARS

1 7
13 19 25
31 37 43
49 55 61 67 73 79 85
91 97
103 109 115 121 127 133 139 145 151 157 163 169 175

2 8
14 20 26 32 38
44 50
56 62 68 74 80 86 92 98
104 110
116 122 128
134 140 146 152 158 164 170 176

-59.76
-59.24
-58.56
-57.62
-56.29
-54.49
-52.17
-49.30
-45.95
-42.28
-38.53
-34.99
-32.01
-29.89
-28.88
-29.08
-30.49
-32.92
-36.13
-39.77
-43.53
-47.11
-50.31
-53.00
-55.15
-56.77
-57.96
-58.80
-59.39
-59.85

5
11
17 23 29 35 41 47 53 59 65 71 77 83 89
95 101
107
113 119 125
131 137 143
149 155 161 167 173 179

-59.68
-59.14
-58.43
-57.42
-56.02
-54.14
-51.72
-48.77
-45.36
-41.66
-37.92
-34.45
-31.59
-29.64
-28.83
-29.24
-30.83
-33.41
-36.71
-40.40
-44.15
-47.68
-50.80
-53.40
-55.45
-57.00
-58.12
-58.91
-59.48
-59.92

6
12 18 24 30
36 42 48 54 60 66 72 78 84 90
96 102 108
114 120
126 132
138 144 150 156 162 168 174 180

-59.60
-59.04
-58.28
-57.22
-55.75
-53.78
-51.27
-48.23
-44.76
-41.03
-37.31
-33.92
-31.19
-29.42
-28.81
-29.42
-31.19
-33.92
-37.31
-41.03
-44.76
-48.23
-51.27
-53.78
-55.74
-57.21
-58.27
-59.02
-59.56
-59.99




APPENDIX C
NUMERICAL EXAMPLE 1




BEACH NOURISHMENT PROJECTION
(Numerical Procedure)

General Location: Exavyple. I
Wave Height, H0 (Fig. 22):
Wave Period, T (Fig. 23):
Wave Direction, ao:
Deep Water Contour Orientation, o0:
Longshore Axis Orientation, p:
Grid Dimension, Ax: Time Increment, At:

2.,0 ft.,
6 X_ sec.,
90 o lo 0, i,90' o
.Joo ft 8(,4o sec

Closure Depth, h. (Fig. 8): Berm Height, B: Sand Diameter, D: Transport Factor, K (Fig. 5): VFACT:
Background Transport, QREF: IREF:
IMAX:
NTIMES: No. of Structures, NS:

AT ft.
(G ft. 0. mm
0,7'{
C ft3/s
I
ISo
0

Structure Specificiation
Structure Structure Structure
Number Location, I Length (ft)

Equilibrated Beach Width Ayo

Background Erosion
S(ff.) Erosion Rate, ER, (ft/yr) 0,o

Nourishment Specification

I Range

AN (Fig. 7) or From Profile: Ap (Fig. 7): Volume Per Unit Length: Ayo (Figs. 11 and 12):

ftl/3 ft1/3
ft3/ft
lie ft

80 to /00o 112
Sto
to to to

roV ? o u E- ros5 to w

Ay0




PLANFORM EVOLUTION OVER TIME
NO EROSION (DISTORTED SCALES) NO ER.
400.0
350.0
I-
U
LLJ
Li 300.0
250.0
LU
C_)
77
CI 200.0
--A B
t-
SH ..EIN.EN T.N.ET............5.ER
o s 150.0
0100.0
-
L50.0
-0.0 0--RR
-I 0 0IIII I1I
0 10000 20000 30000 q0000 50000 60000 70000 80000
0 YEARS SHORELINE LENGTH IN FEET -------------------- YEARS
Figure C-I. Numerical Example 1, Ayo = 112 ft, Nourishment 10 YEARS
Length = 2 Miles, Zero Background Erosion. __20 YEARS
- 30 YEARS




Y (T) VERSUS TIME
2 MILE PLRNFORM WITH NO EROSION NO ER
200.0
LU 175.0
_J 150.0 LU
cc
D 125.0
100.0
Li.. 75.0
75.0 Location A
50. .... ................................ Lo a io.
b-50.0 U.
2:25.0 Location C
.- -P -- --------- ~- - - -- -- - - - -- - - -
0.0 ...
c
-25.0
-50.0
-75.0
-100.0 I I I I I I I I I I I I I I I I
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 144500 TIME IN 'ER-RS ................... 49500
Figure C-2. Numerical Example 2, Shoreline Position Variation 59500
with Time at Locations Indicated and Shown in
Figure C-1.




INPUT FILE: DNRBS.INP
(Example No. 1)

EXAMPLE
2.00
17.0
0.0
90000.
80 10 80 11 81 11 82 11. 83 11 84 II: 85 11 86 II 87 11 88 1i 89 11. 90 II 91 1i 92 II: 93 II 94 II 95 II 96 II 97 II 98 II 99 II 100 II

NO. 1 NO BACK.
6.0 90.0 6.0 0.77 0.0 90000.
3.0 100000.
0
2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0

EROS. 90.0 1.0 0.0 3.0

NO STRUC.
180.0
0.0
49500. 140000.

2 MILE PROJ. 500.0 86400.0
1 180 10950
2.0 60000.
2.0

0
3.0




OUTPUT FILE: DNRBS.OUT
(Example No. 1)
EXAMPLE NO. 1 NO BACK. EROS. NO STRUC. 2 MILE PROJ.
HO = 2.00 FT., T = 6.00 SEC., ALPO = 90.00 DEG., BTAO = 90.00 DEG., XMU = 180.00 DEG., DX = 500.00 FT., DT = 86400.00 SEC. HSTR = 17.00 FT., B = 6.00 FT., XK = .77 VFACT = 1.00
QBKREF = .00 FT.**3/SEC.
IREF = 1, IMAX = 180, NTIMES = 10950, NS = 0

.00 .90E+05
3.00 .10E+06

.00 .50E+05 3.00 .14E+06

2.00 .60E+05
2.00

BACKGROUND EROSION TRANSPORT RATES

1 6
11
16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101
106 ill
116 121 126 131 136 141 146 151 156 161

.000 .000 .000 .000
.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

2 7
12 17 22 27 32 37 42 47 52 57 62 67 72 77 82 87 92 97'
102 107 112 117 122 127
132 137 142 147 152 157 162

.000
000 000 .000 000 000 .000 000 000 .000 .000 .000 .000 .000 .000 .000 000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 000 .000 000 .000 .000

3 8
13 18
23 28 33 38
43 48 53 58 63 68 73 78 83 88 93 98
103 108 113 118 123 128 133 138 143 148 153 158
163

. OOE+00 .90E+05

3.00

.000
.000 000 .000 .000 000 .000
* 000 000 .000 000 .000 .000
* 000 .000 .000 000 .000 .000 .000 .000 .000 .000 .000 .000 000 .000 .000 89
000 .000

4 9
14 19 24 29 34 39 44 49 54 59 64 69 74 79 84 89 94 99 104 109
114 119 124 129 134
139 144
149 154 159 164

.000
.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

5
10
15 20 25 30 35 40 45 50 55 60 65 70 75 80
85 90
95 10o 105 110
115 120 125 130
135 140
145 150
155 160
165

.000
.000 000 000 000 .000 .000 .000 .000 .000 .000 .000 .000 000 .000 .000 000 .000 .000 000 .000 000 .000 .000 .000 000 000 .000 .000 .000 .000 .000 .000

ririri *1 ,ri




171 176
181

.000 .000 .000

172
177

80 100
INITIAL SHORELINE

1
3
5
7
9
11
13 15
17 19
21 23 25 27 29 31 33 35 37 39 41
43 45 47 49 51 53 55 57
59 61
63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93
95 97 99
101
103 105 107 109 i1
113

0.
1000. 2000.
3000. 4000. 5000. 6000. 7000. 8000. 9000. 10000. 11000. 12000. 13000. 14000. 15000.
16000. 17000. 18000. 19000. 20000. 21000. 22000. 23000. 24000. 25000. 26000. 27000. 28000. 29000.
30000. 31000. 32000. 33000. 34000. 35000. 36000.
37000.
38000. 39000. 40000. 41000. 42000. 43000. 44000. 45000. 46000. 47000. 48000. 49000. 50000. 51000. 52000. 53000. 54000. 55000. 56000.

(INCL. NOURISHMENT) POSITION

.00
.00 .00 .00
.00
.00 .00
.00 .00
.00
.00 .00 .00 .00 .00 .00 .00 .00 .00
.00 .00 .00 .00
.00
.00 .00 .00 .00 .00
.00
.00 .00 .00 .00 .00
.00 .00 .00 .00 .00
112.00 112.00 112.00 112.00 112.00 112.00 112.00 112.00 112.00 112.00
.00 .00 .00 .00 .00 .00
.00

2
4
6
8
10
12 14
16 18 20
22 24 26 28 30
32 34 36 38 40 42 44 46 48 50
52 54 56 58 60 62 64 66 68 70
72 74 76 78 80 82 84 86 88 90
92 94 96 98 100
102 104 106 108
110
112
114

500.
1500.
2500. 3500. 4500. 5500. 6500. 7500. 8500. 9500.
10500.
11500. 12500. 13500. 14500. 15500. 16500. 17500. 18500. 19500. 20500. 21500. 22500.
23500.
24500. 25500. 26500. 27500. 28500. 29500. 30500.
31500. 32500. 33500. 34500.
35500.
36500. 37500. 38500. 39500. 40500. 41500. 42500. 43500. 44500. 45500. 46500. 47500. 48500. 49500. 50500. 51500. 5250 5350 545C 55500. 56500.

.00 .00 .00
.00
.00
.00
.00
.00 .00 .00 .00 .00 .00
.00
.00
.00
.00
.00
.00
.00
.00 .00 .00 .00
.00 .00 .00 .00 .00 .00
.00
.00 .00 .00
.00
.00 .00 .00 .00 112.00 112.00 112.00 112 .00 112.00 112.00 112.00 112.00 112.00 112 .00 112.00
.00 .00 90 .00
.00 .00
.00 .00

.000 173 .000 178

.000 174 .000 179

.000 175
.000 180

.000 .000

C 117 r% n r% n *1 11 1 m P7 r A A r% n

t !f|'' f'f I f ,% I 1 I II f I II T




Full Text

PAGE 1

Development of Methodology for Thirty-Year Shoreline Projections in the Vicinity of Beach Nourishment Projects December 15, 1989 Prepared for: Division of Beaches and Shores Florida Department of Natural Resources 3900 Commonwealth Boulevard Tallahassee, FL 32399 Prepared by: R. G. Dean and Jonathan Grant Coastal and Oceanographic Engineering Department University of Florida 336 Well Hall Gainesville, FL 32611

PAGE 2

UFL/COEL-89/026 DEVELOPMENT OF METHODOLOGY FOR THIRTY-YEAR SHORELINE PROJECTIONS IN THE VICINITY OF BEACH NOURISHMENT PROJECTS by Robert G. Dean and Jonathan Grant Prepared for: Division of Beaches and Shores Florida Department of Natural Resources 3900 Commonwealth Boulevard Tallahassee, FL 32399 December 15, 1989 ____________________________________________

PAGE 3

TABLE OF CONTENTS INTRODUCTION 1 BACKGROUND 1 General Description of Sediment Transport Processes in the Vicinity of A Beach Nourishment Project .................... ............ 1 Profile Equilibration .................... ............. 2 "Spreading Out" Losses .................. :. ........... 2 Background Erosion ..................... ............ 5 Role of Retention Structures ............................ 5 Role of Sediment Size on Transport Rates ................... .... 5 Significance of Wave Height ................... .......... 10 W ave Direction ................... .................... 10 General Characteristics of Equilibrium Beach Profiles .............. 10 METHODOLOGY 12 Profile Equilibration ................... ............... .12 Longshore Sediment Transport ........................... 20 Combined Linearized Equations ................... ........ 22 Rectangular Beach Nourishment Project ................... ...25 Erosion Adjacent to a Littoral Barrier ................... ..... 30 Numerical Solution .................................. 33 Boundary Conditions ................... ............... .36 Wave and Other Parameters of Use in Applying the Methodology ........ 38 STEP-BY-STEP DISCUSSION OF METHODOLOGY 38 Graphical Procedure ................... ................ 38 CASE A -NOURISHMENT ALONG AN UNINTERRUPTED SHORELINE 41 Step 1 -Specify Beach Nourishment Project Characteristics ........... 41 Step 2 -Determine the Equilibrated Project Width, Ayo ............. 41 Step 3 -Calculate Effective Alongshore Diffusivity, G .............. 41 Step 4 -Calculate Shoreline Position Due to Spreading Out Losses ...... ...43 Step 5 -Calculate Background Erosion Losses .................. 43 Step 6 -Calculate Resulting Shoreline Position .................. 43 ii

PAGE 4

CASE B -NOURISHMENT DOWNDRIFT OF A LITTORAL BARRIER 43 Step 1 -Specify Beach Nourishment Characteristics ............... 44 Step 2 -Determine the Equilibrated Project Width, Ayo ............. .44 Step 3 -Calculate Effective Alongshore Diffusivity, G ............... 44 Step 4 -Calculate Shoreline Position Due to Spreading Out Losses ...... ...46 Step 5 -Calculate Background Erosion Losses ................... 46 Step 6 -Calculate Resulting Shoreline Position .................. 46 NUMERICAL PROCEDURE 47 CASE A -NOURISHMENT ALONG AN UNINTERRUPTED SHORELINE 47 STEP 1 -Specify Beach Nourishment Project Characteristics .......... 47 STEP 2 -Determine Equilibration Project Width, Ayo ............. .47 STEP 3 -Develop Background Erosion Data as Piecewise Linear Segments ..47 STEP 4 -Develop Input File ............................ 47 STEP 5 -Run Program .................... ........... 51 STEP 6 -Examine Output in File DNRBS.OUT ................. 51 CASE B -NOURISHMENT WITH STRUCTURES PRESENT 57 STEP 4B -Specify a Reference Background Transport .............. 57 STEP 5B -Specify Structure Location(s) and Length(s) in Program ...... 57 EXAMPLES ILLUSTRATING APPLICATION OF METHODOLOGY 59 Graphical Examples .................... ............. 59 Numerical Examples .................... ............. 59 REFERENCES 65 APPENDIX A 66 APPENDIX B 72 APPENDIX C 84 APPENDIX D 94 APPENDIX E 104 111

PAGE 5

APPENDIX F 114 APPENDIX G 125 APPENDIX H 134 APPENDIX I 144 iv

PAGE 6

LIST OF FIGURES 1 Effect of Nourishment Material Scale Parameter, AF, on Width of Resulting Dry Beach. Four Examples of Decreasing A. ................ .... 3 2 "Spreading Out" Losses Occurring Due to Mobilization of Sediments by Waves. 4 3a Variation of Shoreline Position with Time at Various Locations Relative to a Nourishment Project. No Background Erosion. .................6 3b Variation of Shoreline Positions with Time at Various Locations Relative to a Nourishment Project. Uniform Background Erosion of 2 ft/yr. ........7 4 Illustration of Nourishment Stabilization by Terminal Structure. ........8 5 Plot of K vs D. Results of Present and Previous Studies (modified from Dean, 1978). ........................................... 9 6 Shoreline Orientation Downdrift of a Complete Littoral Barrier .......... 11 7 Beach Profile Factor, A, vs Sediment Diameter, D, in Relationship h = Ay2/3 (modified from Moore, 1982). Note: A(ftl/3) = 1.5 A(ml/) .......... 13 8 Recommended Distribution of h. Along the Sandy Shoreline of Florida. ....14 9 Three Generic Types of Nourished Profiles. ................... ..15 10 Effect of Increasing Volume of Sand Added on Resulting Beach Profile, AF = 0.1 m1/3,AN = 0.2 m1/3, h = 6m, B = Im.......... .......... 17 11 Variation of Non-Dimensional Shoreline Advancement Ayo/W. with A' and V'. Results Shown for h,/B = 2.0. .......................... 18 12 Variation of Non-Dimensional Shoreline Advancement Ayo/W. with A' and V'. Results Shown for h./B = 4.0. .......................... 19 13 Definition Sketch ................... ............... .21 14 Variation of Ratio C,/Co vs h,/Lo. ......................... 23 15 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, n = 0.78, h. From Fig. 8, B Estimates Ranging from 6 to 9 ft, Ho from Figure 23, T From Figure 24. .................. 24 16 Example of Evolution of Initially Rectangular Nourished Beach Planform. Example for Project Length, £, of 4 Miles and Effective Wave Height, H, of 2 Feet and Initial Nourished Beach Width of 100 Feet. .............. 26 17a Evolution of an Initially Rectangular Beach Planform on an Otherwise Straight Shoreline. Results for t' = 0, 0.1, 0.2, 0.5 and 1.0. ............... 27a 17b Evolution of an Initially Rectangular Beach Planform on an Otherwise Straight Beach. Results for t' = 0, 2.0, 4.0, 6.0 and 8.0. ................. 27b v

PAGE 7

17c Evolution of an Initially Rectangular Beach Planform on an Otherwise Straight Beach. Results for t' = 0, 10.0, 15.0, 20.0 and 30.0. ............... 27c 18 Percentage of Material Remaining in Region Placed vs. the Parameter VUGt7 .29 19 Example of Shoreline Evolution in Response to Littoral Barrier. Based on Method of Pelnard-Considere. Longshore Sediment Transport Rate Used in Example = 180,000 cubic yards per year. Littoral Barrier Length = 160 ft. 31 20 PelnardConsidere Solution for Shoreline Recession Downdrift of a Complete Littoral Barrier .......... .. .... ................... .32 21 Two Alternative Methods for Predicting Beach Nourishment Performance Downdrift of a Littoral Barrier ............................. 34 22 Computational Scheme Used in Numerical Method. ............... 35 23 Recommended Values of Effective Deep Water Wave Height, Ho, Along Florida's Sandy Shoreline. ................... ............... 39 24 Recommended Values of Effective Deep Water Wave Period, T, Along Florida's Sandy Shoreline. ................... ............... 40 25 Form for Computation of Performance Along Uninterrupted Shoreline .....42 26 Form for Computations of Performance Downdrift of a Littoral Barrier ....45 27 Data Input Preparation Form for Numerical Procedure ............. 48 28 Input File DNRBS.INP for Example 2 ....................... .49 29 Example of Output File DNRBS.OUT for Input File in Figure 27. Example No. 1. (Total of 11 Pages of Output. ......................... 52 30 Estimates of Net Annual Longshore Sediment Transport Along Florida's East Coast ......................................... 58 C-1 Numerical Example 1, Ayo = 112 ft, Nourishment Length = 2 miles, Zero Background Erosion ................... .. ........ ..... .86 C-2 Numerical Example 2, Shoreline Position Variation with Time at Locations Indicated and Shown in Figure C-1. ................. ...... .87 D-1 Numerical Example 2, Ayo = 112 ft, Nourishment Length = 2 miles, Uniform Background Erosion = 2 ft/yr. .......................... 96 D-2 Numerical Example 2, Shoreline Position Variation with Time at Locations Indicated and Shown in Figure D-1. ........................ 97 E-1 Numerical Example 3, Ayo = 112 ft, Nourishment Length = 2 miles, Variable Background Erosion ............................... .106 E-2 Numerical Example 2, Shoreline Position Variation with Time at Locations Indicated and Shown in Figure E-1 .......................... 107 vi

PAGE 8

F-1 Numerical Example 4, Ayo = 112 ft, Nourishment Length = 1,000 ft, No Background Erosion ................... .................116 F-2 Numerical Example 2, Shoreline Position Variation with Time at Locations Indicated and Shown in Figure F-............. ... ............. 117 G-1 Numerical Example 5, 112 ft Long Structure at North End of Project, Nourishment Length = 2 miles, No Background Erosion. ................ 126 G-2 Numerical Example 2, Shoreline Position Variation with Time at Locations Indicated and Shown in Figure G-1. ................. ...... .127 H-1 Numerical Example 6, 112 ft Long Structure at South End of Project, Nourishment Length = 2 miles, Uniform Background Erosion. ............. 136 H-2 Numerical Example 2, Shoreline Position Variation with Time at Locations Indicated and Shown in Figure H-1. ........................ 137 I-1 Numerical Example 7, 112 ft Long Structure at South End of Project, Nourishment Length = 2 miles, Variable Background Erosion. ............. 146 I-2 Numerical Example 2, Shoreline Position Variation with Time at Locations Indicated and Shown in Figure I-1.......................... 147 vii

PAGE 9

DEVELOPMENT OF METHODOLOGY FOR THIRTY-YEAR SHORELINE PROJECTIONS IN THE VICINITY OF BEACH NOURISHMENT PROJECTS INTRODUCTION The purpose of this report is to develop and illustrate with examples readily applied methodologies for calculating the response of shorelines in the vicinity of beach nourishment projects. The need for such methodology is a result of Florida Statutes 161.053(G) and Rule 16B-33.024(3)(e) which require, with minor exceptions, coastal structures to be located landward of a thirtyyear projection of the Seasonal High Water Shoreline (SHWL). The conceptual interpretation of these Statutes and Rule is that the performance of the beach nourishment project should be considered in projecting the Seasonal High Water Line (SHWL) position to a time thirty years into the future. This requires consideration of both the background erosion rate which is the normal rate in areas that have not been nourished and the shoreline retreat component due to "spreading out" losses from the beach nourishment project. BACKGROUND General Description of Sediment Transport Processes in the Vicinity of a Beach Nourishment Project In general, when sand is placed in conjunction with a beach nourishment project, this project represents an "anomaly" to the shoreline planform and the natural processes will tend to smooth out this anomaly. In addition, many times the placed profile will be steeper than the natural profile and the profile will tend to equilibrate over time. The sections below describe the individual processes and characteristics of the response of a beach nourishment project. 1

PAGE 10

Profile Equilibration As noted, beach nourishment projects are generally placed with profiles which are steeper than the natural profile for the size of sediment that is used in the beach nourishment project. Thus over the years this profile will tend to equilibrate to its natural shape. In addition, if the sediment size used in the beach nourishment is fine, the profile will tend to be rather mild in slope and the shoreline advancement will be small for a given volume of beach nourishment per unit length of beach. Figure 1 shows the qualitative effect of grain size in terms of the dry beach width for the same added volume per unit length of beach. The upper panel presents the profile that would result for a beach nourishment grain size which is larger than the native sand resulting in a fairly wide dry beach width. The three lower panels illustrate the effect of decreasing grain size maintaining the volume per unit beach length the same. It is seen that with decreasing grain size the dry beach width progressively decreases to a point where in the lower panel the dry beach width is zero. For this condition all of the sand that has been placed has been moved offshore in a profile which is consistent with the grain size used in the nourishment. "Spreading Out" Losses The placement of a beach nourishment project results in a planform anomaly which interacts with the waves to result in sediment transport away from this anomaly. This process is illustrated in Figure 2 and shows the transport occurring away from the anomaly in a manner that will result in a smoothing or spreading out of the sediment. The term "spreading out" losses actually refers to a redistribution of the sediment and not a total loss to the system but rather a loss from the region in which the sediment is placed. As will become evident later, this loss from the nourished area is manifested as a gain of sediment volume in the nourishment-adjacent areas. 2

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---) 92.4m [h,= 6m a) Intersecting Profiles, AN= 0.1m/ AF = 0.14m1/3 .. 45.3m h. = 6m b) Non-Intersecting Profiles AN= AF= 0.m1/3 .-. ..:. S11-5.9m Sh, = 6m c) Non-Intersecting Profiles AN= 0.lm1/3AF = 0.09ml/3 1z 10 O -< '-h, = 6m 5I -d) Limiting Case of Nourishment Advancement, 13 Non-Intersecting Profiles, AN= 0.1m1/3,AFl= 0.085m I I I I I I 0 100 200 300 400 500 600 OFFSHORE DISTANCE (m) Figure 1. Effect of Nourishment Material Scale Parameter, AF,on Width of Resulting Dry Beach. Four Examples of Decreasing AF. 3

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S "Spreading Out" Losses SWaves S Planform Anomaly Due to Beach Nourishment "Spreading Out" Losses (From Region Placed) Figure 2. "Spreading Out" Losses Occurring Due to Mobilization of Sediments by Waves. 4

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Background Erosion Usually the need for a beach nourishment project is due to a background erosion which, for an ideal project, is relatively slow. With the placement of the beach nourishment project, there will be two components of shoreline retreat. It will be assumed that the two components of shoreline recession, i.e. background erosion and the component due to spreading out losses, can be added linearly. The background erosion which was present prior to the placement of the beach nourishment project will continue. Figure 3 illustrates qualitatively the superposition of these two components for several locations within and adjacent to a beach nourishment project. Figure 3a presents the case for no background erosion and Figure 3b for a uniform background erosion of 2 ft/yr. Role of Retention Structures In some cases, especially short beach nourishment projects, it may be worthwhile to consider the use of retention structures to extend the life of the projects. Figure 4 illustrates qualitatively one such application. Structures must be used with great care, especially in areas where there is a substantial longshore transport magnitude. An additional situation in which retention structures have been used effectively to prevent loss of sediment in Florida has been at the ends of littoral systems such as at the termini of barrier islands. Two such locations are the north jetty at John's Inlet in Pinellas County and the two small terminal structures at the south end of Gasparilla Island in Lee County. Role of Sediment Size on Transport Rates It has been noted that the dominant losses due to a beach nourishment project are due to spreading out losses or transport away from the region where the sediment is placed. The sediment transport is proportional to a coefficient, K, which has been found to depend on sediment size as shown in Figure 5; thus with the use of coarser grained material, the project will perform much more effectively. Although there has not been any substantial documentation to illustrate adverse effects of using material which is substantially coarser 5

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ZP B 100 _A c in --D 00nSBPlanform Showing 0L O 0 Locations Plotted ZJ= 50^ IJ 0 00 I I I I 0 5 10 15 20 25 30 TIME (Years) AFTER NOURISHMENT Figure 3a. Variation of Shoreline Position with Time at Various Locations Relative to a Nourishment Project. No Background Erosion.

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100 \ AA OT B-Y r A 0 c OE 50 --!---D C1 O Planform Showing ,Z0 e Locations Plotted NrJ -50 hent I I I I I 0 5 10 15 20 25 30 TIME (Years) AFTER NOURISHMENT Figure 3b. Variation of Shoreline Positions with Time at Various Locations Relative to a Nourishment Project. Uniform Background Erosion of 2 ft/yr.

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*I Figure 4. Illustration of Nourishment Stabilization by Terminal Structure. 8

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2.0 1 Result From This Study, -_ Santa Barbara \ Relationship Suggested h 1.0 -Previously 0 III I 0 0.5 1.0 DIAMETER, D (mm) Figure 5. Plot of K vs. D. Results of Present and Previous Studies (modified from Dean, 1978).

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than the native material, it has been hypothesized that if such material is used it may effectively armor the beach in the nourishment area thereby resulting in less transport from the area nourished and a deficit and associated erosion on the area downdrift of the project. Significance of Wave Height After placement of a beach nourishment project, it is evident intuitively that the mobilizing effects of wave height cause profile equilibration and the spreading out losses mentioned earlier. Thus the determination of reliable, effective wave heights is important to the prediction of the performance of any beach nourishment projects. As will be described later, for two identical projects which are placed in areas where the wave height differs by a factor of two, the longevity of these projects would differ by a factor of 5.3. Wave Direction It is somewhat surprising that on a long, uninterrupted shoreline the effect of wave direction is relatively unimportant to the performance of a beach nourishment project. The interpretation of this insensitivity will be discussed in a later portion of this report. However, wave direction is extremely important in the case of a beach nourishment project located adjacent to a structure which interferes with the longshore sediment transport. Figure 6 illustrates such a situation where sand is placed immediately downdrift of a jetty and the orientation of the beach planform immediately adjacent to the jetty is parallel to the incident wave crests. Thus, it will be necessary to provide estimates of wave direction or to develop alternative methodologies which do not require accurate estimates of wave direction. General Characteristics of Equilibrium Beach Profiles In general, equilibrium beach profiles tend to be concave upward and the profiles tend to be milder in slope for the finer sediment and steeper for coarser sediment. Equilibrium beach profiles have been found by Bruun (1954) and Dean (1977) to be reasonably well 10

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Inlet .I \ \ Figure 6. Shoreline Orientation Downdrift of a Complete Littoral Barrier. 11

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represented by the form h(y) = Ay2/3 (1) in which h is the depth at a distance y seaward of the shoreline and A is a scale parameter. A significant contribution to the objectives of this report was developed by Moore (1982) in the form of a plot of the sediment scale parameter, A, in terms of the sediment size, Figure 7. A second important relationship to the objectives of this study is that of closure depth, h,. Closure depth is a concept which describes the maximum depth to which sediments will be mobilized by the waves. Although in general this closure depth is expected to be dependent on wave height and wave period, for purposes of this study, the closure depth will be regarded as a value dependent on position around the state of Florida. The recommended closure depth versus location around the state is presented in Figure 8. METHODOLOGY Profile Equilibration In considering the profiles resulting from beach nourishment, generically there are three types of nourished, equilibrated profiles. These are presented in Figure 9. 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,. 12

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1.0 E Suggested Empirical Relationship tj From Hughes' Feld Results From Individual Field Profiles where a .,, Range of Sand Sizes was given .0.10 ---A 1From Swart's o 6A Laboratory Results w LI
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24 S20------S16=--h.(Feet) -_12 16 20 24 12 JA MA ST CC CL VB VE a VWP Ml 12 16 20 24 h* (Feet) Figure 8. Recommended Distribution of h, Along the Sandy Shoreline of Florida. 14

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AyB Added Sand .h, a) Intersecting Profile AF>AN '-. W*AyAdded Sand | b) Non-Intersecting Profile Ay ---i-.^ .I Virtual Origin of '~:. Nourished Profile -I Added Sand c) Submerged Profile AF
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The third type of profile that can occur is the submerged profile (Figure 9c) the characteristics of which are shown in greater detail in Figure 10. 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 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, Ayo, resulting in a profile of the second type described. The next major section describes the methodology for calculating planform response to a beach nourishment project. It is assumed that profile equilibration occurs when the material is placed. This assumption is not important to the final thirty year projection. Actually, of course the profile equilibration will occur gradually, but will probably be near completion within a few years. This assumption merely allows the overall response calculations to be carried out in two steps. Following the discussion of profile equilibration, graphical and numerical methods are presented for predicting the shoreline (planform) evolution. As might be expected the numerical method provides greater flexibility for representing realistically the actual situation. It can be shown that the initial additional dry beach width, Ayo, is related to the placed and native sediment characteristics and the closure depth, h,, and berm height, B. To render the results more compact, the results are cast in the following nondimensional form AYO h, f A, V = -f (A/A, V /BW,, (2) in which W, is the width of the active surf zone on the native profile, i.e. W = (h/AN)3/2 (3) Figures 11 and 12 present results of Ayo/W. for h,/B values of 2 and 4, respectively. 16

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OFFSHORE DISTANCE (m) 0 100 200 300 400 500 SI I I I I I E 4 B = 1.5m Z 0 S -h*=6m W10L a) Added Volume = 120 m3/m 0 O0 O c) Added Volume = 900 m/m' d b) Added Volume = 490 m3/m w 0 ICase of Incipient Dry Beach Figure 10. Effect of ncreasing Volume of Sand Added on Resulting 0 0 d) Added Volume = 1660 m3/m ... Case of Incipient Dry Beach Figure 10. Effect of Increasing Volume of Sand Added on Resulting Beach Profile. AF= 0.1m 3, AN= 0.2m1/3, h, = 6m, B = Im. 17

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AV = AV/BW, = 10.0 __ 1.0 --t-o ,o I A / = 0.5 -VO _I -I -Asymptotes I V' = 0.02 for Ayo= 0 I --0-----0.10 -i ~ -I ---3E~^B---h-J-------------------0.001 -Definition Sketch WW-_ 0 1.0 2.0 2.8 A'' =A0./A Figure 11. Variation of Non-Dimensional Shoreline Advancement Asymptoteso with A' and V. Results Shown for h, 0.02 = 2.0. 0 -18 A= 0.005 ..VA AFr = VIBW, = 0.002 0.001 Def inition Sketch 0 1.0 2.0 2.8 A' = AF/AN Figure 11. Variation of Non-Dimensional Shoreline Advancement Ayo/W* with A' and -V'. Results Shown for h, /B = 2.0. 18

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1.0 S0 Non-Intersecting i Profiles i -V =/BW, =5.0 /i Intersecting 2/ Profiles _ _ !m i =L SY V' .05 Wt Asymptotes for Ayo= 0 I 0.02 0.01 0.1 --------,.,---,. ---------.. WA V W V' = 0.002. 0 .01 1.0 i 2 -Definition Sketch A-w--. A F V W -B AN' BW* S0.0001 = 0.002 0.001 0 1.0 2.0 2. 8 A' and V. Results shown for h, /B = 4.0. 19 19

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It is seen that for each nondimensional volume, the non-dimensional additional beach width increases with increase in ratio of sediment scale parameters; however, the increase is relatively small for ratios greater than 1.2. Additionally, there is some lower ratio of scale parameters for each non-dimensional volume below which there will be no additional dry beach width. This corresponds to the case presented in Figure Id. As noted previously, the profile equilibrations will be assumed to occur instantaneously. The stage is now set for consideration of the longshore sediment transport and planform evolution. Longshore Sediment Transport The equations available for representing planform evolution are a sediment transport equation and a sand conservation (or continuity) equation. The transport equation is empirically based and describes the total transport in the longshore direction due to waves arriving at a breaking angle, as to the shoreline. The continuity equation is fundamental and simply balances sediment volume changes with transports into and out of the region under consideration. These equations are: K H5/2 igV sin(P -Yb) cos(f -ab) (4) Transport: Q = 8(s -1)(1 -(4) Continuity: -(5) at ax in which V is sediment volume per unit length of beach, g is gravity, C is the ratio of breaking wave height to water depth (usually taken as 0.78), f represents the azimuth of the outward normal to the shoreline, ab represents the azimuth of the direction from which the breaking waves originate, s is the specific gravity of the sediment (approximately 2.65), p is the inplace porosity of the sediment (usually taken as 0.35) and t is time. Figure 13 presents a definition sketch for aCb and f/. The sign convention used in this report is that the positive x (and Q) direction are to the right as an observer looks offshore. For most shoreline evolution models and those that will be presented here, the model predicts the position of one contour, such as the NGVD contour or the SHWL contour. 20

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0 N '0 R.e:,:-..,Shoreline Reference Base Line +Q x Figure 13. Definition Sketch. 21

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These models assume that as beaches erode or accrete the profile moves without change of form in a landward or seaward direction, respectively. Thus after equilibration occurs, the shoreline change, Ay, associated with a volumetric change, AV, can be shown to be given by Ay = B (6) (h, + B) The two governing equations, namely the transport and conservation equations, can be applied directly to predict the evolution of a beach nourishment project or they can be combined in a linearized manner. Both of these approaches will be described in the following sections. Combined Linearized Equations Eq. (4) describes the sediment transport in terms of the difference between the shoreline orientation and wave direction. Foregoing the algebra, it can be shown that the combined and linearized equation governing the evolution of a beach system is 9y 82y = aG (7) in which the parameter, G, can be interpreted as the "alongshore diffusivity" and is expressed as K HO2.4K o904 cos1W -( -co) cos 2(Po -a.) 8(s -1)(1 -p)C*c0.4(h. + B) cos(/o -a,) ( where the subscript "o" denotes deep water conditions, C, is the wave celerity in the water depth h, and Eq. (8) is derived in Appendix A. The ratio C,/Co is C./Co = tanh ( 2 ) (9) in which Co = gT/2r, CGo = gT/4r and C,/Co is presented vs h,/Lo in Figure 14. Figure 15 presents approximate values of G along the sandy beach shorelines of the state of Florida. Equation (7) is the so-called heat conduction or diffusion equation which is well-known in classical physics and has many known solutions. Two solutions which are of interest 22

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1.0 fe005-------^-----------------------------C O P 0.05--------0 ------T(=| ---0 0.05 0.10 0.15 0.20 h*/Lo Figure 14. Variation of Ratio C*/Co vs. h*/Lo

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0.14 .G(ft2/s) _.02 0.0060.10 0.14 0.02. 0.02 0.06 0.10 0.14 G(ft2/S) .. Figure 15. 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, K= 0.78, hFrom Fig. 8., B Estimates Ranging from 6 to 9 ft, Ho from Fig. 23, T from Fig. 24. 24

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here will be discussed below; these solutions pertain to the graphical methodology thereby allowing a first estimate of the performance of a beach nourishment project. These solutions and the development of the combined and linearized equation concepts are due to PelnardConsidere (1956). Rectangular Beach Nourishment Project The first solution of interest is for the evolution of an initially rectangular beach nourishment project of length, £, which projects a distance Ayo from the original shoreline. The solution is aYo 0 2x e 2x y(x,) = erf ( + -erf -1) (10) in which the term "erf" refers to the error function described mathematically as erf(z) =e-" du (11) in which u is a dummy variable. Figure 16 illustrates an example of the performance of such a beach nourishment project and Figures 17a, b and c present the results in non-dimensional form. It can be seen from Eq. (9) that if the term -is the same for two beach nourishment projects the nondimensional performance of the two beach nourishment projects will be the same. Thus, for two projects constructed with the same wave characteristics but with one project twice the length of the second project, the first project will lose the same percentage of sediment as the second project in a duration that is four times as long as that for the second project. Similarly if two projects have the same length but the first project has a wave height onehalf that of the second wave height then the first project will have a longevity which is in excess of five times the longevity of the second project. In general this relationship may be stated as 2 = 1 ()2 )224 (12) 25

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DISTANCE FROM ORIGINAL SHORELINE, y (ft) 1 00 Original Nourished Beach Planform : 1" PPlanform After 3 Months /-8 --10 months -60 7 Years 40 '30 Years -------'.-130 Years Pre-Nourished .--S" / --20 : horeline 6 4 2 0 2 4 6 8 ALONGSHORE DISTANCE, X (miles) Figure 16. Example of Evolution of Initially rectangular Nourished Beach Planform. Example for Project Length, 1, of 4 Miles and Effective Wave Height, H, of 2 feet and Initial Nourished Beach Width of 100 Feet.

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1.2 1.I Gt 1 .t' 16 G 1.0 Initial Planform, t' = 0.0 0.9 -\ \ 0.8 \ \ : O 0.7 -. 0.6 0.5 0. 0.0 --1 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 x/ (/2) 0t t.3 --------------------v-0. Figure 17a. Evolution of an Initially Rectangular Beach Planform -----------t'=0.2 on an Otherwise Straight Shoreline. Results for ------t=0.5 S= 0.2 0.5 and 1.0. ------\= .\ \ 0.0 ---TI II I I I I I I 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1.0 4.5 5.0 5.5 6.0 6.5 7.n 7.5 8.0 ...................... t 0. 1 Figure 17a. Evolution of an Initially Rectangular Beach Planform -----.-t' =0.2 on an Otherwise Straight Shoreline. Results for -t' 0.5 t' = 0, 0.1, 0.2, 0.5 and 1.0. -t'=l.0

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1.2 ---i------.1 1.0 Initial Planform, t' = 0.0 0.9 0.8 t' =16 Gt 0.7 -2 0 0.5 -j ~0.5 ... .. .. ---------..---_....-0 .-...-* 0.3 -----------------0.2 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 x/(Z/2) t' =0.0 t' =2.0 Figure 17b. Evolution of an Initially Rectangular Beach Planform on an t' =.0 Otherwise Straight Shoreline. Results for t' = 0,2.0,4.0, 6.0 and 8.0. t =8.0 _tl'=8.0

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1.2 -. Gt 1.I t' = 16 1.0 1.0 ---. -----------------Initial Planform, t' = 0.0 0.9 0.67 -------.----.------------------------------------0.8 o 0.7
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in which tl and t2 represent the times required for projects 1 and 2 to lose the same percentage of sand from the region placed. Thus, the longevity of a project in terms of the time required to lose a certain percentage of the sediment from the project area varies directly as the square of the length of the project and inversely as the 2.4 power of the wave height. Equation (10) may be integrated to determine the fraction of material, M, remaining within the area placed. This is shown formally as 1 ) /2 M(t) = /2 y(x,t)dx (13) Ayot f-/2 and upon carrying out the integration the result is M(t) = 2 [e-/2v + erf (14) which is plotted in Figure 18 where the horizontal axis is the parameter encountered previously in the solution for the evolution of this particular planform. If we are interested in the time required for 50% of the nourished material to be transported out of the area placed, then from Figure 17 we see that the appropriate value of G-/£e is 0.46. Thus the time required to lose 50% of the sediment from the region placed is t5o = 0.21(15) G in which all variables are in consistent units. A more readily applied form is 5o = 8.7 2 (16) where t50 is in years, e is in miles and Hb is the breaking wave height in feet. As an example a project 2 miles in length with an effective breaking wave height of 2 ft would "lose" 50% of the volume placed due to spreading out losses in 22 tso = 8.7 = 6.15 years (17) It is emphasized that this solution is for a long unobstructed shoreline and includes only spreading out losses, i.e. no background erosion. 28 L___________

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S/Gt/-, SO 1.0 0.5 1.0 -'ZLU t = Time After Placement S0 N) G= Alongshore Diffusivity Initial UL .-Asymptote Planform OZz0.5M=1 -: z---^ :j t0 z 0 -. M -O.0 Ow 0 1 2 3 4 5 6 Figure 18. Percentage of Material Remaining In Region Placed vs. the Parameter Gt/j

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Erosion Adjacent to a Littoral Barrier The second analytical solution of relevance to this study is that of the downdrift erosion adjacent to a littoral barrier as shown in Figure 19. The solution for this situation is applicable for an initial condition of a straight and uniform shoreline and a wave arriving at a constant direction. The solution is presented as tan__ 0 --(18) (X, t) = Gexp -( < erfc ( )] (18) y(x,t) = Yerfc ( -, t t > t, (19) where erfc(z) = 1erf(z) (20) Y1r t 4G tan2 (21) in which Y is the length of the structure, 0 represents the angle of the approach wave and tc is the time at which bypassing commences. Because we are interested primarily in the beach response downdrift of a barrier and there is usually no bypassing, Eq. (18) would be the solution of primary interest. Figure 20 presents the nondimensional solution, y/( \i tan 0), versus nondimensional distance, x/IV4Gt, from the downdrift jetty. There are two approaches to predicting shoreline changes downdrift of a littoral barrier, such as a jetty. One method, that just described, requires knowledge and specification of an effective wave direction. Available information to define wave directions is quite limited, especially on the west coast of Florida. Fortunately a second method, which will be recommended here, requires data which are more readily available along the Florida coastline. The recommended procedure utilizes background erosion data rather than an effective wave direction. The justification for the use of background erosion data rather than wave 30

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* S0 YEARS a 2 £ 2 V DISTANCE LANDWARD (ft) 0.5,.~ Litt .Littoral 1 0.5 100 Barrier ,DISTNDISTANCE 2 \ SSEAWARD (ft) 020 \ \ -Initial Shoreline a) 50. \ \ \ \ 1 A \ u. :., -J \ 2 u.£ Z O 0 m w Vi3 0, -0 J 4 Figure 19. Example of Shoreline Evolution in Response to Littoral Barrier. Based on Method of Pelnard-Considere. Longshore Sediment Transport Rate Used in Example =180,000 cubic yards per year. Littoral Barrier Length = 160 ft. 31

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NON-DIMENSIONAL DISTANCE DOWNDRIFT OF COMPLETE LITTORAL BARRIER x/I-/4i 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 W 0 O2 Littoral Barrier Waves U) -0.2 ( "-y O z Z o -0.4 C.) Jw Z x x Z -0.6 Figure 20. Pelnard -Consldere Solution For Shoreline Recession Downdrlft of a Complete Littoral Barrier.

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direction is that the local background erosion rates in the vicinity of a littoral barrier are due to and a manifestation of waves arriving at the shoreline. This alternate recommended method would not be possible in the case where an inlet is to be cut because at that time there are no a priori background erosion data. Fortunately, in Florida, quite reliable background erosion data exist in the vicinity of most inlets. For the recommended approach, the modifications to the graphical method described previously for an uninterrupted shoreline are small and are illustrated diagrammatically in Figure 21. The only changes are that (a) the effective length of the project, e', is twice the physical length of the project, e, and (b) the waves are considered as advancing normal to shore. This accomplishes the desired effect of a zero transport at the littoral barrier, since the transport at the center of a project for normally incident waves is zero. The methods described here will be illustrated by later examples. Numerical Solution The numerical solution that will be presented here is a socalled explicit scheme in which the equations for sediment transport and continuity are solved sequentially. In particular referring to Figure 22, the shoreline positions are held constant for a time step, At, while the sediment transport is computed. Following this operation, the sediment transport is held constant for a time step and the equation of continuity is applied to these transport values to update the shoreline positions. This type of explicit model referred to here has a stability criterion which limits the maximum time step, At, that can be utilized. The maximum time step is given approximately by 1 AX2 (At)maz = (22) 2G and G is defined in Equation (8) and approximate values presented in Figure 15. For most purposes in Florida, a time step of 86,400 seconds (1 Day) and a grid size (Az) of 500 feet are reasonable. From Eqs. (8) and (22) it is seen that the larger the wave height, the smaller the allowable time step. Also, the smaller the grid size, the smaller the allowable time step. 33 k _ _________________________________

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I Littoral ILittoral Barrier I Bartler SBarier Waves 3-a o) =0 i *J • L I SI a) I b) Recommended Method With Waves at a Specific Angle. Background Approaching Normal to Shoreline. Erosion Without Effect of Littoral Background Erosion Includes Effect Barrier of Littoral Barrier. Figure 21. Two Alternative Methods For Predicting Beach Nourishment Performance Downdrift of a Littoral Barrier i I I I " I ; I a) Method With Waves Approaching | b) Recommended Method With Waves at a Specific Angle. Background Approaching Normal to Shoreline. Erosion Without Effect of Littoral Background Erosion Includes Effect Barrier of Littoral Barrier. Figure 21. Two Alternative Methods For Predicting Beach Nourishment Performance Downdrift of a Littoral Barrier

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Q l-l \^0^ Figure 22. Computational Scheme Used in Numerical Method. 35

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As noted previously, one of the primary advantages of the numerical solution is the much greater flexibility of specifying initial conditions and input to the model. Additionally, with minor modifications to the program, renourishments could be represented. To effectively utilize the greater flexibility inherent in the numerical procedure and in particular to include structures where desired, the background erosion rates are translated into background transport rates. Formally the background transport rates, QB(x), are determined from the continuity equation QB(x) = QB(xo) -(h. + B) yB dx (23) in which 2is the background shoreline change rate and xo is a reference shoreline location at which a reference transport QB(Xo) is specified. Boundary Conditions The application of the sediment transport and continuity equations with initial planform conditions require specification of boundary conditions at the two ends of the grid system in order to complete the problem formulation. In general, there are two types of boundary conditions. The first that will be discussed is a specified shoreline position at one or both of the ends of the computational domain. A simple example of the specified shoreline positions would be that the shoreline is fixed at its initial value or the value could be prescribed over the computational time period. A second boundary condition that could be applied is a specified discharge at one or both ends of the computational domain. Examples of situations in which each of these boundary conditions would be applied are discussed below. The fixed boundary condition could be applied at the ends of a computational domain for the case of a beach nourishment project on an uninterrupted shoreline; however, if the ends of the computational domain are too close to the changes that would occur due to the nourishment, then these conditions can adversely affect the accuracy of the results. A useful and direct approach to evaluating whether the fixed boundary conditions are sufficiently distant from the point of interest is to simply double the extent of the computational domain 36

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and to evaluate the effects on the shoreline changes in the region of interest over the period for which the computations are carried out. The second type of boundary condition of interest is the specified transport boundary condition. Examples where a specified transport boundary condition would be appropriate are immediately downdrift of a partial or complete littoral barrier. If the barrier were a complete obstruction to the longshore sediment transport, then a specified discharge of zero would be appropriate; however, if there was some bypassing around the littoral barrier, then the volume per unit time of the bypassing would be the appropriate input transport boundary condition. Obviously in this case since the discharge values are centered at the grid lines, it would be appropriate to locate a grid line at the littoral barrier. The transport boundary condition could also be applied at the ends of the computational grid. If this were done, the shoreline displacement would be free to vary with time. If the transport boundary condition is specified as zero at the ends of the computational grid, there would be no change of volume within the computational domain. This could be the case in which complete littoral barriers existed at the two ends of the system of interest. In the model developed for this project, the boundary condition imposed at the two ends of the computational domain is the transport condition with the background transport as the imposed values. A situation in which the boundary condition will change within the computational period might be a case where a groin of specified length was included somewhere within the computational domain. As the shoreline advances seaward toward the groin tip, the boundary condition would be a zero transport condition. However after the shoreline reached the end of the groin then the shoreline would remain fixed at that position which would in effect then be a fixed shoreline position boundary condition. In a case where the longshore sediment transport direction changed with time, the boundary condition at a structure could alternate between a fixed transport boundary condition and a specified shoreline position. 37

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Wave and Other Parameters of Use in Applying the Methodology Four parameters will be presented and recommended for applying the methodology developed in conjunction with this study. The first parameter of interest is the limiting depth of motion, h.. Although this quantity is not known precisely, recommended values for h. have been presented in Figure 8. The berm height, B, is also required and appropriate values can be determined from profiles at the site of interest. Generally, berm heights range between 6 and 9 ft (above NGVD) in Florida. A third parameter of interest is the effective wave height. The recommended distribution of wave heights around the Florida peninsula is shown in Figure 23. These wave heights were based primarily on the Coastal Data Network results where available. It is seen that, on the Florida east coast, the wave heights vary from the largest near the Florida/Georgia border and decrease toward the southern portions of the state. On the Florida west coast, the heights decrease toward the north with very low values along the Big Bend area, then increase toward the Florida/Alabama border. Finally, estimates of effective wave period are presented for the coast of Florida in Figure 24. Approximate values of the longshore diffusivity parameter, G, have been presented in Figure 15 and may be used as a reasonable approximation. STEP-BY-STEP DISCUSSION OF METHODOLOGY In this section the limitations and the step-by-step application of the graphical and numerical procedures will be presented. Graphical Procedure The graphical procedure as presented here pertains to (1) a rectangular nourishment on an uninterrupted shoreline, and (2) a rectangular beach nourishment immediately downdrift of a complete littoral barrier such as a jetty. In both of these cases it is considered that the shoreline change is the linear sum of the result of the spreading out losses and the background erosion rate as determined by historical data; 38

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3 5H 4 3 Heff2(feet) 1 3 5 8 JA MA | ST --CC -CL VE WP MI 1 3 5 8 H eff 2(feet) Figure 23. Recommended Values of Effective Deep Water Wave Height, Ho, Along Florida's Sandy Shoreline. 39

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S14 10 *0 --.. Wave Period, T(sec) mn 2 6 10 14 2 MA x VB x VE WP MI 2 6 10 14 Wave Period, T(sec) Figure 24. Recommended Values of Effective Wave Period, T, Along Florida's Sandy Shoreline. 40

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CASE A -NOURISHMENT ALONG AN UNINTERRUPTED SHORELINE The computation sheet presented as Figure 25 has been developed and should be referenced when reviewing the step-by-step procedure described below. Step 1 -Specify Beach Nourishment Project Characteristics These include Project Length, e Sediment Size, D Volume Added Per Unit Length, V Step 2 -Determine the Equilibrated Project Width, Ayo To accomplish this h, from Figure 8 Estimate B from local profile data berm height Determine AF and AN from Figure 7 from sediment sizes and local profile data, respectively Calculate Ayo/W. from Figures 11 and 12, interpolating if necessary. Step 3 -Calculate Effective Alongshore Diffusivity, G The alongshore diffusivity, G, is obtained as expressed by Eq. (8) and is calculated from the wave, sediment and other local factors (G can also be estimated from Figure 15). Determine Ho from Figure 23 Determine T from Figure 24 Determine C. from Figure 14 41

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BEACH NOURISHMENT PROJECTION (Graphical Computations, Uninterrupted Shoreline) General Location: Wave Height, Ho (Fig. 23): ft, Closure Depth, h, (Fig. 8): ft Wave Period, T (Fig. 24): sec, Sediment Size, D: mm Wave Direction, ao: 0, Transport Factor, K (Fig. 5): Berm Height, B: ft Alongshore Diffusivity, G (From Equation below or Figure 15). K H~4C~Cg0.4 cos(/o -ao) cos 2(3o -a,) G = 8 (s -1)(1 -p)C,0o.4(h. + B) cos(Po -a*) = =_ft2/s Background Erosion Equilibrated Beach Width, Ayo x Erosion Rate (ER) AN (Fig. 7) or From Profile: ftf/3 -ft/yr Ap (Fig. 7): ft1/3 SVolume Per Unit Length: ft3/ft -Ayo (Figs. 11 and 12): ft SProject Length, £, = __ miles = ft For 30 years Gt G(30x365x24x3600) 162 162 (1) (2) (3) (4) (5) (6) Distance Y( ) /Ayo Ys YB(ft)= N = From Center, x(ft) (Fig. 17) (ft) 30 x ER y, -Yb (ft) Figure 25. Form for Computation of Performance Along Uninterrupted Shoreline. 42

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* Other Recommended Values: S= -0.78 s = 2.65 p = 0.35 g = 32.2 Step 4 -Calculate Shoreline Position Due to Spreading Out Losses Calculate non-dimensional time for t = 30 years or other time of interest Gt t' = 16 where all variables are in consistent units Calculate x/(t/2) at locations of interest (Column 2, Bottom Table in Figure 25) Determine y/Ayo from Figure 17 (Column 3, Bottom Table in Figure 25) Step 5 -Calculate Background Erosion Losses Estimate background erosion rate from DNR data base Multiply rate by time (30 years) to obtain background erosion component (Column 5, Bottom Table in Figure 25) Step 6 -Calculate Resulting Shoreline Position Add linearly the changes due to spreading out losses and background erosion to obtain the total changes. If the area of interest is not within the project area, apply the same methodology, however, here the spreading out losses (from the project area) will result in a shoreline advancement (see Figure 3). CASE B -NOURISHMENT DOWNDRIFT OF A LITTORAL BARRIER As discussed previously, there are two methods for calculating response downdrift of a littoral barrier. It is recommended that the method utilizing background erosion data be 43

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applied rather than the method requiring the wave approach angle. The recommended method is described below. The computation sheet presented as Figure 26 for this case has been developed and should be referenced along with the step-by-step procedure described. Step 1 -Specify Beach Nourishment Characteristics These include (same as for Case A) Project Length, e (Effective Length, e' = 2e) Sediment Size, D Volume Added Per Unit Length, V Step 2 -Determine the Equilibrated Project Width, Ayo (Same procedure as for Case A) h. from Figure 8 Estimate B from local profile data berm height Determine AF and AN from Figure 7 and local profile data, respectively Calculate Ayo/W. from Figures 11 and 12, interpolating if necessary. Step 3 -Calculate Effective Alongshore Diffusivity, G (Same as for Case A) The alongshore diffusivity, G, is obtained as expressed by Eq. (8) and is calculated from the wave, sediment and other local factors (G can also be estimated from Figure 15). Determine Ho from Figure 23 Determine T from Figure 24 Determine C, from Figure 14 44

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BEACH NOURISHMENT PROJECTION (Graphical Computations, Downdrift of a Littoral Barrier) General Location: Wave Height, Ho (Fig. 23): ft, Closure Depth, h. (Fig. 8): ft Wave Period, T (Fig. 24): sec, Sediment Size, D: mm Wave Direction, ao: 0, Transport Factor, K (Fig. 5): Berm Height, B: __ ft Alongshore Diffusivity, G(From Equation Below or Figure 15) K H4C2 g04 cos(f -ao) cos 2(8o -a.) G = 8 (s -1)(1 -p)C,c0 4(h. + B) cos(Po -a*) = = ft2/s Background Erosion Equilibrated Beach Width, Ayo x Erosion Rate (ER) AN (Fig. 7) or From Profile: ftl/3 __ ft/yr AF (Fig. 7): ft1/3 _Volume Per Unit Length: ft3/ft -_ Ayo (Figs. 11 and 12): ft -_ _Project Length, £, = miles = ft _Effective Project -_ Length, e' = 2 = __ miles = ft For 30 years Gt = 16G(30x365x24x3600) 16)2 =16 = = (1) (2) (3) (4) (5) (6) Distance y (2) /Ayo Ys YB(ft) = YN = From Littoral Barrier, x(ft) (Fig. 17) (ft) 30 x ER y, -Yb (ft) Figure 26. Form for Computation of Performance Downdrift of a Littoral Barrier. 45

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* Other Recommended Values: K = 0.78 s = 2.65 p = 0.35 g = 32.2 Step 4 -Calculate Shoreline Position Due to Spreading Out Losses Calculate non-dimensional time for t = 30 years or other time of interest 16 Gt 4 Gt where all variables are in consistent units. (Note: Different coefficient from Case A) Calculate x/(£'/2) at locations of interest where the origin of x is at the littoral barrier Calculate y/Ayo from Figure 17 (Note in this case, the horizontal axis in Figure 17 is to be interpreted as x/(£'/2) or equivalently, x/..) Step 5 -Calculate Background Erosion Losses Estimate background erosion rate from DNR data base Multiply rate by time to obtain background erosion component Step 6 -Calculate Resulting Shoreline Position Add linearly the changes due to spreading out losses and background erosion to obtain the total changes. If the area of interest is not within. the project area, apply the same methodology, however, here the spreading out losses (from the project area) will result in a shoreline advancement (see Figure 3). 46 L

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NUMERICAL PROCEDURE As noted previously, the numerical procedure provides greater flexibility for representing shoreline and beach nourishment conditions. Prior to using the program, there is a certain amount of data preparation that is required. Some of this preparation is similar to that for the graphical procedure as described earlier. The numerical procedure also allows input of structures of arbitrary lengths at any location within the computational domain. At this stage, the program is straightforward, but not overly "user friendly". As for the case of the "Graphical Procedure", the methodology will be illustrated below for the case of nourishment along an uninterrupted shoreline and for the case of structures present. The preparation sheet presented as Figure 27 has been developed to assist in data preparation and should be referenced along with the step-by-step procedure described below. CASE A -NOURISHMENT ALONG AN UNINTERRUPTED SHORELINE STEP 1 -Specify Beach Nourishment Project Characteristics This is the same as described previously for the Graphical Procedure. The only difference is that now greater flexibility is available with the numerical procedure allowing varying volumes of nourishment along the shoreline including any number of nourishment segments. STEP 2 -Determine Equilibration Project Width, Ayo Utilize same method as described for Graphical Procedure STEP 3Develop Background Erosion Data. as Piecewise Linear Segments STEP 4 -Develop Input File A description of the input file (DNRBS.INP) is given below and Figure 28 presents an example input file. 47

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BEACH NOURISHMENT PROJECTION (Numerical Procedure) General Location: Wave Height, Ho (Fig. 23): ft., Closure Depth, h, (Fig. 8): ft. Wave Period, T (Fig. 24): sec., Berm Height, B: ft. Wave Direction, co0: , Sand Diameter, D: mm Deep Water Contour Orientation, f/o: , Transport Factor, K (Fig. 5): Longshore Axis Orientation, ip: , VFACT: Grid Dimension, Ax: ft Background Transport, QREF: ft3/s Time Increment, At: sec IREF: IMAX: NTIMES: No. of Structures, NS: Structure Specificiation Background Erosion Structure Structure Structure Number Location, I Length (ft) x Erosion Rate, ER, (ft/yr) 2 3 4 5 6 Equilibrated Beach Width Ayo Nourishment Specification I Range AYo AN (Fig. 7) or From Profile: ftl/3 to AF (Fig. 7): ft1/3 to Volume Per Unit Length: ft3/ft to Ayo (Figs. 11 and 12): ft to to Figure 27. Data Input Preparation Form for Numerical Procedure. 48 48

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EXAMPLE OF INPUT FILE: DNRBS.INP (Example No. 2) EXAMPLE NO. 2 UNIF. BACK. EROS. NO STRUC. 2 MILE PROJ. ~ TdeC+Cred*i ^-\wit M ~pi-a ^+t^o/-.efPlAT-tTb. COreIo) <„ -. ~ w/w ,-^MeCt^'>^/ Ve<:<" ^: 0 f 2.00 6.0 90.0 90.0 180.0 500.0 86400.0 V.te-pf 0 o4A"five M+vi r ec., A ita 17.0 6.0 0.77 1.0 0.0 1 180 10950 0 0.0 2.0 90000. 2.0 49500. 2.0 60000. 3.07 PltrS of~DS+ ~e-s, 90000. 3.0 100000. 3.0 140000. 2.0 -J -ro Rcs) -Frr < t~ Cj Ce-I /Jocjrirsc"s, tk3Oi -Prof74r Cel l -Mour .ske. ( 0A orS 80 100 80 112.0 81 112.0 82 112.0 83 112.0 84 112.0 85 112.0 86 112.0 87 112.0 88 112.0 89 112.0 90 112.0 I ars A Voli-J 91 112.0 92 112.0 93 112.0 94 112.0 95 112.0 96 112.0 97 112.0 98 112.0 99 112.0 100 112.0 /Vofe> 7-he. ~E \Cwt. L< lS +eeen Cbd' LOer prov;dcl re4er vrAnnor 1'ov% lrfoserS Figure 28. Input File DNRBSoINP For Example 2 49

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Card 1 (Format: 20A4): Identification Card with 80 Characters of Alphanumeric Input Card 2 Format: 8F8.2): Contains the Following Input Parameters First Parameter: Deep Water Effective Wave Height in Feet, Ho (From Figure 23) Second Parameter: Wave Period in Seconds, T (From Figure 24) Third Parameter: Deep Water Wave Direction, ao, in Degrees Fourth Parameter: Deep Water Contour Orientation, Po, in Degrees Fifth Parameter: Longshore Axis Orientation, p, in Degrees Sixth Parameter: Grid Dimension, Ax, in Feet Seventh Parameter: Time Increment, At, in Seconds Card 3 Format: 5F8.2,4I6): Contains the Following Input Parameters First Parameter: Depth of Limiting Motion, h,, in Feet (From Figure 8) Second Parameter: Berm Height, B, in Feet Third Parameter: Sediment Transport Parameter, K (From Figure 5) Fourth Parameter: Factor to Increase or Decrease Proportionally All Input Beach Widths, Ayo Fifth Parameter: Background Transport, QBKREF (cubic feet/sec) (See Eq. (23)) Sixth Parameter: Grid Line Index, IREF, at Which QBKREF is to Apply Seventh Parameter: Number of Grids, IMAX Eighth Parameter: Number of Time Steps, NTIMES Ninth Parameter: Number of Structures, NS Card 4 Format: 5(I6,F8.3)): Note this Card (and Possibly a Subsequent Card if NS > 5) is only Present if NS > 0 and Contains NS Pairs of Grid Lines and Structure Lengths. At Present the Program is Dimensioned to Accommodate Up To 10 Structures Cards 5 and 6 Format (8F8.2): These Two Cards Contain Pairs of (x, EB(x)) where x is in Feet and EB is the Location Background Erosion in Feet/Year. The Program is Presently Configured for Seven Pairs; However, it is Possible to Specify Background Erosion Conditions with as Little as Two Pairs. For Example, if the Background Erosion is Uniform at Two Feet/Year and the Computational Domain is 60,000 ft in Length, the Two Active Pairs Could be: 0.0 2.0 80000.0 2.0 The Remaining Five Pairs Entered Would be Immaterial. Note it is necessary to provide two cards here, even if all the meaningful information is contained in the first card. Card 7 This Card Specified the First, NNOUS, and Last, NNOUE, Grid Indices for the Nourished Segment Cards 8 and Following (Format: 16, 3F8.2): Each of These Cards Specifies the Grid Index, I, and the Associated Shoreline Advancement, Ayo (I) This completes specification of the input File DNRBS.INP 50

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STEP 5 -Run Program STEP 6 -Examine Output in File DNRBS.OUT A description of the output file DNRBS.OUT is presented below and Figure 29 presents an example of this output with annotations. This output is for the input file presented in Figure 28. Card 1: This card is an image of the first input card which is an identification card Cards 2,3,4,5,6: These cards simply repeat input values Cards 7 and 8: These two cards are pairs of (x, EB(x)) specified in Input Cards 5 and 6 Next Block of Data: Presents pairs of (I,QBI) in which QBI is the background erosion transport across the Ith grid line. The units of QBI are in ft3/sec Next Card: This card repeats the first nourished grid index, NNOUS, and the last nourishment grid index, NNOUE, as provided by Input Card 7 Next Block of Data: Presents three entries per grid: (I,X(I), DYO(I)), in which I is the grid block index, x(I) is the z coordinate of the grid block and DYO(I) is the initial nourished width at the grid block. In the example presented, because there are 450 sets of entries, one for each grid block. Next Block of Data: Provides pairs of I, Y(I) for one year after nourishment for all grid blocks Next Card: Presents the proportion of the additional dry beach area relative to the initial area that remains within the project area after one year. This proportion is denoted PCT(LCUR) Remaining Output: The remaining output consists of detailed shoreline output for 5, 10, 20 and 30 years and the proportional surface area remaining for each of the thirty years. This completes the description of the information in the output file DNRBS.OUT 51

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'/Figure 29. Example of Output File DNRBS.OUT for Input File in Figure 28. Example No. 2. (Total of 5 Pages of Output). EXAMPLE OF OUTPUT FILE: DNRBS.OUT (Example No. 2) EXAMPLE NO. 2 UNIF. BACK. EROS. NO STRUC. 2 MILE PROJ. HO = 2.00 FT., T = 6.00 SEC., ALPO = 90.00 DEG., BTAO = 90.00 DEG., XMU = 180.00 DEG., DX = 500.00 FT., DT = 86400.00 SEC. HSTR = 17.00 FT., B = 6.00 FT., XK = .77 VFACT = 1.00 QBKREF = .00 FT.**3/SEC. IREF = 1, IMAX = 180, NTIMES = 10950, NS = 0 .00E+00 2.00 .90E+05 2.00 .50E+05 2.00 .60E+05 3.00 .90E+05 3.00 .10E+06 3.00 .14E+06 2.00 BACKGROUND EROSION TRANSPORT RATES 1 .000 2 .001 3 .001 4 .002 5 .003 6 .004 7 .004 8 .005 9 .006 10 .007 11 .007 12 .008 13 .009 14 .009 15 .010 16 .011 17 .012 18 .012 19 .013 20 .014 21 .015 22 .015 23 .016 24 .017 25 .018 26 .018 27 .019 28 .020 29 .020 30 .021 31 .022 32 .023 33 .023 34 .024 35 .025 36 .026 37 .026 38 .027 39 .028 40 .028 41 .029 42 .030 43 .031 44 .031 45 .032 46 .033 47 .034 48 .034 49 .035 50 .036 51 .036 52 .037 53 .038 54 .039 55 .039 56 .040 57 .041 58 .042 59 .042 60 .043 61 .044 62 .044 63 .045 64 .046 65 .047 66 .047 67 .048 68 .049 69 .050 70 .050 71 .051 72 .052 73 .053 74 .053 75 .054 76 .055 77 .055 78 .056 79 .057 80 .058 81 .058 82 .059 83 .060 84 .061 85 .061 86 .062 87 .063 88 .063 89 .064 90 .065 91 .066 92 .066 93 .067 94 .068 95 .069 96 .069 97 .070 98 .071 99 .071 100 .072 101 .073 102 .074 103 .074 104 .075 105 .076 106 .077 107 .077 108 .078 109 .079 110 .079 111 .080 112 .081 113 .082 114 .082 115 .083 116 .084 117 .085 118 .085 119 .086 120 .087 121 .088 122 .088 123 .089 124 .090 125 .090 126 .091 127 .092 128 nQ' 129 .093 130 .094 131 .095 132 .096 133 52 134 .097 135 .098 136 .098 137 .099 138 139 .101 140 .101 141 .102 142 .103 143 .104 144 .104 145 .105 146 .106 147 .106 148 .107 149 .108 150 .109

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156 .113 157 .114 158 .115 159 .115 160 .116 161 .117 162 .117 163 .11i 164 .119 165 .120 166 .120 167 .121 168 .122 169 .123 170 .123 171 .124 172 .125 173 .125 174 .126 175 .127 176 .128 177 .128 178 .129 179 .130 180 .131 181 .131 80 100 INITIAL SHORELINE (INCL. NOURISHMENT) POSITION 1 0. .00 2 500. .00 3 1000. .00 4 1500. .00 5 2000. .00 6 2500. .00 7 3000. .00 8 3500. .00 9 4000. .00 10 4500. .00 11 5000. .00 12 5500. .00 13 6000. .00 14 6500. .00 15 7000. .00 16 7500. .00 17 8000. .00 18 8500. .00 19 9000. .00 20 9500. .00 21 10000. .00 22 10500. .00 23 11000. .00 24 11500. .00 25 12000. .00 26 12500. .00 27 13000. .00 28 13500. .00 29 14000. .00 30 14500. .00 31 15000. .00 32 15500. .00 33 16000. .00 34 16500. .00 35 17000. .00 36 17500. .00 37 18000. .00 38 18500. .00 39 19000. .00 40 19500. .00 41 20000. .00 42 20500. .00 43 21000. .00 44 21500. .00 45 22000. .00 46 22500. .00 47 23000. .00 48 23500. .00 49 24000. .00 50 24500. .00 51 25000. .00 52 25500. .00 53 26000. .00 54 26500. .00 55 27000. .00 56 27500. .00 57 28000. .00 58 28500. .00 59 29000. .00 60 29500. .00 61 30000. .00 62 30500. .00 63 31000. .00 64 31500. .00 65 32000. .00 66 32500. .00 67 33000. .00 68 33500. .00 69 34000. .00 70 34500. .00 71 35000. .00 72 35500. .00 73 36000. .00 74 36500. .00 75 37000. .00 76 37500. .00 77 38000. .00 78 38500. .00 79 39000. .00 80 39500. 112.00 81 40000. 112.00 82 40500. 112.00 83 41000. 112.00 84 41500. 112.00 85 42000. 112.00 86 42500. 112.00 87 43000. 112.00 88 43500. 112.00 89 44000. 112.00 90 44500. 112.00 91 45000. 112.00 92 45500. 112.00 93 46000. 112.00 94 46500. 112.00 95 47000. 112.00 96 A-7"n 112.00 97 48000. 112.00 98 53 112.00 99 49000. 112.00 100 112.00 101 50000. .00 102 50500. .00 103 51000. .'00 104 51500. .00 105 52000. .00 106 52500. .00

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111 55000. .00 112 55500. .00 113 56000. .00 114 56500. .00 115 57000. .00 116 57500. .00 117 58000. .00 118 58500. .00 119 59000. .00 120 59500. .00 121 60000. .00 122 60500. .00 123 61000. .00 124 61500. .00 125 62000. .00 126 62500. .00 127 63000. .00 128 63500. .00 129 64000. .00 130 64500. .00 131 65000. .00 132 65500. .00 133 66000. .00 134 66500. .00 135 67000. .00 136 67500. .00 137 68000. .00 138 68500. .00 139 69000. .00 140 69500. .00 141 70000. .00 142 70500. .00 143 71000. .00 144 71500. .00 145 72000. .00 146 72500. .00 147 73000. .00 148 73500. .00 149 74000. .00 150 74500. .00 151 75000. .00 152 75500. .00 153. 76000. .00 154 76500. .00 155 77000. .00 156 77500. .00 157 78000. .00 158 78500. .00 159 79000. .00 160 79500. .00 161 80000. .00 162 80500. .00 163 81000. .00 164 81500. .00 165 82000. .00 166 82500. .00 167 83000. .00 168 83500. .00 169 84000. .00 170 84500. .00 171 85000. .00 172 85500. .00 173 86000. .00 174 86500. .00 175 87000. .00 176 87500. .00 177 88000. .00 178 88500. .00 179 89000. .00 180 89500. .00 100 116 .000 .084 .000 -.542 -.542 .084 .000 TIME = 1 YEARS 1 -2.00 2 -2.00 3 -2.00 4 -2.00 5 -2.00 6 -2.00 7 -2.00 8 -2.00 9 -2.00 10 -2.00 11 -2.00 12 -2.00 13 -2.00 14 -2.00 15 -2.00 16 -2.00 17 -2.00 18 -2.00 19 -2.00 20 -2.00 21 -2.00 22 -2.00 23 -2.00 24 -2.00 25 -2.00 26 -2.00 27 -2.00 28 -2.00 29 -2.00 30 -2.00 31 -2.00 32 -2.00 33 -2.00 34 -2.00 35 -2.00 36 -2.00 37 -2.00 38 -2.00 39 -2.00 40 -2.00 41 -2.00 42 -2.00 43 -2.00 44 -2.00 45 -2.00 46 -2.00 47 -2.00 48 -2.00 49 -2.00 50 -2.00 51 -2.00 52 -2.00 53 -2.00 54 -2.00 55 -2.00 56 -2.00 57 -2.00 58 -2.00 59 -1.99 60 -1.98 61 -1.96 62 -1.93 63 -1.87 64 -1.77 65 -1.60 66 -1.31 67 -.87 68 -.18 69 .84 70 2.31 71 4.34 72 7.07 73 10.62 74 15.06 75 20.45 76 26.75 77 33.87 78 41.64 79 49.83 80 58.16 81 66.34 82 74.10 83 81.19 84 87.43 85 92.71 86 96.98 87 100.24 88 102.52 89 103.87 90 104.31 91 103.87 92 102.52 93 100.24 94 96.98 95 92.71 96 87.43 97 81.19 98 74.10 99 66.34 100 58.16 101 49.83 102 41.64 103 33.87 104 26.75 105 20.45 106 15.06 107 10.62 108 7.07 109 4.34 110 2.31 111 .84 112 -.18 113 -.87 114 -1.31 115 -1.60 116 -1.77 117 -1.87 118 -1.93 119 -1.96 120 -1.98 121 -1.99 122 -2.00 123 -2.00 124 -2.00 125 -2.00 126 -2.00 127 -2.00 128 -2.00 129 -2.00 130 -2.00 131 -2.00 132 -2.00 133 -2.00 134 -2.00 135 -2.00 136 -2.00 137 -2.00 138 -2.00 139 -2.00 140 -2.00 141 -2. -2.00 143 -2.00 144 -2.00 145 -2.00 146 -2.00 147 -2. -2.00 149 -2.00 150 -2.00 151 -2.00 152 -2.00 153 -2.uu iD4 -2.00 155 -2.00 156 -2.00 157 -2.00 158 -2.00 159 -2.00 160 -2.00 161 -2.00 162 -2.00 163 -2.00 164 -2.00 165 -2.00 166 -2.00 167 -2.00 168 -2.00

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175 -2.00 176 -2.00 177 -2.00 178 -2.00 179 -2.00 180 -2.00 LCUR = 1 PCT(LCUR) = .78 LCUR = 2 PCT(LCUR) = .68 LCUR = 3 PCT(LCUR) = .60 LCUR = 4 PCT(LCUR) = .53 TIME = 5 YEARS 1 -10.00 2 -10.00 3 -10.00 4 -10.00 5 -10.00 6 -10.00 7 -10.00 8 -10.00 9 -10.00 10 -10.00 11 -10.00 12 -10.00 13 -10.00 14 -10.00 15 -10.00 16 -10.00 17 -10.00 18 -10.00 19 -10.00 20 -10.00 21 -10.00 22 -10.00 23 -10.00 24 -10.00 25 -10.00 26 -10.00 27 -10.00 28 -10.00 29 -10.00 30 -10.00 31 -10.00 32 -10.00 33 -9.99 34 -9.99 35 -9.99 36 -9.98 37 -9.98 38 -9.97 39 -9.96 40 -9.94 41 -9.92 42 -9.90 43 -9.86 44 -9.82 45 -9.77 46 -9.70 47 -9.61 48 -9.50 49 -9.37 50 -9.21 51 -9.00 52 -8.76 53 -8.46 54 -8.10 55 -7.68 56 -7.17 57 -6.58 58 -5.89 59 -5.09 60 -4.17 61 -3.12 62 -1.93 63 -.59 64 .91 65 2.57 66 4.40 67 6.41 68 8.58 69 10.91 70 13.41 71 16.05 72 18.82 73 21.71 74 24.70 75 27.75 76 30.84 77 33.93 78 37.00 79 40.01 80 42.92 81 45.69 82 48.29 83 50.69 84 52.84 85 54.71 86 56.29 87 57.54 88 58.45 89 59.00 90 59.18 91 59.00 92 58.45 93 57.54 94 56.29 95 54.71 96 52.84 97 50.69 98 48.29 99 45.69 100 42.92 101 40.01 102 37.00 103 33.93 104 30.84 105 27.75 106 24.70 107 21.71 108 18.82 109 16.05 110 13.41 111 10.91 112 8.58 113 6.41 114 4.40 115 2.57 116 .91 117 -.59 118 -1.93 119 -3.12 120 -4.17 121 -5.09 122 -5.89 123 -6.58 124 -7.17 125 -7.68 126 -8.10 127 -8.46 128 -8.76 129 -9.00 130 -9.21 131 -9.37 132 -9.50 133 -9.61 134 -9.70 135 -9.77 136 -9.82 137 -9.86 138 -9.90 139 -9.92 140 -9.94 141 -9.96 142 -9.97 143 -9.98 144 -9.98 145 -9.99 146 -9.99 147 -9.99 148 -10.00 149 -10.00 150 -10.00 151 -10.00 152 -10.00 153 -10.00 154 -10.00 155 -10.00 156 -10.00 157 -10.00 158 -10.00 159 -10.00 160 -10.00 161 -10.00 162 -10.00 163 -10.00 164 -10.00 165 -10.00 166 -10.00 167 -10.00 168 -10.00 169 -10.00 170 -10.00 171 -10.00 172 -10.00 173 -10.00 174 -10.00 175 -10.00 176 -10.00 177 -10.00 178 -10.00 179 -10.00 180 -10.00 LCUR = 5 PCT(LCUR) = .47 LCUR = 6 PCT(LCUR) = .42 LCUR = 7 PCT(LCUR) = .38 LCUR = 8 PCT(LCUR) = .33 LCUR = 9 PCT(LCUR) = .30 TIME = 10 YEARS 1 -20.00 2 -20.00 3 -20.00 4 -20.00 5 -20.00 6 -20.00 7 -20.00 8 -20.00 9 -20.00 10 -20.00 11 -20.00 12 -20.00 13 -19.99 14 -19.99 15 -19.99 16 -19.99 17 -19.99 18 -19.98 19 -19.98 20 -19.97 21 -19.97 22 -19.96 23 -19.95 24 -19.94 25 -19.92 26 -19.91 27 -19.89 28 -19.86 29 -19.83 30 -19..80 31 -19.76 32 -19.71 33 -19.65 34 -19.59 35 -19.51 36 -19.42 37 -19.31 38 -19.19 39 -19.05 40 -18.89 41 -18.70 42 -18.49 43 -18.25 44 -17.98 45 -17.68 46 -17.34 47 -16.96 48 -16.53 49 -16.05 50 -15.53 51 -14.95 52 -14.32 53 -13.62 54 -12.86 55 -12.04 56 -11.15 57 -10.19 58 -9.16 59 -8.06 60 -6.88 61 -5.64 62 -4.33 63 -2.96 64 -1.51 65 -.01 66 1.54 67 -3.15 68 4.80 69 6.48 70 8.19 71 9.92 .72 11.66 73 13.40 74 15.12 75 16.82 76 18.48 77 20.10 78 21.66 79 23.14 80 24.55 81 25.85 82 27.06 83 28.14 84 29.10 85 29.93 86 30.62 87 31.16 88 31.55 89 31.79 90 31.87 91 31.79 92 31.55 93 31.16 94 30.62 95 29.93 96 29.10 97 28.14 98 27.06 99 25.85 100 24.55 101 23.14 102 21.66 103 20.10 104 18.48 105 16.82 10i 15.12 107 13.40 108 11.66 109 9.92 110 8.19 111 6 4.80 113 3.15 114 1.54 115 -.01 116 -1.51 117 -2 5 -4.33 119 -5.64 120 -6.88 121 -8.06 122 -9.16 123 -10.1~ i41 -11.15 125 -12.04 126 -12.86 127 -13.62 128 -14.31 129 -14.95 130 -15.53 131 -16.05 132 -16.53 133 -16.96 134 -17.34 135 -17.68 136 -17.98 137 -18.25 138 -18.49 _______ ____ ---___ -----*-a ------.* < ------^ -a a ---i --* ---.--

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145 -19.51 146 -19.59 147 -19.65 148 -19.71 149 -19.76 150 -19.80 151 -19.83 152 -19.86 153 -19.89 154 -19.91 155 -19.92 156 -19.94 157 -19.95 158 -19.96 159 -19.97 160 -19.97 161 -19.98 162 -19.98 163 -19.99 164 -19.99 165 -19.99 166 -19.99 167 -19.99 168 -20.00 169 -20.00 170 -20.00 171 -20.00 172 -20.00 173 -20.00 174 -20.00 175 -20.00 176 -20.00 177 -20.00 178 -20.00 179 -20.00 180 -20.00 LCUR = 10 PCT(LCUR) = .26 LCUR = 11 PCT(LCUR) = .23 LCUR = 12 PCT(LCUR) = .19 LCUR = 13 PCT(LCUR) = .16 LCUR = 14 PCT(LCUR) = .13 LCUR = 15 PCT(LCUR) = .10 LCUR = 16 PCT(LCUR) = .08 LCUR = 17 PCT(LCUR) = .05 LCUR = 18 PCT(LCUR) = .02 LCUR = 19 PCT(LCUR) = .00 LCUR = 20 PCT(LCUR) = -.03 LCUR = 21 PCT(LCUR) = -.05 LCUR = 22 PCT(LCUR) = -.08 LCUR = 23 PCT(LCUR) = -.10 LCUR = 24 PCT(LCUR) = -.13 LCUR = 25 PCT(LCUR) = -.15 LCUR = 26 PCT(LCUR) = -.17 LCUR = 27 PCT(LCUR) = -.20 LCUR = 28 PCT(LCUR) = -.22 LCUR = 29 PCT(LCUR) = -.24 TIME = 30 YEARS 1 -59.99 2 -59.92 3 -59.84 4 -59.76 5 -59.68 6 -59.60 7 -59.52 8 -59.43 9 -59.34 10 -59.24 11 -59.14 12 -59.04 13 -58.93 14 -58.82 15 -58.69 16 -58.56 17 -58.43 18 -58.28 19 -58.13 20 -57.97 21 -57.80 22 -57.62 23 -57.42 24 -57.22 25 -57.01 26 -56.78 27 -56.54 28 -56.29 29 -56.02 30 -55.75 31 -55.45 32 -55.15 33 -54.83 34 -54.49 35 -54.14 36 -53.78 37 -53.40 38 -53.00 39 -52.59 40 -52.17 41 -51.72 42 -51.27 43 -50.80 44 -50.31 45 -49.81 46 -49.30 47 -48.77 48 -48.23 49 -47.68 50 -47.11 51 -46.54 52 -45.95 53 -45.36 54 -44.76 55 -44.15 56 -43.53 57 -42.91 58 -42.28 59 -41.66 60 -41.03 61 -40.40 62 -39.77 63 -39.15 64 -38.53 65 -37.92 66 -37.31 67 -36.71 68 -36.13 69 -35.55 70 -34.99 71 -34.45 72 -33.92 73 -33.41 74 -32.92 75 -32.46 76 -32.01 77 -31.59 78 -31.19 79 -30.83 80 -30.49 81 -30.17 82 -29.89 83 -29.64 84 -29.42 85 -29.24 86 -29.08 87 -28.97 88 -28.88 89 -28.83 90 -28.81 91 -28.83 92 -28.88 93 -28.97 94 -29.08 95 -29.24 96 -29.42 97 -29.64 98 -29.89 99 -30.17 100 -30.49 101 -30.83 102 -31.19 103 -31.59 104 -32.01 105 -32.45 106 -32.92 107 -33.41 108 -33.92 109 -34.45 110 -34.99 111 -35.55 112 -36.13 113 -36.71 114 -37.31 115 -37.92 116 -38.53 117 -39.15 118 -39.77 119 -40.40 120 -41.03 121 -41.66 122 -42.28 123 -42.91 124 -43.53 125 -44.15 126 -44.76 127 -45.36 128 -45.95 129 -46.54 130 -47.11 131 -47.68 132 -48.23 133 -48.77 134 -49.30 135 -49.81 136 -50.31 137 -50.80 138 -51.27 139 -51.72 140 -52.16 141 -52.59 142 -53.00 143 -53.40 144 -53.78 145 -54.14 146 -54.49 147 -54.83 148 -55.15 149 -55.45 150 -55.74 151 -56.02 152 -56.28 153 -56.54 154 -56.77 155 -57.00 156 -57.21 157 -57.42 158 -57.61 159 -57.79 160 -57.96 161 -58.12 162 -58.27 163 -58.41 164 -58.55 165 -58.68 166 -58.80 167 -58.91 168 -59.02 169 -59.12 170 -59.21 171 -59.31 172 -59.39 173 -59.48 174 -59.56 175 -59.63 176 -59.71 177 -59.78 178 -59.85 179 -59.92 180 -59.99 LCUR = 30 PCT(LCUR) = -.26 56

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CASE B -NOURISHMENT WITH STRUCTURES PRESENT In this case, all of the description presented for Case A is relevant with the exceptions noted below. Because Steps 1, 2, 3, and 4 are identical, they will not be repeated here. STEP 4B -Specify a Reference Background Transport As has been described earlier, in situations where structures are present, it is necessary to establish the net background longshore transport rate as this will interact with the structure. The net longshore background transport on the east coast of Florida could be estimated from Figure 30. Since background transport rates on the west coast are so variable spatially, no attempt will be made here to provide a recommendation. Rather, it is suggested that each rate should be developed on a case-by-case basis. The background transport rate is specified to the program on Card 3 as QBKREF and the grid index value associated with the background transport rate QBKREF is specified as IREF on Card 3. Note that QREF must be specified in units of ft3/second and that the conversion factor from cubic yards per year to cubic feet per second is Q(cubic feet per second) = 8.56 x 10-7 Q(cubic yards per year) STEP 5B -Specify Structure Location(s) and Length(s) in Program In the current version of the program, up to 10 structures can be specified including the grid line and length. The structures interact with the background sediment transport and the transport induced by the beach nourishment project. Specification of the structure number, location and length is by Card 4 (this card present only if structures are specified). 57

PAGE 68

7 SANTA I IHOLM JACKSON "A ROSA A I i. F RNANDINA WALTO N -JA(IL N A600,000 yd3/yr L ./ / HAMLTON. JACKSONVILLE S .T R 1 ,, MADISON'p I I'LIBERTY WAKULLA4/' i/ U BAKER ( M T AYOLORR GULF FRANKLN F YLOR ,.A ST. AUGUSTINE G IL-I ST.ON CHRIsT oN MARINELAND DIXE -I,. ALACHUA; PUTN \ GU.o 'LEVY F--' \ LE\ T -x AYTONA 3 S'' -I voARLuI 500,000 yd /yr .EW SMYRNA 0 CITUS I LAXKE -'. A -1 ,SUMTE'R 7I-voL' O \z HERNANbDOb\ -I I ORANGE Q SPASCO ^'-"/ I APE CANAVERAL r, 1 -.* -.-. -C \\ O SS CE O LA v \ l \ l z SPOLK \SSCEOLA 350,000 yd /yr 4I I IIR S nE I CHBEE ST. \ SLEE -Y PALR RO BEACH SMANATEE HARDEE O 120,000 yd /yr 4 --1 1--HLCHUECIE FiT. PIERCE 7 ^oE soTo --a xOR AOKE MARTI AMI OKEECHO---JUPITER I. OTT BI 230,000 ylyr dJ.-o.'. I PALM BEACH *T LEI ;HENDRY I PALM BEACH Along Florida's East Coast. -58H ----EERFELD COLLIER BROWARo 120,000 yd3/yr ^^ BAKERS HAULOVER *4 10,000 yd 3/yr t DADE MIAMI Figure 30. Estimates of Net Annual Longshore Sediment Transport Along Florida's East Coast. 58

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EXAMPLES ILLUSTRATING APPLICATION OF METHODOLOGIES In this section, a number of examples are presented illustrating application of the methodologies. The purpose of these examples is to familiarize the reader thoroughly with the methodologies and the anticipated results. As in preceding sections of this report, the examples will be organized by "Graphical Methodology" and "Numerical Methodology". Graphical Example The following four examples illustrate application of the methodology to the following situations. Graphical Example 1: Uninterrupted Shoreline, No Background Erosion Graphical Example 2: Uninterrupted Shoreline, Uniform Background Erosion Graphical Example 3: Uninterrupted Shoreline; Non-Uniform Background Erosion Graphical Example 4: Downdrift of a Littoral Barrier, Non-Uniform Background Erosion The computations and results are presented on the following four worksheets. Numerical Examples A number of examples were run with the numerical methodology and are described briefly on the following page. Because the documentation for each example is fairly extensive, each example is presented in an individual appendix. 59

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Numerical Example 1: Uninterrupted Shoreline, No Background Erosion, Nourishment Length = 2 Miles, Initial Added Width = 112 ft, Wave Height = 2.0 ft, Waves Normally Incident, Results Presented in Appendix C. Numerical Example 2: Uninterrupted Shoreline, Uniform Background Erosion of 2 ft/yr, Nourishment Length = 2 Miles, Initial Added Width = 112 ft, Wave Height = 2.0 ft, Waves Normally Incident, Results Presented in Appendix D. Numerical Example 3: Uninterrupted Shoreline, Variable Background Erosion, Nourishment Length of 2 Miles, Initial Added Width = 112 ft, Wave Height = 2.0 ft, Waves Normally Incident, Results Presented in Appendix E. Numerical Example 4: Uninterrupted Shoreline, No Background Erosion, Nourishment Length = 3,500 ft, Wave Height = 2.0 ft, Waves Normally Incident, Results Presented in Appendix F. Numerical Example 5: One Structure 112 ft Long Located at North End of Nourishment Project, Nourishment Length = 2 Miles, Initial Added Width = 112 ft, Wave Height = 2.0 ft, Waves Normally Incident, No Background Erosion, Results Presented in Appendix G. Numerical Example 6: One Structure 112 ft Long Located at South End of Nourishment Project, Uniform Background Erosion of 2 ft/yr, Waves Normally Incident, Nourishment Length = 2 Miles, Initial Added Width = 112 ft, Wave Height = 2.0 ft, Results Presented in Appendix H. Numerical Example 7: One Structure 112 ft Long Located at South End of Nourishment Project, Waves Approaching at 100 Angle to Shoreline, Variable Background Erosion, Nourishment Length = 2 Miles, Initial Added Width = 112 ft, Wave Height = 2.0 ft, Results Presented in Appendix I. For each numerical example, the input file, DNRBS.INP, and output file, DNRBS.OUT, are presented and the results are discussed and plotted. 60

PAGE 71

BEACH NOURISHMENT PROJECTION (Graphical Computations, Uninterrupted Shoreline) General Location: Wave Height, Ho (Fig. 23): a ft, Closure Depth, h. (Fig. 8): /7 ft Wave Period, T (Fig. 24): (6 sec, Sediment Size, D: mm Wave Direction, ao: 0 o, Transport Factor, K (Fig. 5): 0,77 Berm Height, B: bo ft Alongshore Diffusivity, G (From Equation below or Figure 15). SK H2^C g0o4 cos(go -ao) cos 2(A80 -a.) 8 (s -1)(1 -p)C.0.4(h. + B) cos(8o -a.) 0,77 Yo.ll. ($ = .-7117 ft2/ g ( l, ) (o, 6 5) (.. )bp O ').,-3oBackground Erosion Equilibrated Beach Width, Ayo x Erosion Rate (ER) ^ p/3 Erosion Rate (ER) AN (Fig. 7) or From Profile: O 5 ft/3 S< ft/yr AF (Fig. 7): O0 0 ft'/3 Volume Per Unit Length: 5/ ft3/ft Ayo (Figs. 11 and 12): /l2. ft Project Length, £, = 2 O miles = /0 ',O) ft For 30 years Gt G(30x365x24x3600) 16 /= 16= .= (1) (2) (3) (4) (5) (6) Distance Y (~2) /Ayo y, YB(ft) = N = From Center, x(ft) (Fig. 17) (ft) 30 x ER y, -ys, (ft) o.o _,0 O 2_ 3l.t o .31,. 528o 1,0 fct ___ t_ o _2_4__ __o 2.11 1'.2. 0 ___ 61

PAGE 72

(^(CPAI c L C -`,AmPLE 2 CUn-f orm a(o und Erosrn BEACH NOURISHMENT PROJECTION (Graphical Computations, Uninterrupted Shoreline) General Location: Wave Height, Ho (Fig. 23): .0 ft, Closure Depth, h. (Fig. 8): 17 ft Wave Period, T (Fig. 24): (0oO sec, Sediment Size, D: mm Wave Direction, ao: Oo __, Transport Factor, K (Fig. 5): 01'7 Berm Height, B: & ft Alongshore Diffusivity, G (From Equation below or Figure 15). K H2-4Cg0-4 cos(Po -ao) cos 2(fo -a,) G -8 (s -1)(1 -p)C.c0.4(h. + B) cos(/o -a.) = =,t/ 0,/iq-7 ft2/s Background Erosion -Equilibrated Beach Width, Ayo x Erosion Rate (ER) -. -i Erosion ft/yr AN (Fig. 7) or From Profile: O. Z fti/ -o 10,o fo AF (Fig. 7): ;,2e ft /3 Volume Per Unit Length: ,5// 3 ft3/ft -Ayo (Figs. 11 and 12): //2ft Project Length, £, = Au O miles = /, .0 ft For 30 years 16Gt G(30x365x24x3600) 16-= 16 -2= / -= £2 J2 (1) (2) (3) (4) (5) (6) Distance Y Y (1 /Ayo y, /B(ft) = N = From Center, x(ft) (Fig. 17) (ft) 30 x ER y, -ys (ft) So0 .2?8 3.4 &t > -28.6 5Z28O _o 2 C2O 2', I o _-__ lo so o.7z ;o 1 .6b -7Y1 62

PAGE 73

6 RAP I CAL EXAMf^PLE 3 (%NorioUD 4r .-ErosiovY) BEACH NOURISHMENT PROJECTION (Graphical Computations, Uninterrupted Shoreline) General Location: Wave Height, Ho (Fig. 23): 0. ft, Closure Depth, h. (Fig. 8): o 7ft Wave Period, T (Fig. 24): 6., sec, Sediment Size, D: mm Wave Direction, ao: 0. 0 o, Transport Factor, K (Fig. 5): 0T11 Berm Height, B: 4 ,o ft Alongshore Diffusivity, G (From Equation below or Figure 15). G K H^C g0o4 cos(#o -0) cos 2(#0o -0,) G = 8 (s -1)(1 -p)C.0.4(h. + B) cos(Po -a*) a-= o5,3 -<9 -PI ..= _,J,47 f2/s Background Erosion Equilibrated Beach Width, Ayo x Erosion Rate (ER) AN (Fig. 7) or From Profile: O, 2ftl/3 -lo /,o ft/yr AF (Fig. 7): 7, O ft1/3 St__.o -,O Volume Per Unit Length: -s// 3 ft3/ft -Ayo (Figs. 11 and 12): / 2. ft -Project Length, 1, = *' ) miles = /) 56C ft For 30 years SGt = G(30x365x24x3600) --g 16 -= 16 = = (1) (2) (3) (4) (5) (6) Distance 2 y ( ) /Ayo Ys y (ft)= N = From Center, x(ft) (Fig. 17) (ft) 30 x ER y, -yy (ft) -',,o -3. .. ,z .1 30.0 -5. L4 0 o o.2s 331, c 4S.O -13.( 0t12840 Z*76 0.2 .: -23 +__,__0 .42l. 0.1 XI. Cg1 -3X 63

PAGE 74

< RPH\C-AL EYRmPL£4 (NoyI^YI^O"-^ Ernssa o^) BEACH NOURISHMENT PROJECTION (Graphical Computations, Downdrift of a Littoral Barrier) General Location: Wave Height, Ho (Fig. 23): < 'O ft, Closure Depth, h, (Fig. 8): /70 ft Wave Period, T (Fig. 24): (, .sec, Sediment Size, D: mm Wave Direction, ao: 0, Transport Factor, K (Fig. 5): 0o'7 Berm Height, B: -o ft Alongshore Diffusivity, G(From Equation Below or Figure 15) K H4^C g0.4 cos(Po -ao) cos 2(l#o -a.) G = 8 (s -1)(1 -p)C,0o.4(h. + B) cos(Po -a.) -= .O_0, |4W7 ft2/s Background Erosion Equilibrated Beach Width, Ayo Erosion Rate (ER) AN (Fig. 7) or From Profile: 0. 2. ft1/3 0_ -o.0 ft/yr AF (Fig. 7): 0,2 ft'/3 __Bo -) L Volume Per Unit Length: 6//3 ft3/ft o0b59 -8 .Ayo (Figs. 11 and 12): //2 ft 2 Irzo 40 Project Length, e, = miles = /I ~ $7 ft _Effective Project Length, e' = 2 = miles = 2.1, /2 ft For 30 years Gt 1G(30x365x24x3600) -, 16(J = 16---= 3, S 9' == ( )2 ( £)2 (1) (2) (3) (4) (5) (6) Distance y (T ) //Ay y' yB(ft) = N = From Littoral Barrier, X(ft) (Fig. 17) (ft) 30 x ER y, -yb (ft) 0 0 OST. 5g.-i.
PAGE 75

REFERENCES Balsillie, J. (1987) "Offshore Profile Description Using the Power Curve Fit, Part II: Standard Florida Offshore Profile Tables", Beaches and Shores, Technical and Design Memorandum No. 82-1-IIa, Florida Department of Natural Resources, Tallahassee, FL. Bruun, P. (1954) "Coast Erosion and the Development of Beach Profiles", Beach Erosion Board, Technical Memorandum No. 44. Dean, R. G. (1977) "Equilibrium Beach Profiles: U.S. Atlantic and Gulf Coasts", Department of Civil Engineering, Ocean Engineering Report no. 12, University of Delaware, Newark, DE. Dean, R. G. (1978) "Review of Sediment Transport Relationships and the Data Base", Proceedings of a Workshop on Coastal Sediment Transport with Emphasis on the National Sediment Transport Study", Report DEL-SG-15-78, University of Delaware, Newark, DE. Dean, R.G. (1987) "Additional Sediment Input to the Nearshore Region", Shore and Beach, Vol. 55, Nos. 3-4, p. 76-81. Moore, B.D. (1982) "Beach Profile Evolution in Response to Changes in Water Level and Wave Height", Masters Thesis, Department of Civil Engineering, University of Delaware, Newark, DE. Pelnard Considere, R. (1956) "Essai de Theorie de l'Evolution des Formes de Rivate en Plages de Sable et de Galets", 4th Journees de l'Hydraulique, Les Engergies de la Mar, Question III, Rapport No. 1. 65

PAGE 76

APPENDIX A DEEP WATER WAVE EQUIVALENTS FOR SHORELINE MODELING

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APPENDIX A DEEP WATER WAVE EQUIVALENTS FOR SHORELINE MODELING Consider the transport equation Q = C cos(p -ab) sin(, -b) (A. pg(s -1)(1 -p) \ l l • I I I :' I I I s II I I o //. 1 I I /' I I I / / / I / / / I I ... I / I I I I x Definition Sketch The bathymetry of concern will be considered as straight and parallel bottom contours seaward of the effects of a beach nourishment project. This seaward depth limit is denoted as h,. For depths smaller than h., it is assumed that all contours are parallel to the shoreline. The azimuth, ,g, of the outward normal within the depth limit affected by the nourishment 67

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project is related to the azimuth of the outward normal, 0o, outside the limit of the project by =(s) = /o + A/ (x) (A.2) in which A/ is small. Using conservation of energy and Snell's law to transform Eq. (A.1) from the breaker line to the depth contour h,, S E*CGo cos(,6s -a*) sin(1, -a*)(A.3) q =-K Cb (A.3) pgQ -1)(1 -p)C* and using Eq. (A.2) K E, CG, sin 2(Po + Af -a,) CA.4) 2 pg(s -1)(1 -p) C, and expanding KE C. sin 2(ro -~a) cos C 2 pg(s -1)(1 -p) C E. CG, cos 2(flo -) 2 Cb + K sin 2Af(A.5) 2 pg(s1)(1-p) C* Since Ap is small, cos 2A/3 P 1 and sin 2A/p -2Af6, and the first term is recognized as the transport without the project present (the background transport, QB) and the second term the transport induced by project placement, Qp. The background transport will first be expressed in terms of deep water wave characteristics .. iQ K E,*CG cos(?o -c) sin(fo -a*) Cb QBACKGROUND = QB = K QBACKGROUND pg(s -1)(1 -p) C SK EoCGO cos(po -Co) sin(Po -so) Cb pg(s -1)(1 -p) Co Eq. (A.6) contains Cb which we now wish to relate to deep water conditions. Using energy conservation, EbCGb cos(P, -ab) = E*CG. cos(P, -a,) = ECG. cos(fo + Ari -a,) 68

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Therefore EbCGC cos(/a -as) = E.CG. [cos(Po -,a) cos Ap -sin(p3, -a.) sin AP] and since Ap8 is small, the last term can be neglected and cos Ap8 p 1. Finally EbCG cos(,/ -ab) : EoCco cos(/o -cso) and employing the following shallow water approximations CGb Cb -V "gh Hb ; z he (i F 0.78) g2H2Cb cos((, -as) = 92H2CGo cos(3o -ao) ,2'C5 cos(a, -ab) = g2H CGo cos(#o -ao) b = [g2HCoG cos(o -o)2 (A.7) in which cos(p, -as) has been approximated by unity. Returning now to the project transport and using conservation of energy considerations and Snell's law to transform to deep water K EoCGo cos 2(fo -a.) cos(po -aco) C pg(s -1)(1 -p)cos(Poa) C, Employing Eq. (A.7), the project related transport can now be written without reference to shallow water K H2.^C -o04 os12 (fo -o) 1 QP = o cos --a.) AP (A.9) 8(s -1)(1 -p) cos(Po -a,)c0 s24 *'C,A Using Snell's law, ?o -a* = sin-1 [C sin(,o -ao)] (A.10) Lo -s, = sin-J co The shore planform direction anomaly Ap is Ay tan( -(A.11) 69

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Combining Eqs. (A.8) and (A.11) with the continuity equation y 1 Qp (A.12) at (h, + B) ax we find ay K H2 4C1^ g0.4 cosl 2(po -o) cos2(fo -a,) a2y at 8(s -1)(1 -p)Cco.0(h + B) cos(Po -a.) J x2 Defining the longshore diffusivity, =K H4C12g0.4 cos1.2( 3o -ao) cos 2(f6o -a.) (A.13) 8(s -1)(1 -p)C.o.4(h. + B) [ cos(,o -a.) I) and it is noted that G is now expressed entirely in terms of deep water wave quantities (with the use of Eq. (A.10)). The diffusion equation for shoreline evolution is obtained in the usual form By 82y a-= Ga 2 (A.14) at 82 We now consider the equations that will be used for numerical analysis. Commencing with Eq. (A.3) and inserting Eq. (A.2) in the cosine term Q K ECG. [cos(Po -a.) cos Ap -sin(13o -a.) sin A] sin( -(A.15) Q = -in(3, -a.)Cs (A.15) pg(s -1)(1 -p)C, and since Ap is small and using conservation of energy K EoCGo cos(po -ao) Q = 1)(1 -p)C sin(fl, -a,)Cb (A.16) pg(s -1)(1 -p)C. Combining Eq. (A.7) with the expression for deep water wave energy, Eo o =pg (A.17) 8 yields K H2^C g0.4cos12(Po -o) Q = sin(#, -a.) (A.18) 8(s -1)(1 -p)C, 4 s( -(A18) and C, a, = io -sin-1 [sin(fo -ao)] (A.19) which completes the development. It is noted that with the exception of the trigonometric term involving (V, -a,) and the term C., all quantities are expressed in terms of deep water conditions. 70

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Representative Wave Conditions To simplify input conditions it is desirable to define representative wave characteristics. In developments here, we will consider a constant wave direction, but time-varying wave height and period. At each time, the waves will be considered as represented by a single period and a Rayleigh wave height distribution with significant wave height H,. The effective height is thus Heff = [J H4p(H)dH] (A.20) in which all wave heights are in deep water and p(H) is the Rayleigh distribution, p(H) = -e(H/H,)2 (A.21) H2rms Eq. (A.20) can be solved numerically to yield Heff = Krm,Hrm, = K,H, (A.22) where Krms = 1.04 and K, = 0.735. Thus the long-term effective wave height Heff at a particular location is 1 Hff = (KH)4 (A.23) n=1 I A somewhat more appropriate but more cumbersome value of Heff is Heff2 N= -(A.24) N n= 1 n c 1.2 and the effective value of -to be used in Eq. (A.18) is the denominator of Eq. (A.24) raised to the 2.4 power. The recommended values of effective deep water wave height around the state of Florida are plotted in Figure 23. 71

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APPENDIX B PROGRAM LISTING AND SAMPLE INPUT AND OUTPUT Program: DNRBS.FOR Input File: DNRBS.INP Output File: DNRBS.OUT (Note: Input and Output Files Presented for Numerical Example 2)

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PROGRAM LISTING: DNRBS.FOR C C THIS PROGRAM DEVELOPED FOR DIVISION OF BEACHES AND SHORES, C DEPARTMANT OF NATURAL RESOURCES FOR USE IN PREDICTING C THIRTY YEAR EROSION PROJECTIONS ** C C ********************************************************************* C DIMENSION YO(500),YN(500),X(500),Q(500),HB(500),ALP(500), 1 XER(40),EROSB(40),SUMA(50),VTOTA(50),YEARA(50), 2 ITNOUR(10),ISEG(10),IS(10,10),IE(10,10),DY(10,10), 3 WORD(20),YEAR(10),DV(10,10),NSEG(10),PCT(50),DYO(500) 4 ,QBACK(500),YSTRUC(10),ISTRUC(10) OPEN(UNIT=6,FILE='DNRBS2.OUT',STATUS='NEW') OPEN(UNIT=5,FILE='DNRBS2.INP',STATUS='OLD') OPEN(UNIT=7,FILE='DNRBS2.DAT',STATUS='NEW') 55 FORMAT('***** IT = 1, I=1, EROSION RATE = ',E12.2) 120 FORMAT(6(I4,F8.2)) 121 FORMAT(/,5X,'NTIME = ',16,' HB = ',F8.2,' ALP = 'F8.3,' SUM = 1 F8.2,' STDEV = ',F8.2,/) 122 FORMAT(//) 123 FORMAT(5F8.2,416) 124 FORMAT(8F8.2) 125 FORMAT(4(E8.2,F8.2)) 126 FORMAT(20A4) 127 FORMAT(20A4,/) 160 FORMAT(816) 162 FORMAT(F8.2,3I6,2F8.2) 164 FORMAT(816) 165 FORMAT(/) 166 FORMAT(I6,3F8.2) 167 FORMAT(' INITIAL SHORELINE (INCL. NOURISHMENT) POSITION',/) 168 FORMAT(I6,F8.1,2E12.4,F8.2) 170 FORMAT(' HO =',F6.2,' FT., T =',F6.2,' SEC., ALPO = ',F6.2,' DEG. 1, BTAO = ',F6.2,' DEG., 2 ,5X,' XMU =',F8.2,' DEG., DX = ',F8.2,' FT., DT = ',F8.2,' SEC.') 172 FORMAT(' HSTR = ',F8.2,' FT., B = ',F8.2,' FT., XK = ',F8.2, 1' VFACT = ,F8.2,14X,'QBKREF = ',F8.2,' FT.**3/SEC.') 173 FORMAT(' IREF = ',16,', IMAX = ',16,', NTIMES = ',18, 1 ', NS = ',16) 444 FORMAT(20X,'TIME = ',18,' YEARS') 446 FORMAT(' NYEARS = ',18,' DYSITE = ',F8.2) 447 FORMAT(' BACKGROUND EROSION TRANSPORT RATES',/) 448 FORMAT(5(I6,F8.3)) 449 FORMAT(216,8F8.3) GRAV=32.2 NER=7 SG=2.65 POR=0.35 PI=3.14159 PI02=PI/2.0 ITNM=1 XKAP=0.78 QBACK(1)=0.0 73 LCUR=0 READ(5.1261(fWORDf(I).I=1.20)

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WRITE(6,127)(WORD(I),I=1,20) WRITE(7,126)(WORD(I),I=1,15) READ(5,124)HO,T,ALPO,BTAO,XMU,DX,DT READ(5,123)HSTR,B,XK,VFACT,QBKREF,IREF,IMAX,NTIMES,NS IF(NS.GT.O)READ(5,448)(ISTRUC(I),YSTRUC(I),I=1,NS) WRITE(7,170)HO,T,ALPO,BTAO,XMU,DX,DT WRITE(7,172)HSTR,B,XK,VFACT,QBKREF WRITE(6,170)HO,T,ALPO,BTAO,XMU,DX,DT WRITE(6,172)HSTR,B,XK,VFACT,QBKREF WRITE(6,173)IREF,IMAX,NTIMES,NS WRITE(6,165) IF(NS.GT.0) WRITE(6,448)(ISTRUC(I),YSTRUC(I),I=1,NS) ALPO=ALPO*PI/180.0 BTAO=BTAO*PI/180.0 XMU=XMU*PI/180.0 READ(5,124)(XER(I),EROSB(I),I=1,NER) WRITE(6,165) WRITE(6,125)(XER(I),EROSB(I),I=1,NER) WRITE(*,125)(XER(I),EROSB(I),I=1,NER) READ(5,160)NNOUS,NNOUE WRITE(*,160)NNOUS,NNOUE DO 60 I=NNOUS,NNOUE READ(5,166)I,DYO(I) 60 DYO(I)=DYO(I)*VFACT TOTH=HSTR+B IMM1=IMAX-1 IMP1=IMAX+1 DO 30 I=1,IMP1 X(I)=(I-1)*DX YN(I)=0.0 30 YO(I)=0.0 C**** FOLLOWING IS BACKGROUND EROSION AND ASSOCIATED TRANSPORT DO 240 I=1,IMAX CALL INTERP(EROSB,ERC,NER,X,XER,I,DT,QBACK,TOTH,DX,IREF) 240 CONTINUE DQ=QBACK(IREF)-QBKREF DO 241 I=1,IMP1241 QBACK(I)=QBACK(I)-DQ CALL WVNUM(HSTR,T,CC) CO=GRAV*T/(2.0*PI) CGO=CO/2.0 ALPSTR=BTAO-ASIN(CC/CO*SIN(BTAO-ALPO)) C WRITE(6,124)HSTR,T,CC,CO,CGO,ALPO,BTAO,ALPSTR CALP=COS(ALPO-ALPSTR) SALP=SIN(ALPO-ALPSTR) WRITE(6,165) WRITE(6,447) WRITE(6,448)(I,QBACK(I),I=1,IMP1) WRITE(6,165) WRITE(6,160)NNOUS,NNOUE WRITE(6,167) C ***** FOLLOWING IS TIME LOOP DO 300 NT=1,NTIMES IF(MOD(NT,10).EQ.0) WRITE(*,*) NT,NTIMES BB=XK*HO**2.4*CGO**1.2*GRAV**0.4*COS(BTAO-ALPO)**1.2/ 1 (8.0*(SG-1)*(1.0-POR)*CC*XKAP**0.4) SUM=0.0 SUM2=0.0 NFLAG=0 IF(NFLAG.EQ.1) GO TO 302 IF(NT.EQ.1.OR.NT.EQ.0) CALL NOUR(NT,ITNM,YO,IMAX,ITNOUR, 1 NSEG,IS,IE,DY,VTOT,IT,DV,X,NNOUS,NNOUE,DYO,DX,TOTH) C YO(1)=0.0 C YO(IMAX)=0.0 C*****FOLLOWING IS TRANSPORT LOOP

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BTA=XMU-ATAN2((YO(I)-YO(I-1)),(X(I)-X(I-1)))-PI02 COSC=COS(BTA-ALPO) SINC=SIN(BTA-ALPO) Q(I)=BB*SIN(BTA-ALPSTR) QB=QBACK(I) QSAVE=Q(I) CALL STR(NS,YSTRUC,I,YO,Q,IMAX,DX,ALPC,XMU,QB,BB,PI02, 1 ISTRUC,ALPSTR) IF(NT.EQ.100.AND.I.EQ.116)WRITE(6,449)NT,I,Q(I),QB, 1 YSTRUC(1,Y(-1)O(I-,YO(I),QBACK(I),QSAVE Q(I)=Q(I)+QB 100 CONTINUE YN(1)=YO(1) YN(IMAX)=YO(IMAX) Q(1)=QBACK(1)+Q(2)-QBACK(2) Q(IMP1)=QBACK(IMP1)+Q(IMAX)-QBACK(IMAX) C******FOLLOWING IS FOR CONTINUITY EQUATION DO 200 I=1,IMAX IF(I.GT.1)GO TO 266 DX=X(2)-X(1) GO TO 268 266 DX=(X(I+1)-X(I-1))/2.0 268 CONTINUE AA=YO(I) YN(I)=YO(I)-DT/(DX*TOTH)*(Q(I+I)-Q(I)) YO(I)=YN(I) IF(I.NE.1.OR.NT.NE.10)GO TO 200 WRITE(7,449)I,NT,AA,YN(I),DT,DX,TOTH,Q(I+1),Q(I) 200 CONTINUE C WRITE(6,120)(I,YN(I),I=1,IMP1) C WRITE(6,120)(I,Q(I),I=1,IMP1) IF(MOD(NT,365).NE.O) GO TO 300 C IF(MOD(NT,3650).NE.0) GO TO 301 NYEARS=NT/365 NZC=NYEARS IF(NZC.NE.1.AND.NZC.NE.5.AND.NZC.NE.10.AND.NZC.NE.30)GO TO 301 WRITE(6,444)NYEARS WRITE(6,120)(I,YN(I),I=1,IMAX) 301 CALL PERCT(YN,DX,SUM,PCT,VTOT,LCUR,LCURM,SUMA,VTOTA,TOTH,X 1 ,NNOUS,NNOUE) YEARA(LCUR)=1990.0+(NT-1)*DT/31536000.0 300 CONTINUE WRITE(7,168)(L,YEARA(L),SUMA(L),VTOTA(L),PCT(L),L=1,LCURM) DYSITE=0.5*(YN(26)+YN(27))-62.06-NYEARS*2.31 C NZC=NYEARS C IF(NZC.NE.1.OR.NZC.NE.5.OR.NZC.NE.10.OR.NZC.NE.30)GO TO 302 C WRITE(6,446)NYEARS,DYSITE WRITE(7,120)(I,YN(I),I=1,IMP1) C WRITE(6,120)(I,Q(I),I=1,IMP1) 302 CONTINUE CLOSE(UNIT=5) CLOSE(UNIT=6) CLOSE(UNIT=7) STOP END C C r*******X'**********I1* C SUBROUTINE INTERP(EROSB,ERC,NER,X,XER,I,DT,QBACK,TOTH,DXB,IREF) DIMENSION EROSB(40),XER(40),X(400),QBACK(400) 100 FORMAT(216,6F10.3) 101 FORMAT(6E12.4) 75 XC=X(I) CON=DT/31536000.0 DO 10 IER=2,NER *iT / Tm TI r n vr m rn \ \ Iin mrr 1 A____.n II ^n /m -7 nIr nNI

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DX=XER(IER)-XER(IER-1) DXX=XC-XER(IER-1) AA=DXX/DX BB=1.0-AA ERC=-CON*(BB*EROSB(IER-1)+AA*EROSB(IER)) QBACK(1+1)=QBACK(I)-DXB*TOTH*ERC/DT IF(I.NE.2)GO TO 6 C WRITE(6,100)I,IER,ERC,DT,TOTH,DX,AA,BB C WRITE(6,101)QBACK(I),QBACK(I-1),QBACK(I+1),CON,DXB 6 GO TO 20 10 CONTINUE 20 RETURN END C C ********* C c SUBROUTINE NOUR(NT,ITNM,YN,IMAX,ITNOUR,NSEG, 1 IS,IE,DY,VTOT,ITC,DV,X,NNOUS,NNOUE,DYO,DX,TOTH) DIMENSION YN(500),ITNOUR(10),NSEG(10),DY(10,10), 1 IS(10,10),IE(10,10),DV(10,10),YNT(500), 2 X(500),DYO(50) 24 FORMAT(' OUTPUT FROM SR NOUR ',16,' ISC = ',16,' IEC = ',16) 26 FORMAT(' REACHED SR NOUR',216,F8.2) 28 FORMAT(' NOUR EVENT = ',16,' YEAR = ',F8.2, 1 VOL ADDED = ',F8.3,' MILL YDS**3',/) 30 FORMAT(2(I6,F10.0,F8.2)) 32 FORMAT(' TOTAL VOLUME ADDED = ',F12.1 ,' CUBIC YARDS',/) VTOTT=0.0 FACT=1.0 C IF(NT.NE.1)FACT=0.5 DO 6 I=NNOUS,NNOUE 6 YN(I)=YN(I)+DYO(I)*FACT DO 12 I=NNOUS,NNOUE 12 VTOTT=VTOTT+(X(I+1)-X(I-1))/2.0*YN(I) VTOT=VTOTT C WRITE(6,32)VTOT C WRITE(7,32)VTOT WRITE(6,30)(I,X(I),YN(I),I=1,IMAX) RETURN END C C ************* THIS SUBROUTINE CALCULATES PERCENTAGES OF C TOTAL VOLUME REMAINING SUBROUTINE PERCT(YN,DX,SUM,PCT,VTOT,LCUR,LCURM,SUMA,VTOTA,TOTH,X 1 ,NNOUS,NNOUE) DIMENSION YN(400),PCT(50),SUMA(50),VTOTA(50),X(200) 24 FORMAT(5X,'LCUR = ',16,' PCT(LCUR) = ',F8.2) SUM=0.0 DO 20 I=NNOUS,NNOUE 20 SUM=SUM+(X(I+1)-X(I-1))/2.0*YN(I) LCUR=LCUR+1 LCURM=LCUR SUMA(LCUR)=SUM VTOTA(LCUR)=VTOT PCT(LCUR)=SUM/VTOT WRITE(6,24)LCUR,PCT(LCUR) WRITE(*,24)LCUR,PCT(LCUR) RETURN END C C*********THIS SUBROUTINE CHECKS PFR ANn ACCOUNTS FOR THE TRANSPORT C AROUND STRUCTURES 76 C SUBROUTINE STR(NS,YSTRUC,I,YO,Q,IMAX,DX,ALPC,XMU,QB,BB,PIO2, 1 ISTRUC,ALPSTR) ,____h T n -X -T I t \ I rI -i \----

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C 18 FORMAT(316,6F8.2) C WRITE(*,18)NS,I,I,YSTRUC(1) DO 20 IS=1,NS IC=IS 20 IF(I.EQ.ISTRUC(IS))GO TO 40 GO TO 80 40 DYP=YO(I)-YSTRUC(IC) DYM=YO(I-1)-YSTRUC(IC) C WRITE(6,18)I,ISTRUC(IC),IC,DYP,DYM DXC=DX/2.0 IF(DYP.GE.0.0.AND.DYM.GE.0.0)GO TO 80 IF(DYM.LT.0.0.AND.QB.GT.0.0)QB=0.0 IF(DYP.LT.0.0.AND.QB.LT.0.0)QB=0.0 IF(DYM.GE.0.0.OR.DYP.GE.O.O)GO TO 42 Q(I)=0.0 GO TO 80 42 IF(DYM.LT.0.0)GO TO 44 C TO HERE IF DYM.GT.0.0.AND DYP.LT.0.0 BTA=XMU-ATAN2(-DYM,DXC)-PI02 GO TO 46 C TO HERE IF DYP.GT.0.0.AND.DYM.LT.0.0 44 BTA=XMU-ATAN2(DYP,DXC)-PI02 46 Q(I)=BB*SIN(BTA-ALPSTR) 80 RETURN END C C ****** THIS SUBROUTINE CALCULATES WAVE LENGTH AND CELERITY C SUBROUTINE WVNUM(HSTR,T,CC) 20 FORMAT(I6,8F8.3) G=32.17 EPS=0.001 TWOPI=6.283185 SIG=TWOPI/T XK=TWOPI/(T*SQRT(G*HSTR)) DO 100 IT=1,20 ARG=XK*HSTR EK=(G*XK*TANH(ARG))-SIG**2 SECHA=1.0/COSH(ARG) EKPR=G*(ARG*(SECHA**2)+TANH(ARG)) XKNEW=XK-EK/EKPR IF(ABS(XKNEW-XK).LT.ABS(EPS*XKNEW)) GO TO 120 XK=XKNEW 100 CONTINUE 120 XK=XKNEW XL=TWOPI/XK CC=XL/T RETURN END 77

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INPUT FILE: DNRBS.INP (Example No. 2) EXAMPLE NO. 2 UNIF. BACK. EROS. NO STRUC. 2 MILE PROJ. 2.00 6.0 90.0 90.0 180.0 500.0 86400.0 17.0 6.0 0.77 1.0 0.0 1 180 10950 0 0.0 2.0 90000. 2.0 49500. 2.0 60000. 3.0 90000. 3.0 100000. 3.0 140000. 2.0 80 100 80 112.0 81 112.0 82 112.0 83 112.0 84 112.0 85 112.0 86 112.0 87 112.0 88 112.0 89 112.0 90 112.0 91 112.0 92 112.0 93 112.0 94 112.0 95 112.0 96 112.0 97 112.0 98 112.0 99 112.0 100 112.0 78

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OUTPUT FILE: DNRBS.OUT (Example No. 2) EXAMPLE NO. 2 UNIF. BACK. EROS. NO STRUC. 2 MILE PROJ. HO = 2.00 FT., T = 6.00 SEC., ALPO = 90.00 DEG., BTAO = 90.00 DEG., XMU = 180.00 DEG., DX = 500.00 FT., DT = 86400.00 SEC. HSTR = 17.00 FT., B = 6.00 FT., XK = .77 VFACT = 1.00 QBKREF = .00 FT.**3/SEC. IREF = 1, IMAX = 180, NTIMES = 10950, NS = 0 .00E+00 2.00 .90E+05 2.00 .50E+05 2.00 .60E+05 3.00 .90E+05 3.00 .10E+06 3.00 .14E+06 2.00 BACKGROUND EROSION TRANSPORT RATES 1 .000 2 .001 3 .001 4 .002 5 .003 6 .004 7 .004 8 .005 9 .006 10 .007 11 .007 12 .008 13 .009 14 .009 15 .010 16 .011 17 .012 18 .012 19 .013 20 .014 21 .015 22 .015 23 .016 24 .017 25 .018 26 .018 27 .019 28 .020 29 .020 30 .021 31 .022 32 .023 33 .023' 34 .024 35 .025 36 .026 37 .026 38 .027 39 .028 40 .028 41 .029 42 .030 43 .031 44 .031 45 .032 46 .033 47 .034 48 .034 49 .035 50 .036 51 .036 52 .037 53 .038 54 .039 55 .039 56 .040 57 .041 58 .042 59 .042 60 .043 61 .044 62 .044 63 .045 64 .046 65 .047 66 .047 67 .048 68 .049 69 .050 70 .050 71 .051 72 .052 73 .053 74 .053 75 .054 76 .055 77 .055 78 .056 79 .057 80 .058 81 .058 82 .059 83 .060 84 .061 85 .061 86 .062 87 .063 88 .063 89 .064 90 .065 91 .066 92 .066 93 .067 94 .068 95 .069 96 .069 97 .070 98 .071 99 .071 100 .072 101 .073 102 .074 103 .074 104 .075 105 .076 106 .077 107 .077 108 .078 109 .079 110 .079 111 .080 112 .081 113 .082 114 .082 115 .083 116 .084 117 .085 118 .085 119 .086 120 .087 121 .088 122 .088 123 .089 124 .090 125 .090 126 .091 127 .092 128 .093 129 .093 130 .094 131 .095 132 .096 133 .096 134 .097 135 .098 136 .098 137 .099 138 .100 139 .101 140 .101 141 .102 142 .103 143 .104 144 .104 145 .105 146 .106 147 .106 148 .107 149 .108 150 .109 .151 .109 152 .110 153 .111 154 .112 155 .112 156 .113 157 .114 158 .115 159 .115 160 .116 161 .117 162 .117 163 .118 164 .119 165 .120 166 .120 167 .121 168 .122 169 .123 170 .123 171 .124 172 .125 173 .125 174 .126 175 .127 176 .128 177 .128 178 .129 179 .130 180 .131 181 .131 79 goD 100

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1 0. .00 2 500. .00 3 1000. .00 4 1500. .00 5 2000. .00 6 2500. .00 7 3000. .00 8 3500. .00 9 4000. .00 10 4500. .00 11 5000. .00 12 5500. .00 13 6000. .00 14 6500. .00 15 7000. .00 16 7500. .00 17 8000. .00 18 8500. .00 19 9000. .00 20 9500. .00 21 10000. .00 22 10500. .00 23 11000. .00 24 11500. .00 25 12000. .00 26 12500. .00 27 13000. .00 28 13500. .00 29 14000. .00 30 14500. .00 31 15000. .00 32 15500. .00 33 16000. .00 34 16500. .00 35 17000. .00 36 17500. .00 37 18000. .00 38 18500. .00 39 19000. .00 40 19500. .00 41 20000. .00 42 20500. .00 43 21000. .00 44 21500. .00 45 22000. .00 46 22500. .00 47 23000. .00 48 23500. .00 49 24000. .00 50 24500. .00 51 25000. .00 52 25500. .00 53 26000. .00 54 26500. .00 55 27000. .00 56 27500. .00 57 28000. .00 58 28500. .00 59 29000. .00 60 29500. .00 61 30000. .00 62 30500. .00 63 31000. .00 64 31500. .00 65 32000. .00 66 32500. .00 67 33000. .00 68 33500. .00 69 34000. .00 70 34500. .00 71 35000. .00 72 35500. .00 73 36000. .00, 74 36500. .00 75 37000. .00 76 37500. .00 77 38000. .00 78 38500. .00 79 39000. .00 80 39500. 112.00 81 40000. 112.00 82 40500. 112.00 83 41000. 112.00 84 41500. 112.00 85 42000. 112.00 86 42500. 112.00 87 43000. 112.00 88 43500. 112.00 89 44000. 112.00 90 44500. 112.00 91 45000. 112.00 92 45500. 112.00 93 46000. 112.00 94 46500. 112.00 95 47000. 112.00 96 47500. 112.00 97 48000. 112.00 98 48500. 112.00 99 49000. 112.00 100 49500. 112.00 101 50000. .00 102 50500. .00 103 51000. .00 104 51500. .00 105 52000. .00 106 52500. .00 107 53000. .00 108 53500. .00 109 54000. .00 110 54500. .00 111 55000. .00 112 55500. .00 113 56000. .00 114 56500. .00 115 57000. .00 116 57500. .00 117 58000. .00 118 30. .00 119 59000. .00 120 80 )0. .00 121 60000. .00 122 )0. .00 123 61000. .00 124 )0. .00 125 62000. .00 126 62500. .00 127 63000. .00 128 63500. .00

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131 65000. .00 132 65500-U. .UU 131 65000. .00 132 65500. .00 133 66000. .00 134 66500. .00 135 67000. .00 136 67500. .00 137 68000. .00 138 68500. .00 139 69000. .00 140 69500. .00 141 70000. .00 142 70500. .00 143 71000. .00 144 71500. .00 145 72000. .00 146 72500. .00 147 73000. .00 148 73500. .00 149 74000. .00 150 74500. .00 151 75000. .00 152 75500. .00 153 76000. .00 154 76500. .00 155 77000. .00 156 77500. .00 157 78000. .00 158 78500. .00 159 79000. .00 160 79500. .00 161 80000. .00 162 80500. .00 163 81000. .00 164 81500. .00 165 82000. .00 166 82500. .00 167 83000. .00 168 83500. .00 169 84000. .00 170 84500. .00 171 85000. .00 172 85500. .00 173 86000. .00 174 86500. .00 175 87000. .00 176 87500. .00 177 88000. .00 178 88500. .00 179 89000. .00 180 89500. .00 100 116 .000 .084 .000 -.542 -.542 .084 .000 TIME = 1 YEARS 1 -2.00 2 -2.00 3 -2.00 4 -2.00 5 -2.00 6 -2.00 7 -2.00 8 -2.00 9 -2.00 10 -2.00 11 -2.00 12 -2.00 13 -2.00 14 -2.00 15 -2.00 16 -2.00 17 -2.00 18 -2.00 19 -2.00 20 -2.00 21 -2.00 22 -2.00 23 -2.00 24 -2.00 25 -2.00 26 -2.00 27 -2.00 28 -2.00 29 -2.00 30 -2.00 31 -2.00 32 -2.00 33 -2.00 34 -2.00 35 -2.00 36 -2.00 37 -2.00 38 -2.00 39 -2.00 40 -2.00 41 -2.00 42 -2.00 43 -2.00 44 -2.00 45 -2.00 46 -2.00 47 -2.00 48 -2.00 49 -2.00 50 -2.00 51 -2.00 52 -2.00 53 -2.00 54 -2.00 55 -2.00 56 -2.00 57 -2.00 58 -2.00 59 -1.99 60 -1.98 61 -1.96 62 -1.93 63 -1.87 64 -1.77 65 -1.60 66 -1.31 67 -.87 68 -.18 69 .84 70 2.31 71 4.34 72 7.07 73 10.62 74 15.06 75 20.45 76 26.75 77 33.87 78 41.64 79 49.83 80 58.16 81 66.34 82 74.10 83 81.19 84 87.43 85 92.71 86 96.98 87 100.24 88 102.52 89 103.87 90 104.31 91 103.87 92 102.52 93 100.24 94 96.98 95 92.71 96 87.43 97 81.19 98 74.10 99 66.34 100 58.16 101 49.83 102 41.64 103 33.87 104 26.75 105 20.45 106 15.06 107 10.62 108 7.07 109 4.34 110 2.31 111 .84 112 -.18 113 -.87 114 -1.31 115 -1.60 116 -1.77 117 -1.87 118 -1.93 119 -1.96 120 -1.98 121 -1.99 122 -2.00 123 -2.00 124 -2.00 125 -2.00 126 -2.00 127 -2.00 128 -2.00 129 -2.00 130 -2.00 131 -2.00 132 -2.00 133 -2.00 134 -2.00 135 -2.00 136 -2.00 137 -2.00 138 -2.00 139 -2.00 140 -2.00 141 -2.00 142 -2.00 143 -2.00 144 -2.00 145 -2.00 146 -2.00 147 -2.00 148 -2.00 149 -2.00 150 -2.00 151 -2.00 152 -2.00 153 -2.00 154 -2.00 155 -2.00 156 -2.00 157 -2.00 158 -2.00 159 -2.00 160 -2.00 161 -2.00 162 -2.00 163 -2.00 164 -2.00 165 -2.00 166 -2.00 167 -2.00 168 -2.00 169 -2.00 170 -2.00 171 -2.00 172 -2.00 173 -2.00 174 -2.00 175 -2.00 176 -2.00 177 -2.00 178 -2.00 179 -2.00 180 -2.00 LCUR = 1 PCT(LCUR) = .78 LCUR = 2 PCT(LCUR) = 81 .68 LCUR = 3 PCT(LCUR) = .60 LCUR = 4 PCT(LCUR) = .53 TIME = 5 YEARS 1 -10.00 2 -10.00 3 -10.00 4 -10.00 5 -10.00 6 -10.00 7 -10.00 8 -10.00 9 -10.00 10 -10.00 11 -10.00 12 -10.00 13 -10.00 14 -10.00 15 -10.00 16 -10.00 17 -10.00 18 -10.00

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I V -.lV .vu I-u -.u 4.-U U. vv r'-UU ..U v J -.VV -Z .^ 25 -10.00 26 -10.00 27 -10.00 28 -10.00 29 -10.00 30 -10.00 31 -10.00 32 -10.00 33 -9.99 34 -9.99 35 -9.99 36 -9.98 37 -9.98 38 -9.97 39 -9.96 40 -9.94 41 -9.92 42 -9.90 43 -9.86 44 -9.82 45 -9.77 46 -9.70 47 -9.61 48 -9.50 49 -9.37 50 -9.21 51 -9.00 52 -8.76 53 -8.46 54 -8.10 55 -7.68 56 -7.17 57 -6.58 58 -5.89 59 -5.09 60 -4.17 61 -3.12 62 -1.93 63 -.59 64 .91 65 2.57 66 4.40 67 6.41 68 8.58 69 10.91 70 13.41 71 16.05 72 18.82 73 21.71 74 24.70 75 27.75 76 30.84 77 33.93 78 37.00 79 40.01 80 42.92 81 45.69 82 48.29 83 50.69 84 52.84 85 54.71 86 56.29 87 57.54 88 58.45 89 59.00 90 59.18 91 59.00 92 58.45 93 57.54 94 56.29 95 54.71 96 52.84 97 50.69 98 48.29 99 45.69 100 42.92 101 40.01 102 37.00 103 33.,93 104 30.84 105 27.75 106 24.70 107 21.71 108 18.82 109 16.05 110 13.41 111 10.91 112 8.58 113 6.41 114 4.40 115 2.57 116 .91 117 -.59 118 -1.93 119 -3.12 120 -4.17 121 -5.09 122 -5.89 123 -6.58 124 -7.17 125 -7.68 126 -8.10 127 -8.46 128 -8.76 129 -9.00 130 -9.21 131 -9.37 132 -9.50 133 -9.61 134 -9.70 135 -9.77 136 -9.82 137 -9.86 138 -9.90 139 -9.92 140 -9.94 141 -9.96 142 -9.97 143 -9.98 144 -9.98 145 -9.99 146 -9.99 147 -9.99 148 -10.00 149 -10.00 150 -10.00 151 -10.00 152 -10.00 153 -10.00 154 -10.00 155 -10.00 156 -10.00 157 -10.00 158 -10.00 159 -10.00 160 -10.00 161 -10.00 162 -10.00 163 -10.00 164 -10.00 165 -10.00 166 -10.00 167 -10.00 168 -10.00 169 -10.00 170 -10.00 171 -10.00 172 -10.00 173 -10.00 174 -10.00 175 -10.00 176 -10.00 177 -10.00 178 -10.00 179 -10.00 180 -10.00 LCUR = 5 PCT(LCUR) = .47 LCUR = 6 PCT(LCUR) = .42 LCUR = 7 PCT(LCUR) = .38 LCUR = 8 PCT(LCUR) = .33 LCUR = 9 PCT(LCUR) = .30 TIME = 10 YEARS 1 -20.00 2 -20.00 3 -20.00 4 -20.00 5 -20.00 6 -20.00 7 -20.00 8 -20.00 9 -20.00 10 -20.00 11 -20.00 12 -20.00 13 -19.99 14 -19.99 15 -19.99 16 -19.99 17 -19.99 18 -19.98 19 -19.98 20 -19.97 21 -19.97 22 -19.96 23 -19.95 24 -19.94 25 -19.92 26 -19.91 27 -19.89 28 -19.86 29 -19.83 30 -19.80 31 -19.76 32 -19.71 33 -19.65 34 -19.59 35 -19.51 36 -19.42 37 -19.31 38 -19.19 39 -19.05 40 -18.89 41 -18.70 42 -18.49 43 -18.25 44 -17.98 45 -17.68 46 -17.34 47 -16.96 48 -16.53 49 -16.05 50 -15.53 51 -14.95 52 -14.32 53 -13.62 54 -12.86 55 -12.04 56 -11.15 57 -10.19 58 -9.16 59 -8.06 60 -6.88 61 -5.64 62 -4.33 63 -2.96 64 -1.51 65 -.01 66 1.54 67 3.15 68 4.80 69 6.48 70 8.19 71 9.92 72 11.66 73 13.40 74 15.12 75 16.82 76 18.48 77 20.10 78 21.66 79 23.14 80 24.55 81 25.85 82 27.06 83 28.14 84 29.10 85 29.93 86 30.62 87 31.16 88 31.55 89 31.79 90 31.87 91 31.79 92 31.55 93 31.16 94 30.62 95 29.93 96 29.10 97 28.14 98 27.06 99 25.85 100 24.55 101 23.14 102 21.66 103 20.10 104 18.48 105 16.82 106 15.12 107 13.40 108 11.66 109 9.92 110 8.19 111 6.48 112 4.80 113 3.15 114 1.54 115 -.01 116 -1.51 117 -2.95 118 -4.33 119 -5.64 120 -6.88 121 -8.06 122 -9.16 123 -10.19 124 -11.15 125 -12.04 126 -12.86 127 -13.62 128 -14.31 129 -14.95 130 -15.53 131 -16.05 132 -16.53 133 -16.96 134 -17.34 135 -17.68 136 -17.98 137 -18.25 138 -18.49 13.9 -18.70 140 -18.89 141 -19.05 142 -19.19 143 -19.31 144 -19.42 145 -19.51 146 -19.59 147 -19.65 148 -19.71 149 -19.76 150 -19.80 151 -19.83 152 -19.86 153 -19.89 154 -19.91 155 -19.92 156 -19.94 157 -19.95 158 -19.96 159 -19.97 car -19.97 161 -19.98 162 -19.98 163 -19.99 164 -19.99 165 -19.9 82 -19.99 167 -19.99 168 -20.00 169 -20.00 170 -20.00 171 -20.0 -20.00 173 -20.00 174 -20.00 175 -20.00 176 -20.00 177 -20.0 -20.00 179 -20.00 180 -20.00 LCUR = 10 PCT(LCUR) = .26 LCUR = 11 PCT(LCUR) = .23 LCUR = 12 PCT(LCUR) = .19

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LCUR = 13 PCT(LCUR) = .lb LCUR = 14 PCT(LCUR) = .13 LCUR = 15 PCT(LCUR) = .10 LCUR = 16 PCT(LCUR) = .08 LCUR = 17 PCT(LCUR) = .05 LCUR = 18 PCT(LCUR) = .02 LCUR = 19 PCT(LCUR) = .00 LCUR = 20 PCT(LCUR) = -.03 LCUR = 21 PCT(LCUR) = -.05 LCUR = 22 PCT(LCUR) = -.08 LCUR = 23 PCT(LCUR) = -.10 LCUR = 24 PCT(LCUR) = -.13 LCUR = 25 PCT(LCUR) = -.15 LCUR = 26 PCT(LCUR) = -.17 LCUR = 27 PCT(LCUR) = -.20 LCUR = 28 PCT(LCUR) = -.22 LCUR = 29 PCT(LCUR) = -.24 TIME = 30 YEARS 1 -59.99 2 -59.92 3 -59.84 4 -59.76 5 -59.68 6 -59.60 7 -59.52 8 -59.43 9 -59.34 10 -59.24 11 -59.14 12 -59.04 13 -58.93 14 -58.82 15 -58.69 16 -58.56 17 -58.43 18 -58.28 19 -58.13 20 -57.97 21 -57.80 22 -57.62 23 -57.42 24 -57.22 25 -57.01 26 -56.78 27 -56.54 28 -56.29 29 -56.02 30 -55.75 31 -55.45 32 -55.15 33 -54.83 34 -54.49 35 -54.14 36 -53.78 37 -53.40 38 -53.00 39 -52.59 40 -52.17 41 -51.72 42 -51.27 43 -50.80 44 -50.31 45 -49.81 46 -49.30 47 -48.77 48 -48.23 49 -47.68 50 -47.11 51 -46.54 52 -45.95 53 -45.36 54 -44.76 55 -44.15 56 -43.53 57 -42.91 58 -42.28 59 -41.66 60 -41.03 61 -40.40 62 -39.77 63 -39.15 64 -38.53 65 -37.92 66 -37.31 67 -36.71 68 -36.13 69 -35.55 70 -34.99 71 -34.45 72 -33.92 73 -33.41 74 -32.92 75 -32.46 76 -32.01 77 -31.59 78 -31.19 79 -30.83 80 -30.49 81 -30.17 82 -29.89 83 -29.64 84 -29.42 85 -29.24 86 -29.08 87 -28.97 88 -28.88 89 -28.83 90 -28.81 91 -28.83 92 -28.88 93 -28.97 94 -29.08 95 -29.24 96 -29.42 97 -29.64 98 -29.89 99 -30.17 100 -30.49 101 -30.83 102 -31.19 103 -31.59 104 -32.01 105 -32.45 106 -32.92 107 -33.41 108 -33.92 109 -34.45 110 -34.99 111 -35.55 112 -36.13 113 -36.71 114 -37.31 115 -37.92 116 -38.53 117 -39.15 118 -39.77 119 -40.40 120 -41.03 121 -41.66 122 -42.28 123 -42.91 124 -43.53 125 -44.15 126 -44.76 127 -45.36 128 -45.95 129 -46.54 130 -47.11 131 -47.68 132 -48.23 133 -48.77 134 -49.30 135 -49.81 136 -50.31 137 -50.80 138 -51.27 139 -51.72 140 -52.16 141 -52.59 142 -53.00 143 -53.40 144 -53.78 145 -54.14 146 -54.49 147 -54.83 148 -55.15 149 -55.45 150 -55.74 151 -56.02 152 -56.28 153 -56.54 154 -56.77 155 -57.00 156 -57.21 157 -57.42 158 -57.61 159 -57.79 160 -57.96 161 -58.12 162 -58.27 163 -58.41 164 -58.55 165 -58.68 166 -58.80 167 -58.91 168 -59.02 169 -59.12 170 -59.21 171 -59.31 172 -59.39 173 -59.48 174 -59.56 175 -59.63 176 -59.71 177 -59.78 178 -59.85 179 -59.92 180 -59.99 LCUR = 30 PCT(LCUR) = -.26 83

PAGE 94

APPENDIX C NUMERICAL EXAMPLE 1

PAGE 95

BEACH NOURISHMENT PROJECTION (Numerical Procedure) General Location: Earvnpfe. Wave Height, Ho (Fig. 22): 2-.o ft., Closure Depth, h. (Fig. 8): i7 ft. Wave Period, T (Fig. 23): 6 -. sec., Berm Height, B: ( ft. Wave Direction, ao: 9o o, Sand Diameter, D: 0.35 mm Deep Water Contour Orientation, s0: 9O o, Transport Factor, K (Fig. 5): 0,7-' Longshore Axis Orientation, p: 19o 0, VFACT: .,o Grid Dimension, Az: .4oo ft Background Transport, QREF: 0o 0 ft3/s Time Increment, At: 8go,4 sec IREF: I IMAX: I So NTIMES: ( o0? No. of Structures, NS: 0 Structure Specificiation Background Erosion Structure Structure Structure Number Location, I Length (ft) x (ff) Erosion Rate, ER, (ft/yr) 1, --.O o0,o 2 ______ ____0, 0, 3 4 ______ _______ _______ _______ 5 6 Equilibrated Beach Width Ayo Nourishment Specification i No BArou4 I Range Ayo E ros roi AN (Fig. 7) or From Profile: ft1/3 80 to / o I 2_.f AF (Fig. 7): ft1/3 _to Volume Per Unit Length: ft3/ft to Ayo (Figs. 11 and 12): 1ie ft to to 85

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PLANFORM EVOLUTION OVER TIME NO EROSION (DISTORTED SCALES) NO ER. 400.0 350.0 HLU LULJ Li300.0 Z 250.0 LJ U Cr 200.0 --4 A B 0o -s 150.0 LU, 100.0 ED C ILLLL50.0 -.-"'-' 0.0 -50.0 -100.0 I II 0 10000 20000 30000 40000 50000 60000 70000 80000 0 TEARS SHORELINE LENGTH IN FEET ....................5 YEARS Figure C-1. Numerical Example 1, Ay = 112 ft, Nourishment --.10 YEARS Length = 2 Miles, Zero Background Erosion. -20 YEARS -._30 YEARS

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Y (T) VERSUS TIME 2 MILE PLANFORM WITH NO EROSION NO ER 200.0 W 175.0 _J 150.0 LU CC 0 125.0 100.0 75.0 -Location A ..--.-----....... Location B 25.0 -L ocation C .---o -------------------------------------------------------S50.0 -LL Z 25.0 Location C c-n '' -25.0 -50.0 -75.0 -100.0 -I I I I I I I I I I I I I I I 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 44500 TIME IN YERRS ................. 49500 Figure C-2. Numerical Example 2, Shoreline Position Variation -------59500 with Time at Locations Indicated and Shown in Figure C-1.

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INPUT FILE: DNRBS.INP (Example No. 1) EXAMPLE NO. 1 NO BACK. EROS. NO STRUC. 2 MILE PROJ. 2.00 6.0 90.0 90.0 180.0 500.0 86400.0 17.0 6.0 0.77 1.0 0.0 1 180 10950 0 0.0 0.0 90000. 0.0 49500. 2.0 60000. 3.0 90000. 3.0 100000. 3.0 140000. 2.0 80 100 80 112.0 81 112.0 82 112.0 83 112.0 84 112.0 85 112.0 86 112.0 87 112.0 88 112.0 89 112.0 90 112.0 91 112.0 92 112.0 93 112.0 94 112.0 95 112.0 96 112.0 97 112.0 98 112.0 99 112.0 100 112.0 88 L____________________________________________________________

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OUTPUT FILE: DNRBS.OUT (Example No. 1) EXAMPLE NO. 1 NO BACK. EROS. NO STRUC. 2 MILE PROJ. HO = 2.00 FT., T = 6.00 SEC., ALPO = 90.00 DEG., BTAO = 90.00 DEG., XMU = 180.00 DEG., DX = 500.00 FT., DT = 86400.00 SEC. HSTR = 17.00 FT., B = 6.00 FT., XK = .77 VFACT = 1.00 QBKREF = .00 FT.**3/SEC. IREF = 1, IMAX = 180, NTIMES = 10950, NS = 0 .00E+00 .00 .90E+05 .00 .50E+05 2.00 .60E+05 3.00 .90E+05 3.00 .10E+06 3.00 .14E+06 2.00 BACKGROUND EROSION TRANSPORT RATES 1 .000 2 .000 3 .000 4 .000 5 .000 6 .000 7 .000 8 .000 9 .000 10 .000 11 .000 12 .000 13 .000 14 .000 15 .000 16 .000 17 .000 18 .000 19 .000 20 .000 21 .000 22 .000 23 .000 24 .000 25 .000 26 .000 27 .000 28 .000 29 .000 30 .000 31 .000 32 .000 33 .000 34 .000 35 .000 36 .000 37 .000 38 .000 39 .000 40 .000 41 .000 42 .000 43 .000 44 .000 45 .000 46 .000 47 .000 48 .000 49 .000 50 .000 51 .000 52 .000 53 .000 54 .000 55 .000 56 .000 57 .000 58 .000 59 .000 60 .000 61 .000 62 .000 63 .000 64 .000 65 .000 66 .000 67 .000 68 .000 69 .000 70 .000 71 .000 72 .000 73 .000 74 .000 75 .000 76 .000 77 .000 78 .000 79 .000 80 .000 81 .000 82 .000 83 .000 84 .000 85 .000 86 .000 87 .000 88 .000 89 .000 90 .000 91 .000 92 .000 93 .000 94 .000 95 .000 96 .000 97 .000 98 .000 99 .000 100 .000 101 .000 102 .000 103 .000 104 .000 105 .000 106 .000 107 .000 108 .000 109 .000 110 .000 111 .000 112 .000 113 .000 114 .000 115 .000 116 .000 117 .000 118 .000 119 .000 120 .000 121 .000 122 .000 123 .000 124 .000 125 .000 126 .000 127 .000 128 .000 129 .000 130 .000 131 .000 132 .000 133 .000 134 .000 135 .000 136 .000 137 .000 138 .000 139 .000 140 .000 141 .000 142 .000 143 89 ) 144 .000 145 .000 146 .000 147 .000 148 ) 149 .000 150 .000 151 .000 152 .000 153 3 154 .000 155 .000 156 .000 157 .000 158 .000 159 .000 160 .000 161 .000 162 .000 163 .000 164 .000 165 .000 _______ 1 r ^_ ^ f% 'I 7 e n ^ ir n f% r% r___ / n __ ^ n r> __n 1i n -n r% ---

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171 .000 172 .000 173 .000 174 .000 175 .000 176 .000 177 .000 178 .000 179 .000 180 .000 181 .000 80 100 INITIAL SHORELINE (INCL. NOURISHMENT) POSITION 1 0. .00 2 500. .00 3 1000. .00 4 1500. .00 5 2000. .00 6 2500. .00 7 3000. .00 8 3500. .00 9 4000. .00 10 4500. .00 11 5000. .00 12 5500. .00 13 6000. .00 14 6500. .00 15 7000. .00 16 7500. .00 17 8000. .00 18 8500. .00 19 9000. .00 20 9500. .00 21 10000. .00 22 10500. .00 23 11000. .00 24 11500. .00 25 12000. .00 26 12500. .00 27 13000. .00 28 13500. .00 29 14000. .00 30 14500. .00 31 15000. .00 32 15500. .00 33 16000. .00 34 16500. .00 35 17000. .00 36 17500. .00 37 18000. .00 38 18500. .00 39 19000. .00 40 19500. .00 41 20000. .00 42 20500. .00 43 21000. .00 44 21500. .00 45 22000. .00 46 22500. .00 47 23000. .00 48 23500. .00 49 24000. .00 50 24500. .00 51 25000. .00 52 25500. .00 53 26000. .00 54 26500. .00 55 27000. .00 56 27500. .00 57 28000. .00 58 28500. .00 59 29000. .00 60 29500. .00 61 30000. .00 62 30500. .00 63 31000. .00 64 31500. .00 65 32000. .00 66 32500. .00 67 33000. .00 68 33500. .00 69 34000. .00 70 34500. .00 71 35000. .00 72 35500. .00 73 36000. .00 74 36500. .00 75 37000. .00 76 37500. .00 77 38000. .00 78 38500. .00 79 39000. .00 80 39500. 112.00 81 40000. 112.00 82 40500. 112.00 83 41000. 112.00 84 41500. 112.00 85 42000. 112.00 86 42500. 112.00 87 43000. 112.00 88 43500. 112.00 89 44000. 112.00 90 4,4500. 112.00 91 45000. 112.00 92 45500. 112.00 93 46000. 112.00 94 46500. 112.00 95 47000. 112.00 96 47500. 112.00 97 48000. 112.00 98 48500. 112.00 99 49000. 112.00 100 49500. 112.00 101 50000. .00 102 50500. .00 103 51000. .00 104 51500. .00 105 52000. .00 106 5250 90 .00 107 53000. .00 108 5350 .00 109 54000. .00 110 545C .00 111 55000. .00 112 55500. .00 113 56000. .00 114 56500. .00 1 -r-in______ nn a r, _Cnn nn

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117 58000. .00 118 58500. .00 119 59000. .00 120 59500. .00 121 60000. .00 122 60500. .00 123 61000. .00 124 61500. .00 125 62000. .00 126 62500. .00 127 63000. .00 128 63500. .00 129 64000. .00 130 64500. .00 131 65000. .00 132 65500. .00 133 66000. .00 134 66500. .00 135 67000. .00 136 67500. .00 137 68000. .00 138 68500. .00 139 69000. .00 140 69500. .00 141 70000. .00 142 70500. .00 143 71000. .00 144 71500. .00 145 72000. .00 146 72500. ..00 147 73000. .00 148 73500. .00 149 74000. .00 150 74500. .00 151 75000. .00 152 75500. .00 153 76000. .00 154 76500. .00 155 77000. .00 156 77500. .00 157 78000. .00 158 78500. .00 159 79000. .00 160 79500. .00 161 80000. .00 162 80500. .00 163 81000. .00 164 81500. .00 165 82000. .00 166 82500. .00 167 83000. .00 168 83500. .00 169 84000. .00 170 84500. .00 171 85000. .00 172 85500. .00 173 86000. .00 174 86500. .00 175 87000. .00 176 87500. .00 177 88000. .00 178 88500. .00 179 89000. .00 180 89500. .00 100 116 .000 .000 .000 .000 .000 .000 .000 TIME = 1 YEARS 1 .00 2 .00 3 .00 4 .00 5 .00 6 .00 7 .00 8 .00 9 .00 10 .00 11 .00 12 .00 13 .00 14 .00 15 .00 16 .00 17 .00 18 .00 19 .00 20 .00 21 .00 22 .00 23 .00 24 .00 25 .00 26 .00 27 .00 28 .00 29 .00 30 .00 31 .00 32 .00 33 .00 34 .00 35 .00 36 .00 37 .00 38 .00 39 .00 40 .00 41 .00 42 .00 43 .00 44 .00 45 .00 46 .00 47 .00 48 .00 49 .00 50 .00 51 .00 52 .00 53 .00 54 .00 55 .00 56 .00 57 .00 58 .00 59 .01 60 .02 61 .04 62 .07 63 .13 64 .23 65 .40 66 .69 67 1.13 68 1.82 69 2.84 70 4.31 71 6.34 72 9.07 73 12.62 74 17.06 75 22.45 76 28.75 77 35.87 78 43.64 79 51.83 80 60.16 81 68.34 82 76.10 83 83.19 84 89.43 85 94.71 86 98.98 87 102.24 88 104.52 89 105.87 90 106.31 91 105.87 92 104.52 93 102.24 94 98.98 95 94.71 96 89.43 97 83.19 98 76.10 99 68.34 100 60.16 101 51.83 102 43.64 103 35.87 104 28.75 105 22.45 106 17.06 107 12.62 108 9.07 109 6.34 110 4.31 111 2.84 112 1.82 113 1.13 114 .69 115 .40 116 .23 117 .13 118 .07 119 .04 120 .02 121 .01 122 .00 123 .00 124 .00 125 .00 126 .00 127 .00 128 .00 129 .00 130 .00 131 .00 132 .00 133 .00 134 .00 135 .00 136 .00 137 .00 138 .00 139 .00 140 .00 141 .00 142 .00 143 .00 144 .00 145 .00 146 .00 147 .00 148 .00 149 .00 150 .00 151 .00 152 .00 153 .00 154 .00 155 .00 156 .00 157 .00 158 .00 159 .00 1n .00 161 .00 162 .00 163 .00 164 .00 165 .00 91 .00 167 .00 168 .00 169 .00 170 .00 171 .00 .00 173 .00 174 .00 175 .00 176 .00 177 .00 178 .00 179 .00 180 .00 LCUR = 1 PCT(LCUR) = .80

PAGE 102

LCUR = 3 PCT(LCUR) = .65 LCUR = 4 PCT(LCUR) = .60 TIME = 5 YEARS 1 .00 2 .00 3 .00 4 .00 5 .00 6 .00 7 .00 8 .00 9 .00 10 .00 11 .00 12 .00 13 .00 14 .00 15 .00 16 .00 17 .00 18 .00 19 .00 20 .00 21 .00 22 .00 23 .00 24 .00 25 .00 26 .00 27 .00 28 .00 29 .00 30 .00 31 .00 32 .00 33 .01' 34 .01' 35 .01 36 .02 37 .02' 38 .03 39 .04 40 .06 41 .08 42 .10 43 .14 44 .18 -45 .23 46 .30 47 .39 48 .50 49 .63 50 .79 51 1.00 52 1.24 53 1.54 54 1.90 55 2.32 56 2.83' 57 3.42" 58 4.11 59 4.91 60 5.83 61 6.88 62 8.07 63 9.41 64 10.91 65 12.57 66 14.40 67 16.41 68 18.58 69 20.91 70 23.41 71 26.05 72 28.82 73 31.71 74 34.70 75 37.75 76 40.84 77 43.93 78 47.00 79 50.01 80 52.92 81 55.69 82 58.29 83 60.69 84 62.84 85 64.71 86 66.29 87 67.54 88 68.45 89 69.00 90 69.18 91 69.00 92 68.45 93 67.54 94 66.29 95 64.71 96 62.84 97 60.69 98 58.29 99 55.69 100 52.92 101 50.01 102 47.00 103 43.93 104 40.84 105 37.75 106 34.70 107 31.71 108 28.82 109 26.05 110 23.41 111 20.91 112 18.58 113 16.41 114 14.40 115 12.57 116 10.91 117 9.41 118 8.07 119 6.88 120 5.83 121 4.91 122 4.11 123 3.42 124 2.83 125 2.32 126 1.90 127 1.54 128 1.24 129 1.00 130 .79 131 .63 132 .50 133 .39 134 .30 135 .23 136 .18 137 .14 138 .10 139 .08 140 .06 141 .04 142 .03 143 .02 144 .02 145 .01 146 .01 147 .01 148 .00 149 .00 150 .00 151 .00 152 .00 153 .00 154 .00 155 .00 156 .00 157 .00 158 .00 159 .00 160 .00 161 .00 162 .00 163 .00 164 .00 165 .00 166 .00 167 .00 168 .00 169 .00 170 .00 171 .00 172 .00 173 .00 174 .00 175 .00 176 .00 177 .00 178 .00 179 .00 180 .00 LCUR = 5 PCT(LCUR) = .56 LCUR = 6 PCT(LCUR) = .53 LCUR = 7 PCT(LCUR) = .50 LCUR = 8 PCT(LCUR) = .48 LCUR = 9 PCT(LCUR) = .46 TIME = 10 YEARS 1 .00 2 .00 3 .00 4 .00 5 .00 6 .00 7 .00 8 .00 9 .00 10 .00 11 .00 12 .00 13 .01 14 .01 15 .01 16 .01 17 .01 18 .02 19 .02 20 .03 21 .03 22 .04 23 .05 24 .06 25 .08 26 .09 27 .11 28 .14 29 .17 30 .20 31 .24 32 .29 33 .35 34 .41 35 .49 36 .58 37 .69 38 .81 39 .95 40 1.11 41 1.30 42 1.51 43 1.75 44 2.02 45 2.32 46 2.66 47 3.04 48 3.47 49 3.95 50 4.47 51 5.05 52 5.68 53 6.38 54 7.14 55 7.96 56 8.85 57 9.81 58 10.84 59 11.94 60 13.12 61 14.36 62 15.67 63 17.05 64 18.49 65 19.99 66 21.54 67 23.15 68 24.80 69 26.48 70 28.19 71 29.92 72 31.66 73 33.40 74 35.12 75 36.82 76 38.48 77 40.10 78 41.66 79 43.14 80 44.55 81 45.85 82 47.06 83 48.14 84 49.10 85 49.93 86 50.62 87 51.16 88 51.55 89 51.79 90 51.87 91 51.79 92 51.55 93 51.16 94 50.62 95 49.93 96 49.10 97 48.14 98 47.06 99 45.85 100 44.55 101 43.14 102 41.66 103 40.10 104 38.48 105 36.82 106 35.12 107 33.40 108 31.66 109 29.92 110 28.19 111 26.48 112 24.80 113 23.15 114 21.54 115 19.99 116 18.49 117 17.05 118 15.67 119 14.36 120 13.12 121 11.94 122 10.84 123 9.81 124 8.85 125 7.96 126 7.14 127 6.38 128 5.68 129 5.05 130 4.47 131 3.95 132 3.47 133 3.04 134 2.66 135 2. 92 2.02 137 1.75 138 1.51 139 1.30 140 1.11 141 .81 143 .69 144 .58 145 .49 146 .41 147 .Ju % .29 149 .24 150 .20 151 .17 152 .14 153 .11 154 .09 155 .08 156 .06 rin. _ -i 1 fln 1-4 n-cn-I -^-N

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163 .01 164 .01 165 .01 166 .01 167 .01 168 .00 169 .00 170 .00 171 .00 172 .00 173 .00 174 .00 175 .00 176 .00 177 .00 178 .00 179 .00 180 .00 LCUR = 10 PCT(LCUR) = .44 LCUR = 11 PCT(LCUR) = .42 LCUR = 12 PCT(LCUR) = .41 LCUR = 13 PCT(LCUR) = .39 LCUR = 14 PCT(LCUR) = .38 LCUR = 15 PCT(LCUR) = .37 LCUR = 16 PCT(LCUR) = .36 LCUR = 17 PCT(LCUR) = .35 LCUR = 18 PCT(LCUR) = .34 LCUR = 19 PCT(LCUR) = .34 LCUR = 20 PCT(LCUR) = .33 LCUR = 21 PCT(LCUR) = .32 LCUR = 22 PCT(LCUR) = .31 LCUR = 23 PCT(LCUR) = .31 LCUR = 24 PCT(LCUR) = .30 LCUR = 25 PCT(LCUR) = .30 LCUR = 26 PCT(LCUR) = .29 LCUR = 27 PCT(LCUR) = .29 LCUR = 28 PCT(LCUR) = .28 LCUR = 29 PCT(LCUR) = .28 TIME = 30 YEARS 1 .00 2 .08 3 .15 4 .23 5 .31 6 .40 7 .48 8 .57 9 .66 10 .75 11 .85 12 .96 13 1.07 14 1.18 15 1.30 16 1.43 17 1.57 18 1.72 19 1.87 20 2.03 21 2.20 22 2.38 23 2.58 24 2.78 25 2.99 26 3.22 27 3.46 28 3.71 29 3.98 30 4.25 31 4.55 32 4.85 33 5.17 34 5.51 35 5.86 36 6.22 37 6.60 38 7.00 39 7.41 40 7.83 41 8.28 42 8.73 43 9.20 44 9.69 45 10.19 46 10.70 47 11.23 48: 11.77 49 12.32 50 12.89 51 13.46 52 14.05 53 14.64 54 15.24 55 15.85 56 16.47 57 17.09 58 17.72 59 18.34 60 18.97 61 19.60 62 20.23 63 20.85 64 21.47 65 22.08 66 22.69 67 23.29 68 23.87 69 24.45 70 25.01 71 25.55 72 26.08 73 26.59 74 27.08 75 27.55 76 27.99 77 28.41 78 28.81 79 29.17 80 29.51 81 29.83 82 30.11 83 30.36 84 30.58 85 30.76 86 30.92 87 31.04 88 31.12 89 31.17 90 31.19 91 31.17 92 31.12 93 31.04 94 30.92 95 30.76 96 30.58 97 30.36 98 30.11 99 29.83 100 29.51 101 29.17 102 28.81 103 28.41 104 27.99 105 27.55 106 27.08 107 26.59 108 26.08 109 25.55 110 25.01 111 24.45 112 23.87 113 23.29 114 22.69 115 22.08 116 21.47 117 20.85 118 20.23 119 19.60 120 18.97 121 18.34 122 17.72 123 17.09 124 16.47 125 15.85 126 15.24 127 14.64 128 14.05 129 13.46 130 12.89 131 12.32 132 11.77 133 11.23 134 10.70 135 10.19 136 9.69 137 9.20 138 8.73 139 8.28 140 7.84 141 7.41 142 7.00 143 6.60 144 6.22 145 5.86 146 5.51 147 5.17 148 4.85 149 4.55 150 4.26 151 3.98 152 3.72 153 3.46 154 3.23 155 3.00 156 2.79 157 2.58 158 2.39 159 2.21 160 2.04 161 1.88 162 1.73 163 1.59 164 1.45 165 1.32 166 1.20 167 1.09 168 .98 169 .88 170 .78 171 .69 172 .60 173 .52 174 .44 175 .36 176 .29 177 .21 178 .14 179 .07 180 .00 LCUR = 30 PCT(LCUR) = .27 93

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APPENDIX D NUMERICAL EXAMPLE 2

PAGE 105

BEACH NOURISHMENT PROJECTION (Numerical Procedure) General Location: E-w 1fe2 Wave Height, Ho (Fig. 22): .,o ft., Closure Depth, h. (Fig. 8): 1 7 ft. Wave Period, T (Fig. 23): (.,, sec., Berm Height, B: &o ft. Wave Direction, ao: qO 0, Sand Diameter, D: o*3S mm Deep Water Contour Orientation, /o: 1 0, Transport Factor, K (Fig. 5): o0/M Longshore Axis Orientation, p: / o 0, VFACT: o. Grid Dimension, Az: Jo ft Background Transport, QREF: 0 ft3/s Time Increment, At: 86(, 4oo sec IREF: 1 IMAX: I o NTIMES: 10 O o No. of Structures, NS: Q Structure Specificiation Background Erosion Structure Structure Structure Number Location, I Length (ft) z Erosion Rate, ER, (ft/yr) 2'/r 1, _____ _____ 0 o 20 I 1 ---o ., lo 2 qo 0 0D Qo 3 4 6 ) Equilibrated Beach Width Ayo Nourishment Specification I Range Ayo AN (Fig. 7) or From Profile: ft'/3 80 to OI / 0 2 eos AF (Fig. 7): ft'/s _to_ RoAt Volume Per Unit Length: ft3/ft to Ayo (Figs. 11 and 12): 11Z ft to to 95

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PLRNFORM EVOLUTION OVER TIME UNIFORM EROSION (DISTORTED SCALES) UNI ER 300.0 250.0 LLJ LU LL200.0 SA B zC 150.0 LU C) 100.0 ---------------nLL50.0 L-50.0 ---' s --. -" Li C) -100.0 -150.0 -200.0 -I 1 I I I I 0 10000 20000 30000 40000 50000 60000 70000 80000 0 TEARS SHORELINE LENGTH IN FEET ....................5 TEARS Figure D-1. Numerical Example 2, Ay = 112 ft, Nourishment --_-_-0 TEARS Length = 2 Miles, Uniform Background Erosion --------= 2 ft/yr. ---30 ERS

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Y (T) VERSUS TIME 2 MILE PLRNFORM WITH UNIFORM EROSION UNI ER 200.0 LU 175.0 Z 150.0 LUL CC E 125.0 I 100.0 SLocation A CD -75.0 5..0... Location B Z 25.0 0.0 -25.0 -Location C -50.0 -75.0 -100.0 1 1II1 I I I I1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 44500 TIME IN YEARS ............. 95 Figure D-2. Numerical Example 2, Shoreline Position Variation ---59500 with Time at Locations Indicated and Shown in Figure D-l.

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INPUT FILE: DNRBS.INP (Example No. 2) EXAMPLE NO. 2 UNIF. BACK. EROS. NO STRUC. 2 MILE PROJ. 2.00 6.0 90.0 90.0 180.0 500.0 86400.0 17.0 6.0 0.77 1.0 0.0 1 180 10950 0 0.0 2.0 90000. 2.0 49500. 2.0 60000. 3.0 90000. 3.0 100000. 3.0 140000. 2.0 80 100 80 112.0 81 112.0 82 112.0 83 112.0 84 112.0 85 112.0 86 112.0 87 112.0 88 112.0 89 112.0 90 112.0 91 112.0 92 112.0 93 112.0 94 112.0 95 112.0 96 112.0 97 112.0 98 112.0 99 112.0 100 112.0 98

PAGE 109

OUTPUT FILE: DNRBS.OUT (Example No. 2) EXAMPLE NO. 2 UNIF. BACK. EROS. NO STRUC. 2 MILE PROJ. HO = 2.00 FT., T = 6.00 SEC., ALPO = 90.00 DEG., BTAO = 90.00 DEG., XMU = 180.00 DEG., DX = 500.00 FT., DT = 86400.00 SEC. HSTR = 17.00 FT., B = 6.00 FT., XK = .77 VFACT = 1.00 QBKREF = .00 FT.**3/SEC. IREF = 1, IMAX = 180, NTIMES = 10950, NS = 0 .00E+00 2.00 .90E+05 2.00 .50E+05 2.00 .60E+05 3.00 .90E+05 3.00 .10E+06 3.00 .14E+06 2.00 BACKGROUND EROSION TRANSPORT RATES 1 .000 2 .001 3 .001 4 .002 5 .003 6 .004 7 .004 8 .005 9 .006 10 .007 11 .007 12 .008 13 .009 14 .009 15 .010 16 .011 17 .012 18 .012. 19 .013 20 .014 21 .015 22 .015 23 .016 24 .017 25 .018 26 .018 27 .019 28 .020 29 .020 30 .021 31 .022 32 .023 33 .023 34 .024 35 .025 36 .026 37 .026 38 .027 39 .028 40 .028 41 .029 42 .030 43 .031 44 .031 45 .032 46 .033 47 .034 48 .034 49 .035 50 .036 51 .036 52 .037 53 .038 54 .039 55 .039 56 .040 57 .041 58 .042 59 .042 60 .043 61 .044 62 .044 63 .045 64 .046 65 .047 66 .047 67 .048 68 .049 69 .050 70 .050 71 .051 72 .052 73 .053 74 .053 75 .054 76 .055 77 .055 78 .056 79 .057 80 .058 81 .058 82 .059 83 .060 84 .061 85 .061 86 .062 87 .063 88 .063 89 .064 90 .065 91 .066 92 .066 93 .067 94 .068 95 .069 96 .069 97 .070 98 .071 99 .071 100 .072 101 .073 102 .074 103 .074 104 .075 105 .076 106 .077 107 .077 108 .078 109 .079 110 .079 111 .080 112 .081 113 .082 114 .082 115 .083 116 .084 117. .085 118 .085 119 .086 120 .087 121 .088 122 .088 123 .089 124 .090 125 .090 126 .091 127 .092 128 .093 129 .093 130 .094 131 .095 132 .096 133 .096 134 .097 135 .098 136 .098 137 .099 138 .100 139 .101 140 .101 141 .102 142 .103 143 .104 144 .104 145 .105 146 .106 147 .106 148 .107 149 .108 150 .109 151 .109 152 .110 153 .111 154 .112 155 .112 156 .113 157 .114 158 .115 159 .115 160 .116 161 .117 162 .117 163 .118 164 .119 165 .120 166 .120 167 .121 168 ""' 169 .123 170 .123 171 .124 172 .125 173 99 174 .126 175 .127 176 .128 177 .128 178 179 .130 180 .131 181 .131

PAGE 110

80 100 INITIAL SHORELINE (INCL. NOURISHMENT) POSITION 1 0. .00 2 500. .00 3 1000. .00 4 1500. .00 5 2000. .00 6 2500. .00 7 3000. .00 8 3500. .00 9 4000. .00 10 4500. .00 11 5000. .00 12 5500. .00 13 6000. .00 14 6500. .00 15 7000. .00 16 7500. .00 17 8000. .00 18 8500. .00 19 9000. .00 20 9500. .00 21 10000. .00 22 10500. .00 23 11000. .00 24 11500. .00 25 12000. .00 26 12500. .00 27 13000. .00 28 13500. .00 29 14000. .00 30 14500. .00 31 15000. .00 32 15500. .00 33 16000. .00 34 16500. .00 35 17000. .00 36 17500. .00 37 18000. .00 38 18500. .00 39 19000. .00 40 19500. .00 41 20000. .00 42 20500. .00 43 21000. .00 44 21500. .00 45 22000. .00 46 22500. .00 47 23000. .00 48 23500. .00 49 24000. .00 50 24500. .00 51 25000. .00 52 25500. .00 53 26000. .00 54 26500. .00 55 27000. .00 56 27500. .00 57 28000. .00 58 28500. .00 59 29000. .00 60 29500. .00 61 30000. .00 62 30500. .00 63 31000. .00 64 31500. .00 65 32000. .00 66 32500. .00 67 33000. .00 68 33500. .00 69 34000. .00 70 34500. .00 71 35000. .00 72 35500. .00 73 36000. .00 74 36500. .00 75 37000. .00 76 37500. .00 77 38000. .00 78 38500. .00 79 39000. .00 80 39500. 112.00 81 40000. 112.00 82 40500. 112.00 83 41000. 112.00 84 41500. 112.00 85 42000. 112.00 86 42500. 112.00 87 43000. 112.00 88 43500. 112.00 89 44000. 112.00 90 44500. 112.00 91 45000. 112.00 92 45500. 112.00 93 46000. 112.00 94 46500. 112.00 95 47000. 112.00 96 47500. 112.00 97 48000. 112.00 98 48500. 112.00 99 49000. 112.00 100 49500. 112.00 101 50000. .00 102 50500. .00 103 51000. .00 104 51500. .00 105 52000. .00 106 52500. .00 107 53000. .00 108 53500. .00 109 54000. .00 110 54500. .00 111 55000. .00 112 55500. .00 113 56000. .00 114 56500. .00 115 57000. .00 116 100 .00 117 58000. .00 118 .00 119 59000. .00 120 .00 121 60000. .00 122 60500. .00 123 61000. .00 124 61500. .00

PAGE 111

127 63000. .00 128 63500. .00 129 64000. .00 130 64500. .00 131 65000. .00 132 65500. .00 133 66000. .00 134 66500. .00 135 67000. .00 136 67500. .00 137 68000. .00 138 68500. .00 139 69000. .00 140 69500. .00 141 70000. .00 142 70500. .00 143 71000. .00 144 71500. .00 145 72000. .00 146 72500. .00 147 73000. .00 148 73500. .00 149 74000. .00 150 74500. .00 151 75000. .00 152 75500. .00 153 76000. .00 154 76500. .00 155 77000. .00 156 77500. .00 157 78000. .00 158 78500. .00 159 79000. .00 160 79500. .00 161 80000. .00 162 80500. .00 163 81000. .00 164 81500. .00 165 82000. .00 166 82500. .00 167 83000. .00 168 83500. .00 169 84000. .00 170 84500. .00 171 85000. .00 172 85500. .00 173 86000. .00 174 86500. .00 175 87000. .00 176 87500. .00 177 88000. .00 178 88500. .00 179 89000. .00 180 89500. .00 100 116 .000 .084 .000 -.542 -.542 .084 .000 TIME = 1 YEARS 1 -2.00 2 -2.00 3 -2.00 4 -2.00 5 -2.00 6 -2.00 7 -2.00 8 -2.00 9 -2.00 10 -2.00 11 -2.00 12 -2.00 13 -2.00 14 -2.00 15 -2.00 16 -2.00 17 -2.00 18 -2.00" 19 -2.00 20 -2.00 21 -2.00 22 -2.00 23 -2.00 24 -2.00 25 -2.00 26 -2.00 27 -2.00 28 -2.00 29 -2.00 30 -2.00 31 -2.00 32 -2.00 33 -2.00 34 -2.00 35 -2.00 36 -2.00 37 -2.00 38 -2.00 39 -2.00 40 -2.00 41 -2.00 42 -2.00 43 -2.00 44 -2.00 45 -2.00 46 -2.00 47 -2.00 48 -2.00 49 -2.00 50 -2.00 51 -2.00 52 -2.00 53 -2.00 54 -2.00 55 -2.00 56 -2.00 57 -2.00 58 -2.00 59 -1.99 60 -1.98 61 -1.96 62 -1.93 63 -1.87 64 -1.77 65 -1.60 66 -1.31 67 -.87 68 -.18 69 .84 70 2.31 71 4.34 72 7.07 73 10.62 74 15.06 75 20.45 76 26.75 77 33.87 78 41.64 79 49.83 80 58.16 81 66.34 82 74.10 83 81.19 84 87.43 85 92.71 86 96.98 87 100.24 88 102.52 89 103.87 90 104.31 91 103.87 92 102.52 93 100.24 94 96.98 95 92.71 96 87.43 97 81.19 98 74.10 99 66.34 100 58.16 101 49.83 102 41.64 103 33.87 104 26.75 105 20.45 106 15.06 107 10.62 108 7.07 109 4.34 110 2.31 111 .84 112 -.18 113 -.87.114 -1.31 115 -1.60 116 -1.77 117 -1.87 118 -1.93 119 -1.96 120 -1.98 121 -1.99 122 -2.00 123 -2.00 124 -2.00 125 -2.00 126 -2.00 127 -2.00 128 -2.00 129 -2.00 130 -2.00 131 -2.00 132 -2.00 133 -2.00 134 -2.00 135 -2.00 136 -2.00 137 -2.00 138 -2.00 139 -2.00 140 -2.00 141 -2.00 142 -2.00 143 -2.00 144 -2.00 145 -2.00 146 -2.00 147 -2.00 148 -2.00 149 -2.00 150 -2.00 151 -2.00 152 -2.00 153 -2.00 154 -2.00 155 -2.00 156 -2.00 157 -2.00 158 -2.00 159 -2.00 160 -2.00 161 -2.00 162 -2.00 163 -2.00 164 -2.00 165 -2.00 166 -2.00 167 -2.00 168 -2.00 169 -2.00 170 -2.00 171 -2.00 172 -2.00 173 -2.00 174 -2.00 175 -2.00 176 -2.00 177 -2.00 178 -2.00 179 -2.00 180 -2.00 LCUR = 1 PCT(LCUR) = '2 LCUR = 2 PCT(LCUR) = 101 3 LCUR = 3 PCT(LCUR) = 0 LCUR = 4 PCT(LCUR) = 3 TIME = 5 YEARS 1 -10.00 2 -10.00 3 -10.00 4 -10.00 5 -10.00 6 -10.00

PAGE 112

13 -10.00 14 -10.00 15 -10.00 16 -10.00 17 -10.00 18 -10.00 19 -10.00 20 -10.00 21 -10.00 22 -10.00 23 -10.00 24 -10.00 25 -10.00 26 -10.00 27 -10.00 28 -10.00 29 -10.00 30 -10.00 31 -10.00 32 -10.00 33 -9.99 34 -9.99 35 -9.99 36 -9.98 37 -9.98 38 -9.97 39 -9.96 40 -9.94 41 -9.92 42 -9.90 43 -9.86 44 -9.82 45 -9.77 46 -9.70 47 -9.61 48 -9.50 49 -9.37 50 -9.21 51 -9.00 52 -8.76 53 -8.46 54 -8.10 55 -7.68 56 -7.17 57 -6.58 58 -5.89 59 -5.09 60 -4.17 61 -3.12 62 -1.93 63 -.59 64 .91 65 2.57 66 4.40 67 6.41 68 8.58 69 10.91 70 13.41 71 16.05 72 18.82 73 21.71 74 24.70 75 27.75 76 30.84 77 33.93 78 37.00 79 40.01 80 42.92 81 45.69 82 48.29 83 50.69 84 52.84 85 54.71 86 56.29 87 57.54 88 58.45 89 59.00 90 59.18 91 59.00 92 58.45 93 57.54 94 56.29 95 54.71 96 52.84 97 50.69 98 48.29 99 45.69 100 42.92 101 40.01 102 37.00 103 33.93 104 30.84 105 27.75 106 24.70 107 21.71 108 18.82 109 16.05 110 13.41 111 10.91 112 8.58 113 6.41 114 4.40 115 2.57 116 .91 117 -.59 118 -1.93 119 -3.12 120 -4.17 121 -5.09 122 -5.89 123 -6.58 124 -7.17 125 -7.68 126 -8.10 127 -8.46 128 -8.76 129 -9.00 130 -9.21 131 -9.37 132 -9.50 133 -9.61 134 -9.70 135 -9.77 136 -9.82 137 -9.86 138 -9.90 139 -9.92 140 -9.94 141 -9.96 142 -9.97 143 -9.98 144 -9.98 145 -9.99 146 -9.99 147 -9.99 148 -10.00 149 -10.00 150 -10.00 151 -10.00 152 -10.00 153 -10.00 154 -10.00 155 -10.00 156 -10.00 157 -10.00 158 -10.00 159 -10.00 160 -10.00 161 -10.00 162 -10.00 163 -10.00 164 -10.00 165 -10.00 166 -10.00 167 -10.00 168 -10.00 169 -10.00 170 -10.00 171 -10.00 172 -10.00 173 -10.00 174 -10.00 175 -10.00 176 -10.00 177 -10.00 178 -10.00 179 -10.00 180 -10.00 LCUR = 5 PCT(LCUR) = .47 LCUR = 6 PCT(LCUR) = .42 LCUR = 7 PCT(LCUR) = .38 LCUR = 8 PCT(LCUR) = .33 LCUR = 9 PCT(LCUR) = .30 TIME = 10 YEARS 1 -20.00 2 -20.00 3 -20.00 4 -20.00 5 -20.00 6 -20.00 7 -20.00 8 -20.00 9 -20.00 10 -20.00 11 -20.00 12 -20.00 13 -19.99 14 -19.99 15. -19.99 16 -19.99 17 -19.99 18 -19.98 19 -19.98 20 -19.97 21 -19.97 22 -19.96 23 -19.95 24 -19.94 25 -19.92 26 -19.91 27 -19.89 28 -19.86 29 -19.83 30 -19.80 31 -19.76 32 -19.71 33 -19.65 34 -19.59 35 -19.51 36 -19.42 37 -19.31 38 -19.19 39 -19.05 40 -18.89 41 -18.70 42 -18.49 43 -18.25 44 -17.98 45 -17.68 46 -17.34 47 -16.96 48 -16.53 49 -16.05 50 -15.53 51 -14.95 52 -14.32 53 -13.62 54 -12.86 55 -12.04 56 -11.15 57 -10.19 58 -9.16 59 -8.06 60 -6.88 61 -5.64 62 -4.33 63 -2.96 64 -1.51 65 -.01 66 1.54 67 3.15 68 4.80 69 6.48 70 8.19 71 9.92 72 11.66 73 13.40 74 15.12 75 16.82 76 18.48 77 20.10 78 21.66 79 23.14 80 24.55 81 25.85 82 27.06 83 28.14 84 29.10 85 29.93 86 30.62 87 31.16 88 31.55 89 31.79 90 31.87 91 31.79 92 31.55 93 31.16 94 30.62 95 29.93 96 29.10 97 28.14 98 27.06 99 25.85 100 24.55 101 23.14 102 21.66 103 20.10 104 18.48 105 16.82 106 15.12 107 13.40 108 11.66 109 9.92 110 8.19 111 6.48 112 4.80 113 3.15 114 1.54 115 -.01 116 -1.51 117 -2.95 118 -4.33 119 -5.64 120 -6.88 121 -8.06 122 -9.16 123 -10.19 124 -11.15 125 -12.04 126 -12.86 127 -13.62 128 -14.31 129 -14.95 130 -15.53 131 -16.05 132 -16.53 133 -16.96 134 -17.34 135 -17.68 136 -17.98 137 -18.25 138 -18.49 139 -18.70 140 -18.89 141 -19.05 142 -19.19 143 -19.31 144 -19.42 145 -19.51 146 -19.59 147 -19 Cr '1A -19.71 149 -19.76 150 -19.80 151 -19.83 152 -19.86 153 -19 102 -19.91 155 -19.92 156 -19.94 157 -19.95 158 -19.96 159 -19 -19.97 161 -19.98 162 -19.98 163 -19.99 164 -19.99 165 -IF -19.99 167 -19.99 168 -20.00 169 -20.00 170 -20.00 171 -20.00 172 -20.00 173 -20.00 174 -20.00 175 -20.00 176 -20.00 177 -20.00 178 -20.00 179 -20.00 180 -20.00 LCUR = 10 PCT(LCUR) = .26

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LCUR = 12 PCT(LCUR) = .19 LCUR = 13 PCT(LCUR) = .16 LCUR = 14 PCT(LCUR) = .13 LCUR = 15 PCT(LCUR) = .10 LCUR = 16 PCT(LCUR) = .08 LCUR = 17 PCT(LCUR) = .05 LCUR = 18 PCT(LCUR) = .02 LCUR = 19 PCT(LCUR) = .00 LCUR = 20 PCT(LCUR) = .03 LCUR = 21 PCT(LCUR) = -.05 LCUR = 22 PCT(LCUR) = -.08 LCUR = 23 PCT(LCUR) = -.08 LCUR = 24 PCT(LCUR) = -.13 LCUR = 25 PCT(LCUR) = -.15 LCUR = 26 PCT(LCUR) = -.17 LCUR = 27 PCT(LCUR) = -.20 LCUR = 28 PCT(LCUR) = -.22 LCUR = 29 PCT(LCUR) = -.24 LCUR = 29 PCT(LCUR) = -.24 TIME = 30 YEARS 1 -59.99 2 -59.92 3 -59.84 4 -59.76 5 -59.68 6 -59.60 7 -59.52 8 -59.43 9 -59.34 10 -59.24 11 -59.14 12 -59.04 13 -58.93 14 -58.82 15 -58.69 16 -58.56 17 -58.43 18 -58.28 19 -58.13 20 -57.97 21 -57.80 22 -57.62 23 -57.42 24 -57.22 25 -57.01 26 -56.78 27 -56.54 28 -56.29 29 -56.02 30 -55.75 31 -55.45 32 -55.15 33 -54.83 34 -54.49 35 -54.14 36 -53.78 37 -53.40 38 -53.00 39 -52.59 40 -52.17 41 -51.72 42 -51.27 43 -50.80 44 -50.31 45 -49.81 46 -49.30 47 -48.77 48 -48.23 49 -47.68 50 -47.11 51 -46.54 52 -45.95 53 -45.36 54 -44.76 55 -44.15 56 -43.53 57 -42.91 58 -42.28 59 -41.66 60 -41.03 61 -40.40 62 -39.77 63 -39.15 64 -38.53 65 -37.92 66 -37.31 67 -36.71 68 -36.13 69 -35.55 70 -34.99 71 -34.45 72 -33.92 73 -33.41 74 -32.92 75 -32.46 76 -32.01 77 -31.59 78 -31.19 79 -30.83 80 -30.49 81 -30.17 82 -29.89 83 -29.64 84 -29.42 85 -29.24 86 -29.08 87 -28.97 88 -28.88 89 -28.83 90 -28.81 91 -28.83 92 -28.88 93 -28.97 94 -29.08 95 -29.24 96 -29.42 97 -29.64 98 -29.89 99 -30.17 100 -30.49 101 -30.83 102 -31.19 103 -31.59 104 -32.01 105 -32.45 106 -32.92 107 -33.41 108 -33.92 109 -34.45 110 -34.99 111 -35.55 112 -36.13 113 -36.71 114 -37.31 115 -37.92 116 -38.53 117 -39.15 118 -39.77 119 -40.40 120 -41.03 121 -41.66 122 -42.28 123 -42.91 124 -43.53 125 -44.15 126 -44.76 127 -45.36 128 -45.95 129 -46.54 130 -47.11 131 -47.68 132 -48.23 133 -48.77 134 -49.30 135 -49.81 136 -50.31 137 -50.80 138 -51.27 139 -51.72 140 -52.16 141 -52.59 142 -53.00 143 -53.40 144 -53.78 145 -54.14 146 -54.49 147 -54.83 148 -55.15 149 -55.45 150 -55.74 151 -56.02 152 -56.28 153 -56.54 154 -56.77 155 -57.00 156 -57.21 157 -57.42 158 -57.61 159 -57.79 160 -57.96 161 -58.12 162 -58.27 163 -58.41 164 -58.55 165 -58.68 166 -58.80 167 -58.91 168 -59.02 169 -59.12 170 -59.21 171 -59.31 172 -59.39 173 -59.48 174 -59.56 175 -59.63 176 -59.71 177 -59.78 178 -59.85 179 -59.92 180 -59.99 LCUR = 30 PCT(LCUR) = -.26 103

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APPENDIX E NUMERICAL EXAMPLE 3

PAGE 115

BEACH NOURISHMENT PROJECTION (Numerical Procedure) General Location: Exam p\ 3 Wave Height, Ho (Fig. 22): .-O ft., Closure Depth, h. (Fig. 8): L-" ft. Wave Period, T (Fig. 23): .o sec., Berm Height, B: 4 ft. Wave Direction, ao: 1O , Sand Diameter, D: 0,3-5 mm Deep Water Contour Orientation, fo: q9 o, Transport Factor, K (Fig. 5): Longshore Axis Orientation, p: I L o, VFACT: L,. Grid Dimension, Ax: 00 ft Background Transport, QREF: o ft3/s Time Increment, At: 8 (6 L sec IREF: I IMAX: S8o NTIMES: 0I o 0 No. of Structures, NS: o Structure Specificiation Background Erosion Structure Structure Structure [ I/rNumber Location, I Length (ft) z Erosion Rate, ER, (ft/yr) 1 _0 0 .I, o. 2 39 5-oo /, 3 4 q 5c00 o ,o 39roo'. 4 6_____ ,____ o. .o 5 ____ o 0~ 3) -5 6 t Equilibrated Beach Width Ayo Nourishment Specification I Range Ayo < ",o AN (Fig. 7) or From Profile: ftl/3 0 o to /00o / AF (Fig. 7): ft1/3 to Volume Per Unit Length: ft/ft __ to 3 _ Ayo (Figs. 11 and 12): 11ft to to 105

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PLANFORM EVOLUTION OVER TIME NON-UNIF. EROSION (DISTORTED SCRLES) NON-UN 200.0 D A B C 150.0 LL100.0 50.0 I0. 5 -00.0 -. ,D -------------------------------------------------+ ^ ------,--------------------------I3L -150.0 ICD -200.0 -250.0 -300.0 -I IIIIII 0 10000 20000 30000 40000 50000 60000 70000 80000 0 YERRS SHORELINE LENGTH IN FEET ............... 5 EARS Figure E-l. Numerical Example 3, Ay = 112 ft, Nourishment --10 TEARS Length = 2 Miles, Variable Background Erosion. -20 YEARS .--* .30 YEARS

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T (T) VERSUS TIME 2 MILE PLRNFORM WITH NON-UNIF. EROSION N-UNI 200.0 L 175.0 Z _1 150.0 LL 0 125.0 Cn 100.0 n-75.0 -".,#,, --Location A 5. -Location A 75.0 -J S50.0 -< .Location D S25.0 -Location B 00 ........ Location C -50.0 -75.0 -100 .0 I I I I I I I I I I I I I I I I I I I I I I I I 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 39500 4.9500 TIME IN YERRS -------45 Figure E-2. Numerical Example 3, Shoreline Position Variation with Time at Locations Indicated and Shown in Figure E-l.

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INPUT FILE: DNRBS.INP (Example No. 3) EXAMPLE NO. 3 VAR. BACK. EROS. NO STRUC. 2 MILE PROJ. 2.00 6.0 90.0 90.0 180.0 500.0 86400.0 17.0 6.0 0.77 1.0 0.0 1 180 10950 0 0.0 1.0 39500. 1.0 49500. 2.0 60000. 3.0 90000. 3.0 100000. 3.0 140000. 2.0 80 100 80 112.0 81 112.0 82 112.0 83 112.0 84 112.0 85 112.0 86 112.0 87 112.0 88 112.0 89 112.0 90 112.0 91 112.0 92 112.0 93 112.0 94 112.0 95 112.0 96 112.0 97 112.0 98 112.0 99 112.0 100 112.0 108

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OUTPUT FILE: DNRBS.OUT (Example No. 3) EXAMPLE NO. 3 VAR. BACK. EROS. NO STRUC. 2 MILE PROJ. HO = 2.00 FT., T = 6.00 SEC., ALPO = 90.00 DEG., BTAO = 90.00 DEG., XMU = 180.00 DEG., DX = 500.00 FT., DT = 86400.00 SEC. HSTR = 17.00 FT., B = 6.00 FT., XK = .77 VFACT = 1.00 QBKREF = .00 FT.**3/SEC. IREF = 1, IMAX = 180, NTIMES = 10950, NS = 0 .00E+00 1.00 .40E+05 1.00 .50E+05 2.00 .60E+05 3.00 .90E+05 3.00 .10E+06 3.00 .14E+06 2.00 BACKGROUND EROSION TRANSPORT RATES 1 .000 2 .000 3 .001 4 .001 5 .001 6 .002 7 .002 8 .003 9 .003 10 .003 11 .004 12 .004 13 .004 14 .005 15 .005 16 .005 17 .006 18 .006 19 .007 20 .007 21 .007 22 .008 23 .008 24 .008 25 .009 26 .009 27 .009 28 .010 29 .010 30 .011 31 .011 32 .011 33 .012 34 .012 35 .012 36 .013 37 .013 38 .013 39 .014 40 .014 41 .015 42 .015 43 .015 44 .016 45 .016 46 .016 47 .017 48 .017 49 .018 50 .018 51 .018 52 .019 53 .019 54 .019 55 .020 56 .020 57 .020 58 .021 59 .021 60 .022 61 .022 62 .022 63 .023 64 .023 65 .023 66 .024 67 .024 68 .024 69 .025 70 .025 71 .026 72 .026 73 .026 74 .027 75 .027 76 .027 77 .028 78 .028 79 .028 80 .029 81 .029 82 .030 83 .030 84 .030 85 .031 86 .031 87 .032 88 .032 89 .033 90 .033 91 .034 92 .034 93 .035 94 .036 95 .036 96 .037 97 .037 98 .038 99 .039 100 .040 101 .040 102 .041 103 .042 104 .043 105 .043 106 .044 107 .045 108 .046 109 .047 110 .048 111 .049 112 .049 113 .050 114 .051 115 .052 116 .053 117, .054 118 .055 119 .056 120 .057 121 .059 122 .060 123 .061 124 .062 125 .063 126 .064 127 .065 128 .066 129 .067 130 .068 131 .069 132 .071 133 .072 134 .073 135 .074 136 .075 137 .076 138 .077 139 .078 140 .079 141 .080 142 .082 143 .083 144 .084 145 .085 146 .086 147 .087 148 .088 149 .089 150 .090 151 .091 152 .092 153 .094 154 .095 155 .096 156 .097 157 .098 158 .099 159 .100 160 .101 161 .102 162 .103 163 .104 164 .106 165 .107 166 .108 167 .109 168 .110 169 .111 170 .112 171 .113 172 .114 173 174 .117 175 .118 176 .119 177 .120 178 109 179 .122 180 .123 181 .124

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80 100 INITIAL SHORELINE (INCL. NOURISHMENT) POSITION 1 0. .00 2 500. .00 3 1000. .00 4 1500. .00 5 2000. .00 6 2500. .00 7 3000. .00 8 3500. .00 9 4000. .00 10 4500. .00 11 5000. .00 12 5500. .00 13 6000. .00 14 6500. .00 15 7000. .00 16 7500. .00 17 8000. .00 18 8500. .00 19 9000. .00 20 9500. .00 21 10000. .00 22 10500. .00 23 11000. .00 24 11500. .00 25 12000. .00 26 12500. .00 27 13000. .00 28 13500. .00 29 14000. .00 30 14500. .00 31 15000. .00 32 15500. .00 33 16000. .00 34 16500. .00 35 17000. .00 36 17500. .00 37 18000. .00 38 18500. .00 39 19000. .00 40 19500. .00 41 20000. .00 42 20500. .00 43 21000. .00 44 21500. .00 45 22000. .00 46 22500. .00 47 23000. .00 48 23500. .00 49 24000. .00 50 24500. .00 51 25000. .00 52 25500. .00 53 26000. .00 54 26500. .00 55 27000. .00 56 27500. .00 57 28000. .00 58 28500. .00 59 29000. .00 60 29500. .00 61 30000. .00 62 30500. .00 63 31000. .00 64 31500. .00 65 32000. .00 66 32500. .00 67 33000. .00 68 33500. .00 69 34000. .00 70 34500. .00 71 35000. .00 72 35500. .00 73 36000. .00 74 36500. .00 75 37000. .00 76 37500. .00 77 38000. .00 78 38500. .00 79 39000. .00 80 39500. 112.00 81 40000. 112.00 82 40500. 112.00 83 41000. 112.00 84 41500. 112.00 85 42000. 112.00 86 42500. 112.00 87 43000. 112.00 88 43500. 112.00 89 44000. 112.00 90 44500. 112.00 91 45000. 112.00 92 45500. 112.00 93 46000. 112.00 94 46500. 112.00 95 47000. 112.00 96 47500. 112.00 97 48000. 112.00 98 48500. 112.00 99 49000. 112.00 100 49500. 112.00 101 50000. .00 102 50500. .00 103 51000. .00 104 51500. .00 105 52000. .00 106 52500. .00 107 53000. .00 108 53500. .00 109 54000. .00 110 54500. .00 111 55000. .00 112 55500. .00 113 56000. .00 114 56500. .00 115 57000. .00 116 .;'7 .00 117 58000. .00 118 3. .00 119 59000. .00 120 ). .00 121 60000. .00 122 -,3. .00 123 61000. .00 124 61500. .00

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127 63000. .00 128 63500. .00 129 64000. .00 130 64500. .00 131 65000. .00 132 65500. .00 133 66000. .00 134 66500. .00 135 67000. .00 136 67500. .00 137 68000. .00 138 68500. .00 139 69000. .00 140 69500. .00 141 70000. .00 142 70500. .00 143 71000. .00 144 71500. .00 145 72000. .00 146 72500. .00 147 73000. .00 148 73500. .00 149 74000. .00 150 74500. .00 151 75000. .00 152 75500. .00 153 76000. .00 154 76500. .00 155 77000. .00 156 77500. .00 157 78000. .00 158 78500. .00 159 79000. .00 160 79500. .00 161 80000. .00 162 80500. .00 163 81000. .00 164 81500. .00 165 82000. .00 166 82500. .00 167 83000. .00 168 83500. .00 169 84000. .00 170 84500. .00 171 85000. .00 172 85500. .00 173 86000. .00 174 86500. .00 175 87000. .00 176 87500. .00 177 88000. .00 178 88500. .00 179 89000. .00 180 89500. .00 100 116 .000 .053 .000 -.736 -.749 .053 .000 TIME = 1 YEARS 1 -1.00 2 -1.00 3 -1.00 4 -1.00 5 -1.00 6 -1.00 7 -1.00 8 -1.00 9 -1.00 10 -1.00 11 -1.00 12 -1.00 13 -1.00 14 -1.00 15 -1.00 16 -1.00 17 -1.00 18 -1.00 19 -1.00 20 -1.00 21 -1.00 22 -1.00 23 -1.00 24 -1.00 25 -1.00 26 -1.00 27 -1.00 28 -1.00 29 -1.00 30 -1.00 31 -1.00 32 -1.00 33 -1.00 34 -1.00 35 -1.00 36 -1.00 37 -1.00 38 -1.00 39 -1.00 40 -1.00 41 -1.00 42 -1.00 43 -1.00 44 -1.00 45 -1.00 46 -1.00 47 -1.00 48 -1.00 49 -1.00 50 -1.00 51 -1.00 52 -1.00 53 -1.00 54 -1.00 55 -1.00 56 -1.00 '57 -1.00 58 -1.00 59 -.99 60 -.98 61 -.96 62 -.93 63 -.87 64 -.77 65 -.60 66 -.31 67 .13 68 .82 69 1.84 70 3.31 71 5.34 72 8.07 73 11.61 74 16.06 75 21.44 76 27.73 77 34.84 78 42.60 79 50.78 80 59.09 81 67.24 82 74.96 83 82.01 84 88.21 85 93.45 86 97.67 87 100.89 88 103.12 89 104.42 90 104.81 91 104.32 92 102.92 93 100.59 94 97.28 95 92.96 96 87.63 97 81.34 98 74.20 99 66.39 100 58.16 101 49.78 102 41.54 103 33.72 104 26.56 105 20.21 106 14.78 107 10.28 108 6.69 109 3.91 110 1.83 111 .32 112 -.75 113 -1.48 114 -1.98 115 -2.31 116 -2.52 117 -2.67 118 -2.77 119 -2.84 120 -2.89 121 -2.92 122 -2.95 123 -2.97 124 -2.98 125 -2.99 126 -2.99 127 -2.99 128 -3.00 129 -3.00 130 -3.00 131 -3.00 132 -3.00 133 -3.00 134 -3.00 135 -3.00 136 -3.00 137 -3.00 138 -3.00 139 -3.00 140 -3.00 141 -3.00 142 -3.00 143 -3.00 144 -3.00 145 -3.00 146 -3.00 147 -3.00 148 -3.00 149 -3.00 150 -3.00 151 -3.00 152 -3.00 153 -3.00 154 -3.00 155 -3.00 156 -3.00 157 -3.00 158 -3.00 159 -3.00 160 -3.00 161 -3.00 162 -3.00 163 -3.00 164 -3.00 165 -3.00 166 -3.00 167 -3.00 168 -3.00 169 -3.00 170 -3.00 171 -3.00 172 -3.00 173 -3.00 174 -3.00 175 -3.00 176 -3.00 177 -3.00 178 -3.00 179 -3.00 180 -3.00 LCUR = 1 PCT(LCUR) = -7R LCUR = 2 PCT(LCUR) = LCUR = 3 PCT(LCUR) = 111 LCUR = 4 PCT(LCUR) = TIME = 5 YEARS 1 -5.00 2 -5.00 3 -5.00 4 -5.00 5 -5.00 6 -5.00

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13 -5.00 14 -5.00 15 -5.00 16 -5.00 17 -5.00 18 -5.00 19 -5.00 20 -5.00 21 -5.00 22 -5.00 23 -5.00 24 -5.00 25 -5.00 26 -5.00 27 -5.00 28 -5.00 29 -5.00 30 -5.00 31 -5.00 32 -5.00 33 -4.99 34 -4.99 35 -4.99 36 -4.98 37 -4.98 38 -4.97 39 -4.96 40 -4.94 41 -4.92 42 -4.90 43 -4.86 44 -4.82 45 -4.77 46 -4.70 47 -4.61 48 -4.51 49 -4.37 50 -4.21 51 -4.00 52 -3.76 53 -3.46 54 -3.11 55 -2.68 56 -2.18 57 -1.59 58 -.90 59 -.10 60 .81 61 1.86 62 3.04 63 4.38 64 5.87 65 7.52 66 9.34 67 11.33 68 13.48 69 15.80 70 18.27 71 20.88 72 23.62 73 26.47 74 29.41 75 32.40 76 35.42 77 38.44 78 41.42 79 44.33 80 47.12 81 49.76 82 52.22 83 54.45 84 56.42 85 58.12 86 59.50 87 60.55 88 61.25 89 61.59 90 61.55 91 61.14 92 60.37 93 59.23 94 57.74 95 55.93 96 53.82 97 51.43 98 48.80 99 45.96 100 42.95 101 39.81 102 36.56 103 33.26 104 29.93 105 26.61 106 23.32 107 20.11 108 17.00 109 14.00 110 11.14 111 8.43 112 5.88 113 3.51 114 1.30 115 -.72 116 -2.57 117 -4.24 118 -5.75 119 -7.09 120 -8.29 121 -9.33 122 -10.24 123 -11.03 124 -11.71 125 -12.28 126 -12.77 127 -13.18 128 -13.53 129 -13.81 130 -14.05 131 -14.24 132 -14.40 133 -14.53 134 -14.63 135 -14.71 136 -14.78 137 -14.83 138 -14.87 139 -14.90 140 -14.92 141 -14.94 142 -14.96 143 -14.97 144 -14.98 145 -14.98 146 -14.99 147 -14.99 148 -14.99 149 -15.00 150 -15.00 151 -15.00 152 -15.00 153 -15.00 154 -15.00 155 -15.00 156 -15.00 157 -15.00 158 -15.00 159 -15.00 160 -15.00 161 -15.00 162 -15.00 163 -15.00 164 -15.00 165 -15.00 166 -15.00 167 -15.00 168 -15.00 169 -15.00 170 -15.00 171 -15.00 172 -15.00 173 -15.00 174 -15.00 175 -15.00 176 -15.00 177 -15.00 178 -15.00 179 -15.00 180 -15.00 LCUR = 5 PCT(LCUR) = .49 LCUR = 6 PCT(LCUR) = .45 LCUR = 7 PCT(LCUR) = .40 LCUR = 8 PCT(LCUR) = .37 LCUR = 9 PCT(LCUR) = .33 TIME = 10 YEARS 1 -10.00 2 -10.00 3 -10.00 4 -10.00 5 -10.00 6 -10.00 7 -10.00 8 -10.00 9 -10.00 10 -10.00 11 -10.00 12 -10.00 13 -9.99 14 -9.99 15 -9.99 16 -9.99 17 -9.99 18 -9.98 19 -9.98 20 -9.97 21 -9.97 22 -9.96 23 -9.95 24 -9.94 25 -9.92 26 -9.91 27 -9.89 28 -9.86 29 -9.83 30 -9.80 31 -9.76 32 -9.71 33 -9.65 34 -9.59 35 -9.51 36 -9.42 37 -9.31 38 -9.19 39 -9.05 40 -8.89 41 -8.71 42 -8.50 43 -8.26 44 -8.00 45 -7.69 46 -7.35 47 -6.97 48 -6.55 49 -6.08 50 -5.56 51 -4.99 52 -4.36 53 -3.67 54 -2.92 55 -2.11 56 -1.23 57 -.29 58 .72 59 1.80 60 2.95 61 4.16 62 5.44 63 6.79 64 8.19 65 9.64 66 11.15 67 12.69 68 14.28 69 15.89 70 17.51 71 19.15 72 20.78 73 22.40 74 24.00 75 25.56 76 27.06 77 28.50 78 29.86 79 31.13 80 32.30 81 33.35 82 34.27 83 35.05 84 35.70 85 36.19 86 36.53 87 36.71 88 36.72 89 36.57 90 36.25 91 35.76 92 35.11 93 34.30 94 33.33 95 32.21 96 30.94 97 29.54 98 28.02 99 26.37 100 24.62 101 22.78 102 20.85 103 18.86 104 16.81 105 14.71 106 12.58 107 10.43 108 8.28 109 6.13 110 4.00 111 1.89 112 -.18 113 -2.20 114 -4.17 115 -6.08 116 -7.92 117 -9.68 118 -11.37 119 -12.97 120 -14.48 121 -15.90 122 -17.23 123 -18.47 124 -19.61 125 -20.67 126 -21.65 127 -22.55 128 -23.37 129 -24.11 130 -24.79 131 -25.41 132 -25.96 133 -26.46 134 -26.90 135 -27.30 136 -27.66 137 -27.97 138 -28.25 139 -28.49 140 -28.70 141 -28.89 142 -29.05 143 -29.20 144 -29.32 145 -29.42 146 -29.51 147 -29.59 148 -29.66 149 -29.71 150 -29.76 151 -29.80 152 -29.84 153 -29.87 154 -29.89 155 -29.91 156 -29.93 157 -29.94 158 -29.95 159 -29.96 160 -29.97 161 -29.97 162 -29.98 163 -29.98 164 -29.99 165 -29.9 -29.99 167 -29.99 168 -29.99 169 -30.00 170 -30.00 171 -30.0' 112 -30.00 173 -30.00 174 -30.00 175 -30.00 176 -30.00 177 -30.0 -30.00 179 -30.00 180 -30.00 LCUR = 10 PCT(LCUR) = .30

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LCLUK = 12 PCT(LCUR) = .24 LCUR = 12 PCT(LCUR) = .24 LCUR = 13 PCT(LCUR) = .21 LCUR = 14 PCT(LCUR) = .18 LCUR = 15 PCT(LCUR) = .16 LCUR = 16 PCT(LCUR) = .13 LCUR = 17 PCT(LCUR) = .11 LCUR = 18 PCT(LCUR) = .08 LCUR = 19 PCT(LCUR) = .06 LCUR = 20 PCT(LCUR) = .04 LCUR = 21 PCT(LCUR) = .01 LCUR = 22 PCT(LCUR) = -.01 LCUR = 23 PCT(LCUR) = -.03 LCUR = 24 PCT(LCUR) = -.05 LCUR = 25 PCT(LCUR) = -.07 LCUR = 26 PCT(LCUR) = -.09 LCUR = 27 PCT(LCUR) = -.11 LCUR = 28 PCT(LCUR) = -.13 LCUR = 29 PCT(LCUR) = -.15 TIME = 30 YEARS 1 -30.00 2 -29.92 3 -29.85 4 -29.77 5 -29.69 6 -29.61 7 -29.53 8 -29.45 9 -29.36 10 -29.27 11 -29.17 12 -29.07 13 -28.96 14 -28.85 15 -28.73 16 -28.61 17 -28.48 18 -28.34 19 -28.19 20 -28.04 21 -27.88 22 -27.70 23 -27.52 24 -27.33 25 -27.13 26 -26.91 27 -26.69 28 -26.45 29 -26.21 30 -25.95 31 -25.68 32 -25.39 33 -25.10 34 -24.79 35 -24.47 36 -24.14 37 -23.79 38 -23.44 39 -23.07 40 -22.69 41 -22.30 42 -21.89 43 -21.48 44 -21.06 45 -20.63 46 -20.19 47 -19.74 48 -19.29 49 -18.83 50 -18.37 51 -17.90 52 -17.44 53 -16.97 54 -16.50 55 -16.04 56 -15.58 57 -15.12 58 -14.68 59 -14.24 60 -13.82 61 -13.41 62 -13.02 63 -12.65 64 -12.30 65 -11.97 66 -11.67 67 -11.39 68 -11.15 69 -10.94 70 -10.77 71 -10.64 72 -10.55 73 -10.50 74 -10.50 75 -10.55 76 -10.65 77 -10.81 78 -11.02 79 -11.30 80 -11.64 81 -12.04 82 -12.51 83 -13.04 84 -13.63 85 -14.28 86 -15.00 87 -15.77 88 -16.60 89 -17.48 90 -18.41 91 -19.40 92 -20.44 93 -21.52 94 -22.65 95 -23.83 96 -25.04 97 -26.30 98 -27.59 99 -28.91 100 -30.27 101 -31.65 102 -33.06 103 -34.50 104 -35.95 105 -37.42 106 -38.91 107 -40.41 108 -41.91 109 -43.43 110 -44.94 111 -46.45 112 -47.96 113 -49.46 114 -50.96 115 -52.43 116 -53.89 117 -55.33 118 -56.75 119 -58.14 120 -59.50 121 -60.83 122 -62.11 123 -63.37 124 -64.58 125 -65.76 126 -66.90 127 -68.01 128 -69.08 129 -70.11 130 -71.11 131 -72.08 132 -73.01 133 -73.90 134 -74.76 135 -75.59 136 -76.39 137 -77.15 138 -77.88 139 -78.58 140 -79.25 141 -79.89 142 -80.50 143 -81.08 144 -81.64 145 -82.16 146 -82.67 147 -83.14 148 -83.59 149 -84.02 150 -84.43 151 -84.81 152 -85.17 153 -85.52 154 -85.84 155 -86.14 156 -86.43 157 -86.70 158 -86.95 159 -87.19 160 -87.41 161 -87.62 162 -87.82 163 -88.01 164 -88.18 165 -88.34 166 -88.50 167 -88.64 168 -88.78 169 -88.91 170 -89.03 171 -89.14 172 -89.25 173 -89.36 174 -89.46 175 -89.55 176 -89.64 177 -89.73 178 -89.82 179 -89.91 180 -90.00 LCUR = 30 PCT(LCUR) = -.17 113

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APPENDIX F NUMERICAL EXAMPLE 4

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BEACH NOURISHMENT PROJECTION (Numerical Procedure) General Location: E-hple 4 Wave Height, Ho (Fig. 22): 2,Z0 ft., Closure Depth, h, (Fig. 8): .-ft. Wave Period, T (Fig. 23): ,.0 sec., Berm Height, B: 6 ft. Wave Direction, ao: .q 0, Sand Diameter, D: 03,7, mm Deep Water Contour Orientation, 8o: 90 0, Transport Factor, K (Fig. 5): 0'17 Longshore Axis Orientation, p: 180o VFACT: 1 a Grid Dimension, Ax: 40oo ft Background Transport, QREF: c~ ft3/s Time Increment, At: 8 t,40 sec IREF: I IMAX: \&a NTIMES: I10o 0 No. of Structures, NS: Structure Specificiation Background Erosion Structure Structure Structure Number Location, I Length (ft) x (4+) Erosion Rate, ER, (ft/yr) 1, ----cx 0._ 0. 2 ____o __ 0,6 3 5 6 ---d Equilibrated Beach Width Ayo Nourishment Specification E ross. I Range Ayo AN (Fig. 7) or From Profile: ft'/3 8 to 3 11 2. AF (Fig. 7): ft/3 to Volume Per Unit Length: ft3/ft to Ayo (Figs. 11 and 12): / 2ft to to 115

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PLRNFORM EVOLUTION OVER TIME NO EROSION (DISTORTED SCRLES) NO ER 400.0 350.0 LU LU LL 300.0 Z 250.0 LU LJ-) Z CI 200.0 -AB C Cr S150.0 LL S10.0 CO') 50.0 ULL50.0 o.0o -..... ----n. 9 "----------*__T-:=.?. =*M:____r^---------. -50.0 -100.0 I I I I I 1 I 0 10000 20000 30000 40000 50000 60000 70000 80000 0 YEARS SHORELINE LENGTH IN FEET ....................5 YEARS Figure F-1. Numerical Example 4, Ay, = 112 ft, Nourishment ---10 TEARS Length = 1,000 ft, No Background Erosion. 20 YEARS S-30 YEARS

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T (T) VERSUS TIME 1/2 MILE PLANFORM WITH NO EROSION NO ER 200.0 Li 175.0 Z _J 150.0 LLi CC 0 125.0 5CO 100.0 C) S75.0 -Location A U50.0 -Location B LLS25.0 --------------------------------------------------*0.0 0O Location C S-25.0 -50.0 -75.0 -100.0 1111111-I I I III I I11111 11 11111 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 qq 4500 TIME IN YERRS .......... 46000 -..--._ 59500 Figure F-2. Numerical Example 4, Shoreline Position Variation with Time at Locations Indicated and Shown in Figure F-l.

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OUTPUT FILE: DNRBS.INP (Example No. 4) EXAMPLE NO. 4 NO BACK. EROS. NO STRUC. 3500 FT. PROJ. 2.00 6.0 90.0 90.0 180.0 500.0 86400.0 17.0 6.0 0.77 1.0 0.0 90 180 10950 0 0.0 0.0 90000. 0.0 100000. 0.0 49500. 3.0 90000. 3.0 100000. 2.0 140000. 2.0 87 93 87 112.0 88 112.0 89 112.0 90 112.0 91 112.0 92 112.0 93 112.0 118

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OUTPUT FILE: DNRBS.OUT (Example No. 4) EXAMPLE NO. 4 NO BACK. EROS. NO STRUC. 3500 FT. PROJ. HO = 2.00 FT., T = 6.00 SEC., ALPO = 90.00 DEG., BTAO = 90.00 DEG., XMU = 180.00 DEG., DX = 500.00 FT., DT = 86400.00 SEC. HSTR = 17.00 FT., B = 6.00 FT., XK = .77 VFACT = 1.00 QBKREF = .00 FT.**3/SEC. IREF = 90, IMAX = 180, NTIMES = 10950, NS = 0 .00E+00 .00 .90E+05 .00 .10E+06 .00 .50E+05 3.00 .90E+05 3.00 .10E+06 2.00 .14E+06 2.00 BACKGROUND EROSION TRANSPORT RATES 1 .000 2 .000 3 .000 4 .000 5 .000 6 .000 7 .000 8 .000 9 .000 10 .000 11 .000 12 .000 13 .000 14 .000 15 .000 16 .000 17 .000 18 .000 19 .000 20 .000 21 .000 22 .000 23 .000 24 .000 25 .000 26 .000 27 .000 28 .000 29 .000 30 .000 31 .000 32 .000 33 .000 34 .000 35 .000 36 .000 37 .000 38 .000 39 .000 40 .000 41 .000 42 .000 43 .000 44 .000 45 .000 46 .000 47 .000 48 .000 49 .000 50 .000 51 .000 52 .000 53 .000 54 .000 55 .000 56 .000 57 .000 58 .000 59 .000 60 .000 61 .000 62 .000 63 .000 64 .000 65 .000 66 .000 67 .000 68 .000 69 .000 70 .000 71 .000 72 .000 73 .000 74 .000 75 .000 76 .000 77 .000 78 .000 79 .000 80 .000 81 .000 82 .000 83 .000 84 .000 85 .000 86 .000 87 .000 88 .000 89 .000 90 .000 91 .000 92 .000 93 .000 94 .000 95 .000 96 .000 97 .000 98 .000 99 .000 100 .000 101 .000 102 .000 103 .000 104 .000 105 .000 106 .000 107 .000 108 .000 109 .000 110 .000 111 .000 112 .000 113 .000 114 .000 115 .000 116 .000 117 .000 118 .000 119 .000 120 .000 121 .000 122 .000 123 .000 124 .000 125 .000 126 .000 127 .000 128 .000 129 .000 130 .000 131 .000 132 .000 133 .000 134 .000 135 .000 136 .000 137 .000 138 .000 139 .000 140 .000 141 .000 142 .000 143 .000 144 .000 145 .000 146 .000 147 .000 148 .000 149 .000 150 .000 151 .000 152 .000 153 .000 154 .000 155 .000 156 .000 157 .000 158 .000 159 .000 160 .000 161 .000 162 .000 16? n00 164 .000 165 .000 166 .000 167 .000 16E 119 )0 169 .000 170 .000 171 .000 172 .000 17: 00 174 .000 175 .000 176 .000 177 .000 178 .000 179 .000 180 .000 181 .000

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87 93 INITIAL SHORELINE (INCL. NOURISHMENT) POSITION 1 0. .00 2 500. .00 3 1000. .00 4 1500. .00 5 2000. .00 6 2500. .00 7 3000. .00 8 3500. .00 9 4000. .00 10 4500. .00 11 5000. .00 12 5500. .00 13 6000. .00 14 6500. .00 15 7000. .00 16 7500. .00 17 8000. .00 18 8500. .00 19 9000. .00 20 9.500. .00 21 10000. .00 22 10500. .00 23 11000. .00 24 11500. .00 25 12000. .00 26 12500. .00 27 13000. .00 28 13500. .00 29 14000. .00 30 14500. .00 31 15000. .00 32 15500. .00 33 16000. .00 34 16500. .00 35 17000. .00 36 17500. .00 37 18000. .00 38 18500. .00 39 19000. .00 40 19500. .00 41 20000. .00 42 20500. .00 43 21000. .00 44 21500. .00 45 22000. .00 46 22500. .00 47 23000. .00 48 23500. .00 49 24000. .00 50 24500. .00 51 25000. .00 52 25500. .00 53 26000. .00 54 26500. .00 55 27000. .00 56 27500. .00 57 28000. .00 58 28500. .00 59 29000. .00 60 29500. .00 61 30000. .00 62 30500. .00 63 31000. .00 64 31500. .00 65 32000. .00 66 32500. .00 67 33000. .00 68 33500. .00 69 34000. .00, 70 34500. .00 71 35000. .00 72 35500. .00 73 36000. .00 74 36500. .00 75 37000. .00 76 37500. .00 77 38000. .00 78 38500. .00 79 39000. .00 80 39500. .00 81 40000. .00 82 40500. .00 83 41000. .00 84 41500. .00 85 42000. .00 86 42500. .00 87 43000. 112.00 88 43500. 112.00 89 44000. 112.00 90 44500. 112.00 91 45000. 112.00 92 45500. 112.00 93 46000. 112.00 94 46500. .00 95 47000. .00 96 47500. .00 97 48000. .00 98 48500. .00 99 49000. .00 100 49500. .00 101 50000. .00 102 50500. .00 103 51000. .00 104 51500. .00 105 52000. .00 106 52500. .00 107 53000. .00 108 53500. .00 109 54000. .00 110 54500. .00 111 55000. .00 112 55500. .00 113 56000. .00 114 56500. .00 115 57000. .00 116 ")0. .00 117 58000. .00 118 120 )0. .00 119 59000. .00 120 '0. .00 121 60000. .00 122 60500. .00 123 61000. .00 124 61500. .00

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S125 62000. .00 12b 6200. .UU 127 63000. .00 128 63500. .00 129 64000. .00 130 64500. .00 131 65000. .00 132 65500. .00 133 66000. .00 134 66500. .00 135 67000. .00 136 67500. .00 137 68000. .00 138 68500. .00 139 69000. .00 140 69500. .00 141 70000. .00 142 70500. .00 143 71000. .00 144 71500. .00 145 72000. .00 146 72500. .00 147 73000. .00 148 73500. .00 149 74000. .00 150 74500. .00 151 75000. .00 152 75500. .00 153 76000. .00 154 76500. .00 155 77000. .00 156 77500. .00 157 78000. .00 158 78500. .00 159 79000. .00 160 79500. .00 161 80000. .00 162 80500. .00 163 81000. .00 164 81500. .00 165 82000. .00 166 82500. .00 167 83000. .00 168 83500. .00 169 84000. .00 170 84500. .00 171 85000. .00 172 85500. .00 173 86000. .00 174 86500. .00 175 87000. .00 176 87500. .00 177 88000. .00 178 88500. .00 179 89000. .00 180 89500. .00 100 116 .000 .000 .000 .000 .000 .000 .000 TIME = 1 YEARS 1 .00 2 .00 3 .00 4 .00 5 .00 6 .00 7 .00 8 .00 9 .00 10 .00 11 .00 12, .00 13 .00 14 .00 15 .00 16 .00 17 .00 18 .00 19 .00 20 .00 21 .00 22 .00 23 .00 24 .00 25 .00 26 .00 27 .00 28 .00 29 .00 30 .00 31 .00 32 .00 33 .00 34 .00 35 .00 36 .00 37 .00 38 .00 39 .00 40 .00 41 .00 42 .00 43 .00 44 .00 45 .00 46 .00 47 .00 48 .00 49 .00 50 .00 51 .00 52 .00 53 .00 54 .00 55 .00 56 .00 57 .00 58 .00 59 .00 60 .00 61 .00 62 .00 63 .00 64 .00 65 .00 66 .01 67 .02 68 .04 69 .07 70 .13 71 .23 72 .40 73 .68 74 1.12 75 1.79 76 2.77 77 4.18 78 6.11 79 8.67 80 11.93 81 15.93 82 20.62 83 25.90 84 31.56 85 37.30 86 42.76 87 47.55 88 51.30 89 53.69 90 54.51 91 53.69 92 51.30 93 47.55 94 42.76 95 37.30 96 31.56 97 25.90 98 20.62 99 15.93 100 11.93 101 8.67 102 6.11 103 4.18 104 2.77 105 1.79 106 1.12 107 .68 108 .40 109 .23 110 .13 111 .07 112 .04 113 .02 114 .01 115 .00 116 .00 117 .00 118 .00 119 .00 120 .00 121 .00 122 .00 123 .00 124 .00 125 .00 126 .00 127 .00 128 .00 129 .00 130 .00 131 .00 132 .00 133 .00 134 .00 135 .00 136 .00 137 .00 138 .00 139 .00 140 .00 141 .00 142 .00 143 .00 144 .00 145 .00 146 .00 147 .00 148 .00 149 .00 150 .00 151 .00 152 .00 153 .00 154 .00 155 .00 156 .00 157 .00 158 .00 159 .00 160 .00 161 .00 162 .00 163 .00 164 .00 165 .00 166 .00 167 .00 168 .00 169 .00 170 .00 171 .00 172 .00 173 .00 174 .00 175 .00 176 .00 177 .00 178 .00 179 .00 180 .00 LCUR = 1 PCT(LCUR) = .46 LCUR = 2 PCT(LCUR) = o' LCUR = 3 PCT(LCUR) = 121 LCUR = 4 PCT(LCUR) = TIME = 5 YkAKS 1 ___ n -0()_ n 4 -00 r)A-no A nn -j -6 -i --

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7 .00 8 .00 9 .U0 i0 .UU 11 .00 12 .OU 13 .00 14 .00 15 .00 16 .00 17 .00 18 .00 19 .00 20 .00 21 .00 22 .00 23 .00 24 .00 25 .00 26 .00 27 .00 28 .00 29 .00 30 .00 31 .00 32 .00 33 .00 34 .00 35 .00 36 .00 37 .00 38 .00 39 .00 40 .01 41 .01 42 .01 43 .02 44 .02 45 .03 46 .04 47 .05 48 .07 49 .09 50 .12 51 .16 52 .20 53 .26 54 .33 55 .42 56 .53 57 .66 58 .82 59 1.01 60 1.24 61 1.52 62 1.84 63 2.21 64 2.64 65 3.13 66 3.69 67 4.33 68 5.03 69 5.82 70 6.67 71 7.61 72 8.62 73 9.70 74 10.84 75 12.03 76 13.26 77 14.52 78 15.80 79 17.07 80 18.32 81 19.53 82 20.69 83 21.76 84 22.73 85 23.59 86 24.32 87 24.90 88 25.32 89 25.58 90 25.66 91 25.58 92 25.32 93 24.90 94 24.32 95 23.59 96 22.73 97 21.76 98 20.69 99 19.53 100 18.32 101 17.07 102 15.80 103 14.52 104 13.26 105 12.03 106 10.84 107 9.70 108 8.62 109 7.61 110 6.67 111 5.82 112 5.03 113 4.33 114 3.69 115 3.13 116 2.64 117 2.21 118 1.84 119 1.52 120 1.24 121 1.01 122 .82 123 .66 124 .53 125 .42 126 .33 127 .26 128 .20 129 .16 130 .12 131 .09 132 .07 133 .05 134 .04 135 .03 136 .02 137 .02 138 .01 139 .01 140 .01 141 .00 142 .00 143 .00 144 .00 145 .00 146 .00 147 .00 148 .00 149 .00 150 .00 151 .00 152 .00 153 .00 154 .00 155 .00 156 .00 157 .00 158 .00 159 .00 160 .00 161 .00 162 .00 163 .00 164 .00 165 .00 166 .00 167 .00 168 .00 169 .00 170 .00 171 .00 172 .00 173 .00 174 .00 175 .00 176 .00 177 .00 178 .00 179 .00 180 .00 LCUR = 5 PCT(LCUR) = .23 LCUR = 6 PCT(LCUR) = .21 LCUR = 7 PCT(LCUR) = .19 LCUR = 8 PCT(LCUR) = .18 LCUR = 9 PCT(LCUR) = .17 TIME = 10 YEARS 1 .00 2 .00 3 .00 4 .00 5 .00 6 .00 7 .00 8 .00 9 .00 10 .00 11 .00 12 .00 13 .00 14 .00 15 .00 16 .00 17 .00 18 .00 19 .00 20 .00 21 .01 22 .01 23 .01 24 .01 25 .01 26 .02 27 .02 28 .03 29 .03 30 .04 31 .05 32 .06 33 .07 34 .09 35 .11 36 .13 37 .15 38 .18 39 .22 40 .26 41 .31 42 .36 43 .42 44 .50 45 .58 46 .67 47 .78 48 .90 49 1.04 50 1.19 51 1.37 52 1.56 53 1.77 54 2.00 55 2.26 56 2.54 57 2.85 58 3.19 59 3.55 60 3.94 61 4.35 62 4.80 63 5.27 64 5.77 65 6.29 66 6.84 67 7.41 68 8.00 69 8.61 70 9.23 71 9.87 72 10.51 73 11.16 74 11.80 75 12.44 76 13.07 77 13.69 78 14.29 79 14.86 80 15.40 81 15.91 82 16.38 83 16.80 84 17.18 85 17.50 86 17.77 87 17.99 88 18.14 89 18.24 90 18.27 91 18.24 92 18.14 93 17.99 94 17.77 95 17.50 96 17.18 97 16.80 98 16.38 99 15.91 100 15.40 101 14.86 102 14.29 103 13.69 104 13.07 105 12.44 106 11.80 107 11.16 108 10.51 109 9.87 110 9.23 111 8.61 112 8.00 113 7.41 114 6.84 115 6.29 116 5.77 117 5.27 118 4.80 119 4.35 120 3.94 121 3.55 122 3.19 123 2.85 124 2.54 125 2.26 126 2.00 127 1.77 128 1.56 129 1.37 130 1.19 131 1.04 132 .90 133 .78 134 .67 135 .58 136 .50 137 .42 138 .36 139 .31 140 .26 141 .22 142 .18 143 .15 144 .13 145 .11 146 .09 147 .07 148 .06 149 .05 150 .04 151 .03 152 .03 153 .02 122 .02 155 .01 156 .01 157 .01 158 .01 159 .01 .00 161 .00 162 .00 163 .00 164 .00 165 .00 .,, .00 167 .00 168 .00 169 .00 170 .00 171 .00 172 .00 173 .00 174 .00 175 .00 176 .00 177 .00 178 .00 179 .00 180 .00 T.TTD -1 prT I T.rTTP I= 116

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LCUK = 12 PCT(LCUR) = .-1 LCUR = 12 PCT(LCUR) = .15 LCUR = 13 PCT(LCUR) = .14 LCUR = 14 PCT(LCUR) = .14 LCUR = 15 PCT(LCUR) = .13 LCUR = 16 PCT(LCUR) = .13 LCUR = 17 PCT(LCUR) = .12 LCUR = 18 PCT(LCUR) = .12 LCUR = 19 PCT(LCUR) = .12 LCUR = 20 PCT(LCUR) = .12 LCUR = 21 PCT(LCUR) = .11 LCUR = 22 PCT(LCUR) = .11 LCUR = 23 PCT(LCUR) = .11 LCUR = 24 PCT(LCUR) = .11 LCUR = 25 PCT(LCUR) = .10 LCUR = 26 PCT(LCUR) = .10 LCUR = 27 PCT(LCUR) = .10 LCUR = 28 PCT(LCUR) = .10 LCUR = 29 PCT(LCUR) = .10 TIME = 30 YEARS 1 .00 2 .02 3 .05 4 .07 5 .09 6 .12 7 .14 8 .17 9 .20 10 .23 11 .26 12 .29 13 .32 14 .36 15 .40 16 .44 17 .48 18 .53 19 .57 20 .62 21 .68 22 .74 23 .80 24 .86 25 .93 26 1.01 27 1.08 28 1.16 29 1.25 30 1.34 31 1.44 32 1.54 33 1.64 34 1.75 35 1.87 36 1.99 37 2.11 38 2.25 39 2.38 40 2.52 41 2.67 42 2.83 43 2.98 44 3.15 45 3.32 46 3.49 47 3.67 48 3.85 49 4.04 50 4.23 51 4.43 52 4.63 53 4.83 54 5.04 55 5.25 56 5.46 57 5.67 58 5.89 59 6.10 60 6.32 61 6.54 62 6.76 63 6.97 64 7.19 65 7.40 66 7.61 67 7.82 68 8.02 69 8.23 70 8.42 71 8.61 72 8.80 73 8.97 74 9.15 75 9.31 76 9.47 77 9.61 78 9.75 79 9.88 80 10.00 81 10.11 82 10.21 83 10.30 84 10.38 85 10.44 86 10.50 87 10.54 88 10.57 89 10.59 90 10.59 91 10.59 92 10.57 93 10.54 94 10.50 95 10.44 96 10.38 97 10.30 98 10.21 99 10.11 100 10.00 101 9.88 102 9.75 103 9.61 104 9.47 105 9.31 106 9.15 107 8.97 108 8.80 109 8.61 110 8.42 111 8.23 112 8.02 113 7.82 114 7.61 115 7.40 116 7.19 117 6.97 118 6.76 119 6.54 120 6.32 121 6.10 122 5.89 123 5.67 124 5.46 125 5.25 126 5.04 127 4.83 128 4.63 129 4.43 130 4.23 131 4.04 132 3.85 133 3.67 134 3.49 135 3.32 136 3.15 137 2.98 138 2.83 139 2.67 140 2.52 141 2.38 142 2.25 143 2.11 144 1.99 145 1.87 146 1.75 147 1.64 148 1.54 149 1.44 150 1.34 151 1.25 152 1.17 153 1.08 154 1.01 155 .93 156 .87 157 .80 158 .74 159 .68 160 .63 161 .58 162 .53 163 .48 164 .44 165 .40 166 .36 167 .33 168 .30 169 .27 170 .24 171 .21 172 .18 173 .16 174 .13 175 .11 176 .09 177 .06 178 .04 179 .02 180 .00 LCUR = 30 PCT(LCUR) = .09 123

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APPENDIX G NUMERICAL EXAMPLE 5 |

PAGE 135

BEACH NOURISHMENT PROJECTION (Numerical Procedure) General Location: 6-iaynp le Wave Height, Ho (Fig. 22): L,o ft., Closure Depth, h. (Fig. 8): )17ft. Wave Period, T (Fig. 23): G sec., Berm Height, B: (9 ft. Wave Direction, ao: 0 O, Sand Diameter, D: 0-35" mm Deep Water Contour Orientation, 8o: 0 0), Transport Factor, K (Fig. 5): '7Longshore Axis Orientation, pA: 180 0, VFACT: ILO Grid Dimension, Ax: 0Oo ft Background Transport, QREF: 0 ft3/s Time Increment, At: f0a.0o sec IREF: qo IMAX: Io8 NTIMES: o__o No. of Structures, NS: 1 Structure Specificiation Background Erosion Structure Structure Structure Number Location, I Length (ft) z Erosion Rate, ER, (ft/yr) 1. go i0Z 0 0.0 00'_ 2 q_ _ooo .0 0 3 4 6 Equilibrated Beach Width Ayo Nourishment Specification I Range Ayo AN (Fig. 7) or From Profile: ft1/3 go to C,o i zo AF (Fig. 7): ft'/3 to_____ ____ l r Volume Per Unit Length: ft3/ft to _ros Ayo (Figs. 11 and 12): I 2. ft to to 125

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PLANFORM EVOLUTION OVER TIME (N/JETTY) NO EROSION (DISTORTED SCRLES) NO ER 400.0 350.0 ul LU L1L 300.0 Z 250.0 ULl C-J Z CE 200.0 -A B C -CO I. 0.0 150.0 LU S100.0 -100.0 SHORELINE LENGTH IN FEET .................... 5YEARS u-~ -^Figure G-1. Numerical Example 5, 1_12 ft Long Structure --10 YEARS -100.0 -----1 ---[ ---\ --------------| ---| ---i ---at North End of Project, Nourishment Length .20 YEARS 2 Miles, No Background Erosion. 30 YERS

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-o I-l I 0 C-1 z Nco o oD rn LA o *Hr =r (7 UF) Hii C--r I-tI -U to a) 0 -L) -P SI -0LLJ 'NO c| H.. L:J 0o >0 / LU .,-0 I I I i I I I o --o \ ) 0 • -, I I I I 2 I I I -00 0o .Ei. S o -I rz Ui 0r n I1 I oI 1 27 P i n W Fri S ---i i i i ]NI1]HOHS NO04 *l] N1 *ISJG 127 CV ~ ~ c 0 I) r -Pl 3NI~3DHS O~~ 'J NI'Is4

PAGE 138

INPUT FILE: DNRBS.INP (Example No. 5) EXAMPLE NO. 5 NO BACK. EROS. ONE STRUC. 2.00 6.0 90.0 90.0 180.0 500.0 86400.0 17.0 6.0 0.77 1.0 0.0 90 180 10950 1 80 112.0 0.0 0.0 90000. 0.0 100000. 0.0 49500. 3.0 90000. 3.0 100000. 2.0 140000. 2.0 80 100 80 112.0 81 112.0 82 112.0 83 112.0 84 112.0 85 112.0 86 112.0 87 112.0 88 112.0 89 112.0 90 112.0 91 112.0 92 112.0 93 112.0 94 112.0 95 112.0 96 112.0 97 112.0 98 112.0 99 112.0 100 112.0 128

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OUTPUT FILE: DNRBS.OUT (Example No. 5) EXAMPLE NO. 5 NO BACK. EROS. ONE STRUC. HO = 2.00 FT., T = 6.00 SEC., ALPO = 90.00 DEG., BTAO = 90.00 DEG., XMU = 180.00 DEG., DX = 500.00 FT., DT = 86400.00 SEC. HSTR = 17.00 FT., B = 6.00 FT., XK = .77 VFACT = 1.00 QBKREF = .00 FT.**3/SEC. IREF = 90, IMAX = 180, NTIMES = 10950, NS = 1 80 112.000 .00E+00 .00 .90E+05 .00 .10E+06 .00 .50E+05 3.00 .90E+05 3.00 .10E+06 2.00 .14E+06 2.00 BACKGROUND EROSION TRANSPORT RATES 1 .000 2 .000 3 .000 4 .000 5 .000 6 .000 7 .000 8 .000 9 .000 10 .000 11 .000 12 .000 13 .000 14 .000 15 .000 16 .000 17 .000 18 .000 19 .000 20 .000 21 .000 22 .000 23 .000 24 .000 25 .000 26 .000 27 .000 28 .000 29 .000 30 .000 31 .000 32 .000 33 .000 34 .000 35 .000 36 .000 37 .000 38 .000 39 .000 40 .000 41 .000 42 .000 43 .000 44 .000 45 .000 46 .000 47 .000 48 .000 49 .000 50 .000 51 .000 52 .000 53 .000 54 .000 55 .000 56 .000 57 .000 58 .000 59 .000 60 .000 61 .000 62 .000 63 .000 64 .000 65 .000 66 .000 67 .000 68 .000 69 .000 70 .000 71 .000 72 .000 73 .000 74 .000 75 .000 76 .000 77 .000 78 .000 79 .000 80 .000 81 .000 82 .000 83 .000 84 .000 85 .000 86 .000 87 .000 88 .000 89 .000 90 .000 91 .000 92 .000 93 .000 94 .000 95 .000 96 .000 97 .000 98 .000 99 .000 100 .000 101 .000 102 .000 103 .000 104 .000 105 .000 106 .000 107 .000 108 .000 109 .000 110 .000 111 .000 112 .000 113 .000 114 .000 115 .000 116 .000 117 .000 118 .000 119 .000 120 .000 121 .000 122 .000 123 .000 124 .000 125 .000 126 .000 127 .000 128 .000 129 .000 130 .000 131 .000 132 .000 133 .000 134 .000 135 .000 136 .000 137 .000 138 .000 139 .000 140 .000 141 .000 142 .000 143 .000 144 .000 145 .000 146 .000 147 .000 148 .000 149 .000 150 .000 151 .000 152 .000 153 .000 154 .000 155 .000 156 .000 157 .000 158 -nn0 159 .000 160 .000 161 .000 162 .000 163 129 0 164 .000 165 .000 166 .000 167 .000 168 0 169 .000 170 .000 171 .000 172 .000 173 0 174 .000 175 .000 176 .000 177 .000 178 .000 179 .000 180 .000 181 .000

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80 100 INITIAL SHORELINE (INCL. NOURISHMENT) POSITION 1 0. .00 2 500. .00 3 1000. .00 4 1500. .00 5 2000. .00 6 2500. .00 7 3000. .00 8 3500. .00 9 4000. .00 10 4500. .00 11 5000. .00 12 5500. .00 13 6000. .00 14 6500. .00 15 7000. .00 16 7500. .00 17 8000. .00 18 8500. .00 19 9000. .00 20 9500. .00 21 10000. .00 22 10500. .00 23 11000. .00 24 11500. .00 25 12000. .00 26 12500. .00 27 13000. .00 28 13500. .00 29 14000. .00 30 14500. .00 31 15000. .00 32 15500. .00 33 16000. .00 34 16500. .00 35 17000. .00 36 17500. .00 37 18000. .00 38 18500. .00 39 19000. .00 40 19500. .00 41 20000. .00 42 20500. .00 43 21000. .00 44 21500. .00 45 22000. .00 46 22500. .00 47 23000. .00 48 23500. .00 49 24000. .00 50 24500. .00 51 25000. .00 52 25500. .00 53 26000. .00 54 26500. .00 55 27000. .00 56 27500. .00 57 28000. .00 58 28500. .00 59 29000. .00 60 29500. .00 61 30000. .00 62 30500. .00 63 31000. .00 64 31500. .00 65 32000. .00 66 32500. .00 67 33000. .00 68 33500. .00 69 34000. .00 70 34500. .00 71 35000. .00 72 35500. .00 73 36000. .00 74 36500. .00 75 37000. .00 76 37500. .00 77 38000. .00 78 38500. .00 79 39000. .00 80 39500. 112.00 81 40000. 112.00 82 40500. 112.00 83 41000. 112.00 84 41500. 112.00 85 42000. 112.00 86 42500. 112.00 87 43000. 112.00 88 43500. 112.00 89 44000. 112.00 90 44500. 112.00 91 45000. 112.00 92 45500. 112.00 93 46000. 112.00 94 46500. 112.00 95 47000. 112.00 96 47500. 112.00 97 48000. 112.00 98 48500. 112.00 99 49000. 112.00 100 49500. 112.00 101 50000. .00 102 50500. .00 103 51000. .00 104 51500. .00 105 52000. .00 106 52500. .00 107 53000. .00 108 53500. .00 109 54000. .00 110 54500. .00 111 55000. .00 112 55500. .00 113 56000. .00 114 130 .00 115 57000. .00 116 .00 117 58000. .00 118 .00 119 59000. .00 120 :oZuu. .00 121 60000. .00 122 60500. .00

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123 61000. .00 124 61500. .00 125 62000. .00 126 62500. .00 127 63000. .00 128 63500. .00 129 64000. .00 130 64500. .00 131 65000. .00 132 65500. .00 133 66000. .00 134 66500. .00 135 67000. .00 136 67500. .00 137 68000. .00 138 68500. .00 139 69000. .00 140 69500. .00 141 70000. .00 142 70500. .00 143 71000. .00 144 71500. .00 145 72000. .00 146 72500. .00 147 73000. .00 148 73500. .00 149 74000. .00 150 74500. .00 151 75000. .00 152 75500. .00 153 76000. .00 154 76500. .00 155 77000. .00 156 77500. .00 157 78000. .00 158 78500. .00 159 79000. .00 160 79500. .00 161 80000. .00 162 80500. .00 163 81000. .00 164 81500. .00 165 82000. .00 166 82500. .00 167 83000. .00 168 83500. .00 169 84000. .00 170 84500. .00 171 85000. .00 172 85500. .00 173 86000. .00 174 86500. .00 175 87000. .00 176 87500. .00 177 88000. .00 178 88500. .00 179 89000. .00 180 89500. .00 100 116 .000 .000 112.000 .000 .000 .000 .000 TIME = 1 YEARS 1 .00 2 .00 3 .00 4 .00 5 .00 6 .00 7 .00 8 .00 9 .00 10 .00 11 .00 12 .00 13 .00 14 .00 15 .00 16 .00 17 .00 18 .00 19 .00 20 .00 21 .00 22 .00 23 .00 24 .00 25 .00 26 .00 27 .00 28 .00 29 .00 '30 .00 31 .00 32 .00 33 .00 34 .00 35 .00 36 .00 37 .00 38 .00 39 .00 40 .00 41 .00 42 .00 43 .00 44 .00 45 .00 46 .00 47 .00 48 .00 49 .00 50 .00 51 .00 52 .00 53 .00 54 .00 55 .00 56 .00 57 .00 58 .00 59 .00 60 .00 61 .00 62 .00 63 .00 64 .00 65 .00 66 .00 67 .00 68 .00 69 .00 70 .00 71 .00 72 .00 73 .00 74 .00 75 .00 76 .00 77 .00 78 .00 79 .00 80 111.99 81 111.98 82 111.96 83 111.93 84 111.87 85 111.77 86 111.60 87 111.31 88 110.87 89 110.18 90 109.16 91 107.69 92 105.66 93 102.93 94 99.38 95 94.94 96 89.55 97 83.25 98 76.13 99 68.36 100 60.17 101 51.83 102 43.64 103 35.87 104 28.75 105 22.45 106 17.06 107 12.62 108 9.07 109 6.34 110 4.31 111 2.84 112 1.82 113 1.13 114 .69 115 .40 116 .23 117 .13 118 .07 119 .04 120 .02 121 .01 122 .00 123 .00 124 .00 125 .00 126 .00 127 .00 128 .00 129 .00 130 .00 131 .00 132 .00 133 .00 134 .00 135 .00 136 .00 137 .00 138 .00 139 .00 140 .00 141 .00 142 .00 143 .00 144 .00 145 .00 146 .00 147 .00 148 .00 149 .00 150 .00 151 .00 152 .00 153 .00 154 .00 155 .00 156 .00 157 .00 158 .00 159 .00 160 .00 161 .00 162 .00 163 .00 164 .00 165 .00 166 .00 167 .00 168 .00 169 .00 170 .00 171 .00 172 .00 173 .00 174 .00 175 .00 176 .00 177 .00 178 .00 179 .00 180 .00 LCUR = 1 PCT(LCUR) = ^ LCUR = 2 PCT(LCUR) = 131 LCUR = 3 PCT(LCUR) = LCUR = 4 PCT(LCUR) = ________________________-ru t, -_______ c v rA D 0 _________________________

PAGE 142

1 .0U 2 .7U O .0 .UU 5.UU b .UU 7 .00 8 .00 9 .00 10 .00 11 .00 12 .00 13 .00 14 .00 15 .00 16 .00 17 .00 18 .00 19 .00 20 .00 21 .00 22 .00 23 .00 24 .00 25 .00 26 .00 27 .00 28 .00 29 .00 30 .00 31 .00 32 .00 33 .00 34 .00 35 .00 36 .00 37 .00 38 .00 39 .00 40 .00 41 .00 42 .00 43 .00 44 .00 45 .00 46 .00 47 .00 48 .00 49 .00 50 .00 51 .00 52 .00 53 .00 54 .00 55 .00 56 .00 57 .00 58 .00 59 .00 60 .00 61 .00 62 .00 63 .00 64 .00 65 .00 66 .00 67 .00 68 .00 69 .00 70 .00 71 .00 72 .00 73 .00 74 .00 75 .00 76 .00 77 .00 78 .00 79 .00 80 102.93 81 102.69 82 102.22 83 101.52 84 100.58 85 99.41 86 98.00 87 96.36 88 94.50 89 92.41 90 90.10 91 87.57 92 84.85 93 81.94 94 78.86 95 75.62 96 72.25 97 68.75 98 65.17 99 61.52 100 57.83 101 54.12 102 50.42 103 46.76 104 43.16 105 39.64 106 36.24 107 32.96 108 29.82 109 26.84 110 24.04 111 21.41 112 18.96 113 16.71 114 14.64 115 12.75 116 11.05 117 9.51 118 8.15 119 6.94 120 5.87 121 4.94 122 4.13 123 3.44 124 2.84 125 2.33 126 1.90 127 1.55 128 1.25 129 1.00 130 .80 131 .63 132 .50 133 .39 134 .30 135 .23 136 .18 137 .14 138 .10 139 .08 140 .06 141 .04 142 .03 143 .02 144 .02 145 .01 146 .01 147 .01 148 .00 149 .00 150 .00 151 .00 152 .00 153 .00 154 .00 155 .00 156 .00 157 .00 158 .00 159 .00 160 .00 161 .00 162 .00 163 .00 164 .00 165 .00 166 .00 167 .00 168 .00 169 .00 170 .00 171 .00 172 .00 173 .00 174 .00 175 .00 176 .00 177 .00 178 .00 179 .00 180 .00 LCUR = 5 PCT(LCUR) = .77 LCUR = 6 PCT(LCUR) = .75 LCUR = 7 PCT(LCUR) = .73 LCUR = 8 PCT(LCUR) = .71 LCUR = 9 PCT(LCUR) = .69 TIME = 10 YEARS 1 .00 2 .00 3 .00 4 .00 5 .00 6 .00 7 .00 8 .00 9 .00 10 .00 11 .00 12 .00 13 .00 14 .00 15 .00 16 .00 17 .00 18 .00 19 .00 20 .00 21 .00 22 .00 23 .00 24 .00 25 .00 26 .00 27 .00 28 .00 29 .00 30 .00 31 .00 32 .00 33 .00 34 .00 35 .00 36 .00 37 .00 38 .00 39 .00 40 .00 41 .00 42 .00 43 .00 44 .00 45 .00 46 .00 47 .00 48 .00 49 .00 50 .00 51 .00 52 .00 53 .00 54 .00 55 .00 56 .00 57 .00 58 .00 59 .00 60 .00 61 .00 62 .00 63 .00 64 .00 65 .00 66 .00 67 .00 68 .00 69 .00 70 .00 71 .00 72 .00 73 .00 74 .00 75 .00 76 .00 77 .00 78 .00 79 .00 80 87.69 81 87.51 82 87.16 83 86.63 84 85.92 85 85.05 86 84.02 87 82.82 88 81.48 89 79.98 90 78.35 91 76.59 92 74.70 93 72.71 94 70.61 95 68.42 96 66.15 97 63.81 98 61.41 99 58.97 100 56.49 101 53.99 102 51.47 103 48.95 104 46.45 105 43.96 106 41.50 107 39.08 108 36.71 109 34.39 110 32.14 111 29.95 112 27.84 113 25.81 114 23.86 115 22.00 116 20.23 117 18.55 118 16.96 119 15.47 120 14.07 121 12.75 122 11.53 123 10.40 124 9.35 125 8.38 126 7.49 127 6.67 128 5.93 129 5.25 130 4.64 131 4.08 132 3.58 133 3.14 134 2.74 135 2.38 136 2.07 137 1.79 138 1.54 139 1.32 140 1.13 141 .97 142 .82 143 .70 144 .59 145 .50 146 .42 147 .3" IAQ .29 149 .24 150 .20 151 .17 152 .14 153 .132 .09 155 .08 156 .06 157 .05 158 .04 159 ..03 161 .02 162 .02 163 .01 164 .01 165 .01 166 .01 167 .01 168 .00 169 .00 170 .00 171 .00 172 .00 173 .00 174 .00 1"75 nn 17( .nn 177 .nn 17A .00 179 .00 ISO 00

PAGE 143

LCUR = -U PLT(LCUR) = .bb LCUR = 11 PCT(LCUR) = .66 LCUR = 12 PCT(LCUR) = .65 LCUR = 13 PCT(LCUR) = .64 LCUR = 14 PCT(LCUR) = .62 LCUR = 15 PCT(LCUR) = .61 LCUR = 16 PCT(LCUR) = .60 LCUR = 17 PCT(LCUR) = .59 LCUR = 18 PCT(LCUR) = .58 LCUR = 19 PCT(LCUR) = .57 LCUR = 20 PCT(LCUR) = .56 LCUR = 21 PCT(LCUR) = .55 LCUR = 22 PCT(LCUR) = .54 LCUR = 23 PCT(LCUR) = .54 LCUR = 24 PCT(LCUR) = .53 LCUR = 25 PCT(LCUR) = .52 LCUR = 26 PCT(LCUR) = .51 LCUR = 27 PCT(LCUR) = .51 LCUR = 28 PCT(LCUR) = .50 LCUR = 29 PCT(LCUR) = .50 TIME = 30 YEARS 1 .00 2 .00 3 .00 4 .00 5 .00 6 .00 7 .00 8 .00 9 .00 10 .00 11 .00 12 .00 13 .00 14 .00 15 .00 16 .00 17 .00 18 .00 19 .00 20 .00 21 .00 22 .00 23 .00 24 .00 25 .00 26 .00 27 .00 28 .00 29 .00 30 .00 31 .00 32 .00 33 .00 34 .00 35 .00 36 .00 37 .00 38 .00 39 .00 40 .00 41 .00 42 .00 43 .00 44 .00 45 .00 46 .00 47 .00 48 .00 49 .00 50 .00 51 .00 52 .00 53 .00 54 .00 55 .00 56 .00 57 .00 58 .00 59 .00 60 .00 61 .00 62 .00 63 .00 64 .00 65 .00 66 .00 67 .00 68 .00 69 .00 70 .00 71 .00 72 ,00 73 .00 74 .00 75 .00 76 .00 77 .00 78 .00 79 .00 80 58.69 81 58.63 82 58.52 83 58.35 84 58.12 85 57.84 86 57.50 87 57.12 88 56.67 89 56.18 90 55.64 91 55.05 92 54.41 93 53.73 94 53.00 95 52.23 96 51.43 97 50.59 98 49.71 99 48.80 100 47.86 101 46.89 102 45.90 103 44.88 104 43.84 105 42.79 106 41.72 107 40.64 108 39.54 109 38.44 110 37.33 111 36.22 112 35.10 113 33.99 114 32.88 115 31.78 116 30.68 117 29.59 118 28.51 119 27.44 120 26.38 121 25.35 122 24.32 123 23.32 124 22.33 125 21.37 126 20.43 127 19.50 128 18.60 129 17.73 130 16.88 131 16.05 132 15.25 133 14.47 134 13.72 135 13.00 136 12.30 137 11.63 138 10.98 139 10.36 140 9.76 141 9.19 142 8.64 143 8.12 144 7.62 145 7.14 146 6.69 147 6.25 148 5.84 149 5.46 150 5.09 151 4.74 152 4.41 153 4.09 154 3.80 155 3.52 156 3.26 157 3.01 158 2.78 159 2.56 160 2.36 161 2.17 162 1.99 163 1.82 164 1.66 165 1.51 166 1.37 167 1.24 168 1.11 169 1.00 170 .88 171 .78 172 .68 173 .59 174 .49 175 .41 176 .32 177 .24 178 .16 179 .08 180 .00 LCUR = 30 PCT(LCUR) = .49 133

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APPENDIX H NUMERICAL EXAMPLE 6

PAGE 145

BEACH NOURISHMENT PROJECTION (Numerical Procedure) General Location: Ex, P YPJ~ Wave Height, Ho (Fig. 22): 1 .0 ft., Closure Depth, h. (Fig. 8): 1T ft. Wave Period, T (Fig. 23): &.o sec., Berm Height, B: 6 ft. Wave Direction, ao: qQ O, Sand Diameter, D: 6.5S mm Deep Water Contour Orientation, fo: q, 0, Transport Factor, K (Fig. 5): c7-T Longshore Axis Orientation, p: I 80 0, VFACT: l I_0 Grid Dimension, Az: foo ft Background Transport, QREF: o.0 ft3/s Time Increment, At: 8(bdoosec IREF: g0 IMAX: 8 o NTIMES: 9So No. of Structures, NS: 1 Structure Specificiation Background Erosion Structure Structure Structure Number Location, I Length (ft) z Erosion Rate, ER, (ft/yr) 1' 100 _i__o _____. _0 2 oo_____ _____ Ao 3 -_____ _______ ______ ______ 'A4 -cu 4i Equilibrated Beach Width Ayo Nourishment Specification -I Range Ayo AN (Fig. 7) or From Profile: ftl/s g to 0 // 2o AF (Fig. 7): ft'/3 to .Bc_ oc Volume Per Unit Length: ft3/ft to _____ ____ S: Ayo (Figs. 11 and 12): 1 /2o0 ft to____ to 135

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PLRNFORM EVOLUTION OVER TIME (W/JETTY) UNIFORM EROSION (DISTORTED SCALES) UNI ER 300.0 250.0 LUJ LLJ D B A C LL200.0 150.0 -V V LU CJ CEI 100.0 H50.0 50.0 ', -------100.0 i-i_~~~~--------_ ---1-^ -150.0 -200.0 0 10000 20000 30000 40000 50000 60000 70000 80000 0 TEARS SHORELINE LENGTH IN FEET ................. 5 YEARS Figure H-1. Numerical Example 6, 112 ft Long Structure at --------10 YEARS South End of Project, Nourishment Length = ----___-20 TEARS 2 Miles, Uniform Background Erosion = 2 ft/yr. ---30 YEARS

PAGE 147

Y (T) VERSUS TIME (N/JETTY) 2 MILE PLRNFORM WITH UNIFORM EROSION UNI ER 200.0 LIj 175.0 Z 1 150.0 LU nyC 125.0 cn 100.0 --Location A CD 75.0 -. -...... .Location B -50.0 -. "" S25.0 0 0.0 -. ...--------------.. ........ 0.0 C. -25.0 3 '-~-~^ Location D -50.0 --Location C -75.0 -100 .0 I I I I I I I I I I I I I I I 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 29500 TIME IN YERRS ................... 39500 Figure H-2. Numerical Example 6, Shoreline Position ---44500 Variation with Time at Locations Indicated and ---59500 Shown in Figure H-1.

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INPUT FILE: DNRBS.INP (Example No. 6) EXAMPLE NO. 6 NON-UNIF. BACK. EROS. ONE STRUC. 2.00 6.0 90.0 90.0 180.0 500.0 86400.0 17.0 6.0 0.77 1.0 0.0 90 180 10950 1 101 112.0 0.0 2.0 90000. 2.0 100000. 2.0 49500. 3.0 90000. 3.0 100000. 2.0 140000. 2.0 80 100 80 112.0 81 112.0 82 112.0 83 112.0 84 112.0 85 112.0 86 112.0 87 112.0 88 112.0 89 112.0 90 112.0 91 112.0 92 112.0 93 112.0 94 112.0 95 112.0 96 112.0 97 112.0 98 112.0 99 112.0 100 112.0 138

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OUTPUT FILE: DNRBS.OUT (Example No. 6) EXAMPLE NO. 6 NON-UNIF. BACK. EROS. ONE STRUC. HO = 2.00 FT., T = 6.00 SEC., ALPO = 90.00 DEG., BTAO = 90.00 DEG., XMU = 180.00 DEG., DX = 500.00 FT., DT = 86400.00 SEC. HSTR = 17.00 FT., B = 6.00 FT., XK = .77 VFACT = 1.00 QBKREF = .00 FT.**3/SEC. IREF = 90, IMAX = 180, NTIMES = 10950, NS = 1 101 112.000 .00E+00 2.00 .90E+05 2.00 .10E+06 2.00 .50E+05 3.00 .90E+05 3.00 .10E+06 2.00 .14E+06 2.00. BACKGROUND EROSION TRANSPORT RATES 1 -.065 2 -.064 3 -.063 4 -.063 5 -.062 6 -.061 7 -.061 8 -.060 9 -.059 10 -.058 11 -.058 12 -.057 13 -.056 14 -.055 15 -.055 16 -.054 17 -.053 18 -.053 19 -.052 20 -.051 21 -.050 22 -.050 23 -.049 24 -.048 25 -.047 26 -.047 27 -.046 28 -.045 29 -.044 30 -.044 31 -.043 32 -.042 33 -.042 34 -.041 35 -.040 36 -.039 37 -.039 38 -.038 39 -.037 40 -.036 41 -.036 42 -.035 43 -.034 44 -.034 45 -.033 46 -.032 47 -.031 48 -.031 49 -.030 50 -.029 51 -.028 52 -.028 53 -.027 54 -.026 55 -.026 56 -.025 57 -.024 58 -.023 59 -.023 60 -.022 61 -.021 62 -.020 63 -.020 64 -.019 65 -.018 66 -.018 67 -.017 68 -.016 69 -.015 70 -.015 71 -.014 72 -.013 73 -.012 74 -.012 75 -.011 76 -.010 77 -.009 78 -.009 79 -.008 80 -.007 81 -.007 82 -.006 83 -.005 84 -.004 85 -.004 86 -.003 87 -.002 88 -.001 89 -.001 90 .000 91 .001 92 .001 93 .002 94 .003 95 .004 96 .004 97 .005 98 .006 99 .007 100 .007 101 .008 102 .009 103 .009 104 .010 105 .011 106 .012 107 .012 108 .013 109 .014 110 .015 111 .015 112 .016 113 .017 114 .018 115 .018 116 .019 117 .020 118 .020 119 .021 120 .022 121 .023 122 .023 123 .024 124 .025 125 .026 126 .026 127 .027 128 .028 129 .028 130 .029 131 .030 132 .031 133 .031 134 .032 135 .033 136 .034 137 .034 138 .035 139 .036 140 .036 141 .037 142 .038 143 .039 144 .039 145 .040 146 .041 147 .042 148 .042 149 .043 150 .044 151 .044 152 .045 153 .046 154 .047 155 .047 156 .048 157 .049 158 .050 159 .050 160 .051 161 .052 162 .053 163 .053 164 .054 165 .055 166 .055 167 .056 168 ^ 7 169 .058 170 .058 171 .059 172 .060 172 139 74 .061 175 .062 176 .063 177 .063 176 .. -79 .065 180 .066 181 .066

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80 100 INITIAL SHORELINE (INCL. NOURISHMENT) POSITION 1 0. .00 2 500. .00 3 1000. .00 4 1500. .00 5 2000. .00 6 2500. .00 7 3000. .00 8 3500. .00 9 4000. .00 10 4500. .00 11 5000. .00 12 5500. .00 13 6000. .00 14 6500. .00 15 7000. .00 16 7500. .00 17 8000. .00 18 8500. .00 19 9000. .00 20 9500. .00 21 10000. .00 22 10500. .00 23 11000. .00 24 11500. .00 25 12000. .00 26 12500. .00 27 13000. .00 28 13500. .00 29 14000. .00 30 14500. .00 31 15000. .00 32 15500. .00 33 16000. .00 34 16500. .00 35 17000. .00 36 17500. .00 37 18000. .00 38 18500. .00 39 19000. .00 40 19500. .00 41 20000. .00 42 20500. .00 43 21000. .00 44 21500. .00 45 22000. .00 46 22500. .00 47 23000. .00 48 23500. .00 49 24000. .00 50 24500. .00 51 25000. .00 52 25500. .00 53 26000. .00 54 26500. .00 55 27000. .00 56 27500. .00 57 28000. .00 58 28500. .00 59 29000. .00 60 29500. .00 61 30000. .00 62 30500. .00 63 31000. .00 64 31500. .00 65 32000. .00 66 32500. .00 67 33000. .00 68 33500. .00 69 34000. .00 70 34500. .00 71 35000. .00 72 35500. .00 73 36000. .00 74 36500. .00 75 37000. .00 76 37500. .00 77 38000. .00 78 38500. .00 79 39000. .00 80 39500. 112.00 81 40000. 112.00 82 40500. 112.00 83 41000. 112.00 84 41500. 112.00 85 42000. 112.00 86 42500. 112.00 87 43000. 112.00 88 43500. 112.00 89 44000. 112.00 90 44500. 112.00 91 45000. 112.00 92 45500. 112.00 93 46000. 112.00 94 46500. 112.00 95 47000. 112.00 96 47500. 112.00 97 48000. 112.00 98 48500. 112.00 99 49000. 112.00 100 49500. 112.00 101 50000. .00 102 50500. .00 103 51000. .00 104 51500. .00 105 52000. .00 106 52500. .00 107 53000. .00 108 53500. .00 109 54000. .00 110 54500. .00 111 55000. .00 112 snn. .00 113 56000. .00 114 140 .00 115 57000. .00 116 ..00 117 58000. .00 118 ..00 119 59000. .00 120 syuu. .00 121 60000. .00 122 60500. .00

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ZJ125 620. .00 126 62500i ..0 125 62000. .00 126 62500. .00 127 63000. .00 128 63500. .00 129 64000. .00 130 64500. .00 131 65000. .00 132 65500. .00 133 66000. .00 134 66500. .00 135 67000. .00 136 67500. .00 137 68000. .00 138 68500. .00 139 69000. .00 140 69500. .00 141 70000. .00 142 70500. .00 143 71000. .00 144 71500. .00 145 72000. .00 146 72500. .00 147 73000. .00 148 73500. .00 149 74000. .00 150 74500. .00 151 75000. .00 152 75500. .00 153 76000. .00 154 76500. .00 155 77000. .00 156 77500. .00 157 78000. .00 158 78500. .00 159 79000. .00 160 79500. .00 161 80000. .00 162 80500. .00 163 81000. .00 164 81500. .00 165 82000. .00 166 82500. .00 167 83000. .00 168 83500. .00 169 84000. .00 170 84500. .00 171 85000. .00 172 85500. .00 173 86000. .00 174 86500. .00 175 87000. .00 176 87500. .00 177 88000. .00 178 88500. .00 179 89000. .00 180 89500. .00 100 116 .000 .019 112.000 -.542 -.542 .019 .000 TIME = 1 YEARS 1 -2.00 2 -2.00 3 -2.00 4 -2.00 5 -2.00 6 -2.00 7 -2.00 8 -2.00 9 -2.00 10 -2.00 11 -2.00 12 -2.00 13 -2.00 14 -2.00 15 -2.00 16 -2.00 17 -2.00 18 -2.00 19 -2.00 20 -2.00 21 -2.00 22 -2.00 23 -2.00 24 -2.00 25 -2.00 26 -2.00 27 -2.00 28 -2.00 29 -2.00 30 -2.00 31 -2.00 32 -2.00 33 -2.00 34 -2.00 35 -2.00 36 -2.00 37 -2.00 38 -2.00 39 -2.00 40 -2.00 41 -2.00 42 -2.00 43 -2.00 44 -2.00 45 -2.00 46 -2.00 47 -2.00 48 -2.00 49 -2.00 50 -2.00 51 -2.00 52 -2.00 53 -2.00 54 -2.00 55 -2.00 56 -2.00 57 -2.00 58 -2.00 59 -1.99 60 -1.98 61 -1.96 62 -1.93 63 -1.87 64 -1.77 65 -1.60 66 -1.31 67 -.87 68 -.18 69 .84 70 2.31 71 4.34 72 7.07 73 10.62 74 15.06 75 20.45 76 26.75 77 33.87 78 41.64 79 49.83 80 58.17 81 66.36 82 74.13 83 81.26 84 87.56 85 92.94 86 97.39 87 100.93 88 103.67 89 105.71 90 107.19 91 108.24 92 108.96 93 109.47 94 109.83 95 110.13 96 110.40 97 110.69 98 111.04 99 111.46 100 112.02 101 -4.03 102 -3.48 103 -3.07 104 -2.76 105 -2.53 106 -2.36 107 -2.24 108 -2.15 109 -2.10 110 -2.06 111 -2.04 112 -2.02 113 -2.01 114 -2.01 115 -2.00 116 -2.00 117 -2.00 118 -2.00 119 -2.00 120 -2.00 121 -2.00 122 -2.00 123 -2.00 124 -2.00 125 -2.00 126 -2.00 127 -2.00 128 -2.00 129 -2.00 130 -2.00 131 -2.00 132 -2.00 133 -2.00 134 -2.00 135 -2.00 136 -2.00 137 -2.00 138 -2.00 139 -2.00 140 -2.00 141 -2.00 142 -2.00 143 -2.00 144 -2.00 145 -2.00 146 -2.00 147 -2.00 148 -2.00 149 -2.00 150 -2.00 151 -2.00 152 -2.00 153 -2.00 154 -2.00 155 -2.00 156 -2.00 157 -2.00 158 -2.00 159 -2.00 160 -2.00 161 -2.00 162 -2.00 163 -2.00 164 -2.00 165 -2.00 166 -2.00 167 -2.00 168 -2.00 169 -2.00 170 -2.00 171 -2.00 170 -2.00 173 -2.00 174 -2.00 175 -2.00 176 -2.00 177 -2.0 141 -2.00 179 -2.00 180 -2.00 LCUR = 1 PCT(LCUR) = LCUR = 2 PCT(LCUR) = LCUR = 3 PCT(LCUR) = ., LCUR = 4 PCT(LCUR) = .75 TTME = 5 YEARS

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1 -10.00 2 -1U. 00 3 -U uu 4 -IU.UU 5 --u.UU b --U.UU 7 -10.00 8 -10.00 9 -10.00 10 -10.00 11 -10.00 12 -10.00 13 -10.00 14 -10.00 15 -10.00 16 -10.00 17 -10.00 18 -10.00 19 -10.00 20 -10.00 21 -10.00 22 -10.00 23 -10.00 24 -10.00 25 -10.00 26 -10.00 27 -10.00 28 -10.00 29 -10.00 30 -10.00 31 -10.00 32 -10.00 33 -9.99 34 -9.99 35 -9.99 36 -9.98 37 -9.98 38 -9.97 39 -9.96 40 -9.94 41 -9.92 42 -9.90 43 -9.86 44 -9.82 45 -9.77 46 -9.70 47 -9.61 48 -9.50 49 -9.37 50 -9.20 51 -9.00 52 -8.75 53 -8.45 54 -8.10 55 -7.67 56 -7.16 57 -6.56 58 -5.87 59 -5.06 60 -4.13 61 -3.06 62 -1.85 63 -.48 64 1.05 65 2.76 66 4.65 67 6.72 68 8.98 69 11.43 70 14.06 71 16.88 72 19.87 73 23.02 74 26.32 75 29.75 76 33.29 77 36.93 78 40.64 79 44.40 80 48.18 81 51.97 82 55.73 83 59.45 84 63.11 85 66.68 86 70.15 87 73.51 88 76.75 89 79.86 90 82.82 91 85.65 92 88.33 93 90.88 94 93.28 95 95.54 96 97.68 97 99.68 98 101.56 99 103.32 100 104.96 101 -22.03 102 -20.62 103 -19.34 104 -18.16 105 -17.09 106 -16.13 107 -15.28 108 -14.51 109 -13.84 110 -13.25 111 -12.73 112 -12.28 113 -11.90 114 -11.57 115 -11.29 116 -11.06 117 -10.86 118 -10.70 119 -10.56 120 -10.45 121 -10.36 122 -10.28 123 -10.22 124 -10.17 125 -10.14 126 -10.11 127 -10.08 128 -10.06 129 -10.05 130 -10.04 131 -10.03 132 -10.02 133 -10.02 134 -10.01 135 -10.01 136 -10.01 137 -10.00 138 -10.00 139 -10.00 140 -10.00 141 -10.00 142 -10.00 143 -10.00 144 -10.00 145 -10.00 146 -10.00 147 -10.00 148 -10.00 149 -10.00 150 -10.00 151 -10.00 152 -10.00 153 -10.00 154 -10.00 155 -10.00 156 -10.00 157 -10.00 158 -10.00 159 -10.00 160 -10.00 161 -10.00 162 -10.00 163 -10.00 164 -10.00 165 -10.00 166 -10.00 167 -10.00 168 -10.00 169 -10.00 170 -10.00 171 -10.00 172 -10.00 173 -10.00 174 -10.00 175 -10.00 176 -10.00 177 -10.00 178 -10.00 179 -10.00 180 -10.00 LCUR = 5 PCT(LCUR) = .72 LCUR = 6 PCT(LCUR) = .69 LCUR = 7 PCT(LCUR) = .66 LCUR = 8 PCT(LCUR) = .63 LCUR = 9 PCT(LCUR) = .60 TIME = 10 YEARS 1 -20.00 2 -20.00 3 -20.00 4 -20.00 5 -20.00 6 -20.00 7 -20.00 8 -20.00 9 -20.00 10 -20.00 11 -20.00 12 -20.00 13 -19.99 14 -19.99 15 -19.99 16 -19.99 17 -19.99 18 -19.98 19 -19.98 20 -19.97 21 -19.97 22 -19.96 23 -19.95 24 -19.94 25 -19.92 26 -19.91 27 -19.89 28 -19.86 29 -19.83 30 -19.80 31 -19.76 32 -19.71 33 -19.65 34 -19.58 35 -19.50 36 -19.41 37 -19.30 38 -19.18 39 -19.03 40 -18.87 41 -18.68 42 -18.46 43 -18.21 44 -17.93 45 -17.61 46 -17.26 47 -16.86 48 -16.41 49 -15.91 50 -15.35 51 -14.73 52 -14.05 53 -13.31 54 -12.48 55 -11.59 56 -10.61 57 -9.55 58 -8.40 59 -7.17 60 -5.84 61 -4.42 62 -2.90 63 -1.28 64 .43 65 2.24 66 4.14 67 6.14 68 8.23 69 10.41 70 12.68 71 15.03 72 17.45 73 19.95 74 22.51 75 25.13 76 27.79 77 30.51 78 33.25 79 36.03 80 38.82 81 41.62 82 44.42 83 47.21 84 49.99 85 52.74 86 55.46 87 58.14 88 60.77 89 63.34 90 65.85 91 68.29 92 70.65 93 72.94 94 75.14 95 77.25 96 79.27 97 81.19 98 83.01 99 84.74 100 86.36 101 -38.67 102 -37.23 103 -35.86 104 -34.56 105 -33.34 106 -32.20 107 -31.12 108 -30.12 109 -29.18 110 -28.31 111 -27.50 112 -26.75 113 -26.06 114 -25.43 115 -24.85 116 -24.32 117 -23.84 118 -23.40 119 -23.01 120 -22.65 121 -22.33 122 -22.04 123 -21.78 124 -21.55 125 -21.35 126 -21.17 127 -21.01 128 -20.87 129 -20.75 130 -20.64 131 -20.54 132 -20.46 133 -20.39 134 -20.33 135 -20.28 136 -20.24 137 -20.20 138 -20.17 139 -20.14 140 -20.11 141 -20.0 142 -20.08 143 -20.06 144 -20.05 145 -20.04 146 -20.04 147 -20.0 -20.02 149 -20.02 150 -20.02 151 -20.01 152 -20.01 153 -20.C -20.01 155 -20.01 156 -20.00 157 -20.00 158 -20.00 159 -20.0 -20.00 161 -20.00 162 -20.00 163 -20.00 164 -20.00 165 -20.00 166 -20.00 167 -20.00 168 -20.00 169 -20.00 170 -20.00 171 -20.00 172 -20.00 173 -20.00 174 -20.00 175 -? 0nn 17F -0n 0n 177 -00nn 178 -20.00 179 -20.00 180 -20.00

PAGE 153

LCUR= U PC(Ui ) = LCUR = 11 PCT(LCUR) = .55 LCUR = 12 PCT(LCUR) = .53 LCUR = 13 PCT(LCUR) = .50 LCUR = 14 PCT(LCUR) = .48 LCUR = 15 PCT(LCUR) = .46 LCUR = 16 PCT(LCUR) = .43 LCUR = 17 PCT(LCUR) = .41 LCUR = 18 PCT(LCUR) = .39 LCUR = 19 PCT(LCUR) = .37 LCUR = 20 PCT(LCUR) = .35 LCUR = 21 PCT(LCUR) = .33 LCUR = 22 PCT(LCUR) = .31 LCUR = 23 PCT(LCUR) = .29 LCUR = 24 PCT(LCUR) = .27 LCUR = 25 PCT(LCUR) = .25 LCUR = 26 PCT(LCUR) = .23 LCUR = 27 PCT(LCUR) = .21 LCUR = 28 PCT(LCUR) = .19: LCUR = 29 PCT(LCUR) = .17 TIME = 30 YEARS 1 -59.99 2 -59.91 3 -59.82 4 -59.73 5 -59.64 6 -59.54 7 -59.44 8 -59.34 9 -59.24 10 -59.13 11 -59.01 12 -58.89 13 -58.76 14 -58.62 15 -58.47 16 -58.31 17 -58.15 18 -57.97 19 -57.78 20 -57.58 21 -57.37 22 -57.14 23 -56.89 24 -56.63 25 -56.36 26 -56.07 27 -55.75 28 -55.42 29 -55.07 30 -54.70 31 -54.31 32 -53.89 33 -53.46 34 -52.99 35 -52.50 36 -51.99 37 -51.45 38 -50.88 39 -50.29 40 -49.66 41 -49.01 42 -48.32 43 -47.60 44 -46.86 45 -46.08 46 -45.27 47 -44.42 48 -43.54 49 -42.63 50 -41.69 51 -40.71 52 -39.70 53 -38.65 54 -37.57 55 -36.46 56 -35.31 57 -34.13 58 -32.92 59 -31.67 60 -30.40 61 -29.09 62 -27.75 63 -26.39 64 -24.99 65 -23.57 66 -22.12 67 -20.64 68 -19.15 69 -17.62 70 -16.08 71 -14.52 72 -12.93 73 -11.34 74 -9.72 75 -8.09 76 -6.45 77 -4.79 78 -3.13 79 -1.46 80 .22 81 1.91 82 3.59 83 5.28 84 6.97 85 8.66 86 10.34 87 12.02 88 13.70 89 15.37 90 17.03 91 18.68 92 20.32 93 21.95 94 23.57 95 25.18 96 26.77 97 28.35 98 29.91 99 31.46 100 33.00 101 -94.31 102 -92.83 103 -91.39 104 -90.00 105 -88.65 106 -87.33 107 -86.06 108 -84.83 109 -83.65 110 -82.50 111 -81.39 112 -80.32 113 -79.29 114 -78.29 115 -77.34 116 -76.42 117 -75.54 118 -74.69 119 -73.88 120 -73.11 121 -72.36 122 -71.65 123 -70.97 124 -70.33 125 -69.71 126 -69.12 127 -68.56 128 -68.03 129 -67.52 130 -67.04 131 -66.59 132 -66.16 133 -65.75 134 -65.36 135 -65.00 136 -64.66 137 -64.33 138 -64.03 139 -63.74 140 -63.47 141 -63.22 142 -62.98 143 -62.76 144 -62.55 145 -62.36 146 -62.17 147 -62.00 148 -61.85 149 -61.70 150 -61.56 151 -61.43 152 -61.32 153 -61.21 154 -61.10 155 -61.01 156 -60.92 157 -60.84 158 -60.77 159 -60.70 160 -60.63 161 -60.57 162 -60.52 163 -60.47 164 -60.42 165 -60.38 166 -60.34 167 -60.31 168 -60.27 169 -60.24 170 -60.21 171 -60.18 172 -60.16 173 -60.14 174 -60.11 175 -60.09 176 -60.07 177 -60.05 178 -60.03 179 -60.01 180 -59.99 LCUR = 30 PCT(LCUR) = .15 143

PAGE 154

APPENDIX I NUMERICAL EXAMPLE 7

PAGE 155

BEACH NOURISHMENT PROJECTION (Numerical Procedure) General Location: ? m(P7 Wave Height, Ho (Fig. 22): 2 "o ft., Closure Depth, h. (Fig. 8): 17 ft. Wave Period, T (Fig. 23): bo sec., Berm Height, B: ft. Wave Direction, ao: so: ", Sand Diameter, D: 03. mm Deep Water Contour Orientation, Po: 90 O, Transport Factor, K (Fig. 5): 0-77 Longshore Axis Orientation, Xp: /8c o, VFACT: I,0o Grid Dimension, Ax: 50.0 ft Background Transport, QREF: O0D ft /s Time Increment, At: 8Gt4oo sec IREF: q o IMAX: 18g NTIMES: oqt5o No. of Structures, NS: I Structure Specificiation -Background Erosion Structure Structure Structure Number Location, I Length (ft) z Erosion Rate, ER, (ft/yr) / 1. \00' 1__> ._0 .1 2 3_9 soo Too 3 5 -o00o 3 4 0 ooo 0. 3 0 5 6 Equilibrated Beach Width Ayo Nourishment Specification I Range Ayo -.. AN (Fig. 7) or From Profile: ft1/3 8o to o _0 ;/ 2. .Sru+c+r AF (Fig. 7): ft1/3 _to Volume Per Unit Length: ft /ft to Ayo (Figs. 11 and 12): J / 2, ft to to 145

PAGE 156

PLRNFORM EVOLUTION OVER TIME (N/JETTY) NON-UNIF. EROSION (DISTORTED SCALES) NON-UN 200.0 D B A C 150.0 j LL100.0 50.0 -j~ ----(__) -n o .o --.. .-...-.---... ... ... .. --------..----50.0 S/ ---------------------( -100.0 ---/E LL--150.0 -200.0 -250.0 -300.0 0 10000 20000 30000 40000 50000 60000 70000 80000 0 YEARS SHORELINE LENGTH IN FEET .................. 5YEARS Figure I-1. Numerical Example 7, 112 ft Long Structure at -------10 YEARS South End of Project, Nourishment Length = ---20 YEARS 2 Miles, Variable Background Erosion. ---30 YEARS

PAGE 157

Y (T) VERSUS TIME (N/JETTY) 2 MILE PLRNFORM WITH NON-UNIF. EROSION NON-UN 150.0 L 125.0 1. ---Location A 5 100.0 f-r C 75.0 -----------------------------------------S. -Location B 50.0 ----------------Jot 50.0 25.0 LLLocation D ILL. Z -25.0 1" ^ -Location C S-50.0 t"' -75.0 -"-100.0 -" -125.0 -150.0I I I I I I I I I I I I 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 29500 TIME IN YEARS ....................39500 Figure 1-2. Numerical Example 7, Shoreline Postiion ----4500 Variation with Time at Locations Indicated and ---------59500 Shown in Figure I-1.

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INPUT FILE: DNRBS.INP (Example No. 7) EXAMPLE NO. 7 NON-UNIF. BACK. EROS. ONE STRUC. WAVE ANG. 2.00 6.0 80.0 90.0 180.0 500.0 86400.0 17.0 6.0 0.77 1.0 0.0 90 180 10950 1 101 112.0 0.0 1.0 39500. 1.0 44500. 2.0 49500. 3.0 90000. 3.0 100000. 2.0 140000. 2.0 80 100 80 112.0 81 112.0 82 112.0 83 112.0 84 112.0 85 112.0 86 112.0 87 112.0 88 112.0 89 112.0 90 112.0 91 112.0 92 112.0 93 112.0 94 112.0 95 112.0 96 112.0 97 112.0 98 112.0 99 112.0 100 112.0 148

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OUTPUT FILE: DNRBS.OUT (Example No. 7) EXAMPLE NO. 7 NON-UNIF. BACK. EROS. ONE STRUC. WAVE ANG. HO = 2.00 FT., T = 6.00 SEC., ALPO = 80.00 DEG., BTAO = 90.00 DEG., XMU = 180.00 DEG., DX = 500.00 FT., DT = 86400.00 SEC. HSTR = 17.00 FT., B = 6.00 FT., XK = .77 VFACT = 1.00 QBKREF = .00 FT.**3/SEC. IREF = 90, IMAX = 180, NTIMES = 10950, NS = 1 101 112.000 .00E+00 1.00 .40E+05 1.00 .45E+05 2.00 .50E+05 3.00 .90E+05 3.00 .10E+06 2.00 .14E+06 2.00 BACKGROUND EROSION TRANSPORT RATES 1 -.034 2 -.034 3 -.033 4 -.033 5 -.033 6 -.032 7 -.032 8 -.032 9 -.031 10 -.031 11 -.030 12 -.030 13 -.030 14 -.029 15 -.029 16 -.029 17 -.028 18 -.028 19 -.028 20 -.027 21 -.027 22 -.026 23 -.026 24 -.026 25 -.025 26 -.025 27 -.025 28 -.024 29 -.024 30 -.024 31 -.023 32 -.023 33 -.022 34 -.022 35 -.022 36 -.021 37 -.021 38 -.021 39 -.020 40 -.020 41 -.020 42 -.019 43 -.019 44 -.018 45 -.018 46 -.018 47 -.017 48 -.017 49 -.017 50 -.016 51 -.016 52 -.015 53 -.015 54 -.015 55 -.014 56 -.014 57 -.014 58 -.013 59 -.013 60 -.013 61 -.012 62 -.012 63 -.011 64 -.011 65 -.011 66 -.010 67 -.010 68 -.010 69 -.009 70 -.009 71 -.009 72 -.008 73 -.008 74 -.007 75 -.007 76 -.007 77 -.006 78 -.006 79 -.006 80 -.005 81 -.005 82 -.005 83 -.004 84 -.004 85 -.003 86 -.003 87 -.002 88 -.001 89 -.001 90 .000 91 .001 92 .001 93 .002 94 .003 95 .004 96 .005 97 .006 98 .007 99 .008 100 .009 101 .010 102 .011 103 .012 104 .013 105 .014 106 .015 107 .017 108 .018 109 .019 110 .020 111 .021 112 .022 113 .023 114 .024 115 .025 116 .026 117 .028 118 .029 119 .030 120 .031 121 .032 122 .033 123 .034 124 .035 125 .036 126 .037 127 .038 12A -040 129 .041 130 .042 131 .043 132 .044 13 )45 134 .046 135 .047 136 .048 137 .049 13. 149 )51 139 .052 140 .053 141 .054 142 .055 14. )56 144 .057 145 .058 146. .059 147 .060 141 161 149 .063 150 .064 151 .065 152 .066 15: 167 154 .068 155 .069 156 .070 157 .071 15k '72 159 .073 160 .075 71 ;n7 162 .077 163 .078 164 .079 165 .080

PAGE 160

171 .087 172 .088 173 .089 174 .090 175 .091 176 .092 177 .093 178 .094 179 .095 180 .096 181 .098 80 100 INITIAL SHORELINE (INCL. NOURISHMENT) POSITION 1 0. .00 2 500. .00 3 1000. .00 4 1500. .00 5 2000. .00 6 2500. .00 7 3000. .00 8 3500. .00 9 4000. .00 10 4500. .00 11 5000. .00 12 5500. .00 13 6000. .00 14 6500. .00 15 7000. .00 16 7500. .00 17 8000. .00 18 8500. .00 19 9000. .00 20 9500. .00 21 10000. .00 22 10500. .00 23 11000. .00 24 11500. .00 25 12000. .00 26 12500. .00 27 13000. .00 28 13500. .00 29 14000. .00 30 14500. .00 31 15000. .00 32 15500. .00 33 16000. .00 34 16500. .00 35 17000. .00 36 17500. .00 37 18000. .00 38 18500. .00 39 19000. .00 40 19500. .00 41 20000. .00 42 20500. .00 43 21000. .00 44 21500. .00 45 22000. .00 46 22500. .00 47 23000. .00 48 23500. .00 49 24000. .00 50 24500. .00 51 25000. .00 52 25500. .00 53 26000. .00 54 26500. .00 55 27000. .00 56 27500. .00 57 28000. .00 58 28500. .00 59 29000. .00 60 29500. .00 61 30000. .00 62 30500. .00 63 31000. .00 64 31500. .00 65 32000. .00 66 32500. .00 67 33000. .00 68 33500. .00 69 34000. .00 70 34500. .00 71 35000. .00 72 35500. .00 73 36000. .00 74 36500. .00 75 37000. .00 76 37500. .00 77 38000. .00 78 38500. .00 79 39000. .00 80 39500. 112.00 81 40000. 112.00 82 40500. 112.00 83 41000. 112.00 84 41500. 112.00 85 42000. 112.00 86 42500. 112.00 87 43000. 112.00 88 43500. 112.00 89 44000. 112.00 90 44500. 112.00 91 45000. 112.00 92 45500. 112.00 93 46000. 112.00 94 46500. 112.00 95 47000. 112.00 96 47500. 112.00 97 48000. 112.00 98 48500. 112.00 99 49000. 112.00 100 .112.00 101 50000. .00 102 1 ..00 103 150. .00 104 103 51000. .00 104 .00 105 52000. .00 106 ..00 107 53000. .00 108 ..00 109 54000. .00 110 ..00 111 55000. .00 112 55500. .00 1 14 9; A ()nnn ____ )nn 114 sf) r tnr n -C

PAGE 161

117 58000. .00 118 58500. .00 119 59000. .00 120 59500. .00 121 60000. .00 122 60500. .00 123 61000. .00 124 61500. .00 125 62000. .00 126 62500. .00 127 63000. .00 128 63500. .00 129 64000. .00 130 64500. .00 131 65000. .00 132 65500. .00 133 66000. .00 134 66500. .00 135 67000. .00 136 67500. .00 137 68000. .00 138 68500. .00 139 69000. .00 140 69500. .00 141 70000. .00 142 70500. .00 143 71000. .00 144 71500. .00 145 72000. .00 146 72500. .00 147 73000. .00 148 73500. .00 149 74000. .00 150 74500. .00 151 75000. .00 152 75500. .00 153 76000. .00 154 76500. .00 155 77000. .00 156 77500. .00 157 78000. .00 158 78500. .00 159 79000. .00 160 79500. .00 161 80000. .00 162 80500. .00 163 81000. .00 164 81500. .00 165 82000. .00 166 82500. .00 167 83000. .00 168 83500. .00 169 84000. .00 170 84500. .00 171 85000. .00 172 85500. .00 173 86000. .00 174 86500. .00 175 87000. .00 176 87500. .00 177 88000. .00 178 88500. .00 179 89000. .00 180 89500. .00 100 116 .309 .026 112.000 -.814 -.814 .026 .309 TIME = 1 YEARS 1 -1.00 2 -1.00 3 -1.00 4 -1.00 5 -1.00 6 -1.00 7 -1.00 8 -1.00 9 -1.00 10 -1.00 11 -1.00 12 -1.00 13 -1.00 14 -1.00 15 -1.00 16 -1.00 17 -1.00 18 -1.00 19 -1.00 20 -1.00 21 -1.00 22 -1.00 23 -1.00 24 -1.00 25 -1.00 26 -1.00 27 -1.00 28 -1.00 29 -1.00 30 -1.00 31 -1.00 32 -1.00 33 -1.00 34 -1.00 35 -1.00 36 -1.00 37 -1.00 38 -1.00 39 -1.00 40 -1.00 41 -1.00 42 -1.00 43 -1.00 44 -1.00 45 -1.00 46 -1.00 47 -1.00 48 -1.00 49 -1.00 50 -1.00 51 -1.00 52 -1.00 53 -1.00 54 -1.00 55 -1.00 56 -1.00 57 -1.00 58 -1.00 59 -.99 60 -.98 61 -.97 62 -.94 63 -.89 64 -.79 65 -.63 66 -.37 67 .05 68 .71 69 1.69 70 3.11 71 5.10 72 7.79 73 11.30 74 15.73 75 21.11 76 27.43 77 34.60 78 42.43 79 50.68 80 59.08 81 67.31 82 75.09 83 82.19 84 88.45 85 93.75 86 98.09 87 101.52 88 104.13 89 106.04 90 107.40 91 108.33 92 108.97 93 109.41 94 109.74 95 110.03 96 110.35 97 110.73 98 111.22 99 111.96 100 112.82 101 -6.59 102 -5.72 103 -4.94 104 -4.41 105 -4.01 106 -3.71 107 -3.49 108 -3.33 109 -3.22 110 -3.14 111 -3.09 112 -3.05 113 -3.03 114 -3.02 115 -3.01 116 -3.01 117 -3.00 118 -3.00 119 -3.00 120 -3.00 121 -3.00 122 -3.00 123 -3.00 124 -3.00 125 -3.00 126 -3.00 127 -3.00 128 -3.00 129 -3.00 130 -3.00 131 -3.00 132 -3.00 133 -3.00 134 -3.00 135 -3. -3.00 137 -3.00 138 -3.00 139 -3.00 140 -3.00 141 -3.' -3.00 143 -3.00 144 -3.00 145 -3.00 146 -3.00 147 -3. 151 -3.00 149 -3.00 150 -3.00 151 -3.00 152 -3.00 153 -3. -3.00 155 -3.00 156 -3.00 157 -3.00 158 -3.00 159 -3. -3.00 161 -3.00 162 -3.00 163 -3.00 164 -3.00 165 -3. -3.00 167 -3.00 168 -3.00 169 -3.00 170 -3.00 171 -3.uu I, -3.00 173 -3.00 174 -3.00 175 -3.00 176 -3.00 177 -3.00 178 -3.00 179 -3.00 180 -3.00 T.TTR = 1 PrNT LTTTPR = .89

PAGE 162

LCUR = 3 PCT(LCUR) = .80 LCUR = 3 PCT(LCUR) = .80 LCUR = 4 PCT(LCUR) = .77 TIME = 5 YEARS 1 -5.00 2 -5.00 3 -5.00 4 -5.00 5 -5.00 6 -5.00 7 -5.00 8 -5.00 9 -5.00 10 -5.00 11 -5.00 12 -5.00 13 -5.00 14 -5.00 15 -5.00 16 -5.00 17 -5.00 18 -5.00 19 -5.00 20 -5.00 21 -5.00 22 -5.00 23 -5.00 24 -5.00 25 -5.00 26 -5.00 27 -5.00 28 -5.00 29 -5.00 30 -5.00 31 -5.00 32 -5.00 33 -4.99 34 -4.99 35 -4.99 36 -4.99 37 -4.98 38 -4.97 39 -4.96 40 -4.95 41 -4.93 42 -4.91 43 -4.88 44 -4.84 45 -4.79 46 -4.73 47 -4.65 48 -4.55 49 -4.43 50 -4.27 51 -4.08 52 -3.85 53 -3.56 54 -3.22 55 -2.81 56 -2.33 57 -1.76 58 -1.08 59 -.30 60 .60 61 1.64 62 2.83 63 4.17 64 5.67 65 7.35 66 9.20 67 11.25 68 13.48 69 15.89 70 18.50 71 21.27 72 24.22 73 27.32 74 30.57 75 33.94 76 37.41 77 40.96 78 44.56 79 48.20 80 51.84 81 55.45 82 59.03 83 62.55 84 66.00 85 69.36 86 72.63 87 75.80 88 78.88 89 81.85 90 84.74 91 87.54 92 90.28 93 92.97 94 95.64 95 98.31 96 101.02 97 103.80 98 106.68 99 109.74 100 112.65 101 -36.44 102 -33.71 103 -31.00 104 -28.66 105 -26.62 106 -24.84 107 -23.30 108 -21.98 109 -20.84 110 -19.87 111 -19.05 112 -18.35 113 -17.76 114 -17.27 115 -16.85 116 -16.51 117 -16.22 118 -15.99 119 -15.79 120 -15.63 121 -15.51 122 -15.40 123 -15.32 124 -15.25 125 -15.19 126 -15.15 127 -15.12 128 -15.09 129 -15.07 130 -15.05 131 -15.04 132 -15.03 133 -15.02 134 -15.02 135 -15.01 136 -15.01 137 -15.01 138 -15.01 139 -15.00 140 -15.00 141 -15.00 142 -15.00 143 -15.00 144 -15.00 145 -15.00 146 -15.00 147 -15.00 148 -15.00 149 -15.00 150 -15.00 151 -15.00 152 -15.00 153 -15.00 154 -15.00 155 -15.00 156 -15.00 157 -15.00 158 -15.00 159 -15.00 160 -15.00 161 -15.00 162 -15.00 163 -15.00 164 -15.00 165 -15.00 166 -15.00 167 -15.00 168 -15.00 169 -15.00 170 -15.00 171 -15.00 172 -15.00 173 -15.00 174 -15.00 175 -15.00 176 -15.00 177 -15.00 178 -15.00 179 -15.00 180 -15.00 LCUR = 5 PCT(LCUR) = .75 LCUR = 6 PCT(LCUR) = .73 LCUR = 7 PCT(LCUR) = .72 LCUR = 8 PCT(LCUR) = .71 LCUR = 9 PCT(LCUR) = .70 TIME = 10 YEARS 1 -10.00 2 -10.00 3 -10.00 4 -10.00 5 -10.00 6 -10.00 7 -10.00 8 -10.00 9 -10.00 10 -10.00 11 -10.00 12 -10.00 13 -10.00 14 -9.99 15 -9.99 16 -9.99 17 -9.99 18 -9.99 19 -9.98 20 -9.98 21 -9.97 22 -9.97 23 -9.96 24 -9.95 25 -9.93 26 -9.92 27 -9.90 28 -9.88 29 -9.85 30 -9.82 31 -9.78 32 -9.74 33 -9.69 34 -9.62 35 -9.55 36 -9.46 37 -9.36 38 -9.25 39 -9.11 40 -8.96 41 -8.78 42 -8.58 43 -8.34 44 -8.08 45 -7.78 46 -7.44 47 -7.06 48 -6.63 49 -6.15 50 -5.62 51 -5.02 52 -4.37 53 -3.65 54 -2.86 55 -1.99 56 -1.05 57 -.02 58 1.09 59 2.29 60 3.58 61 4.96 62 6.43 63 8.00 64 9.66 65 11.41 66 13.26 67 15.20 68 17.23 69 19.34 70 21.54 71 23.81 72 26.16 73 28.57 74 31.05 75 33.59 76 36.17 77 38.80 78 41.47 79 44.17 80 46.90 81 49.64 82 52.41 83 55.20 84 58.02 85 60.87 86 63.76 87 66.69 88 69.67 89 72.70 90 75.80 91 78.97 92 82.23 93 85.58 94 89.04 95 92.62 96 96.33 97 100.19 98 104.22 99 108.43 100 113.76 101 -77.57 102 -72.34 103 -68.35 104 -64.64 105 -61.22 106 -58.06 107 -55.17 108 -52.52 109 -50.09 110 -47.88 111 -45.8: 44.06 113 -42.42 114 -40.95 115 -39.62 116 -38.43 117 -37.3 36.43 119 -35.60 120 -34.86 121 -34.20 122 -33.63 123 -33.1. 1 32.69 125 -32.30 126 -31.97 127 -31.68 128 -31.43 129 -31.2 -31.02 131 -30.86 132 -30.73 133 -30.61 134 -30.51 135 -30.4 -30.35 137 -30.29 138 -30.24 139 -30.20 140 -30.17 141 -30.1 -30.11 143 -30.09 144 -30.07 145 -30.06 146 -30.05 147 -30.04 148 -30.03 149 -30.03 150 -30.02 I151 -In n1 1 -1a -n 1 ( -( 1 1ri-rn1 -.0

PAGE 163

163 -30.00 164 -30.00 165 -30.00 166 -30.00 167 -30.00 168 -30.00 169 -30.00 170 -30.00 171 -30.00 172 -30.00 173 -30.00 174 -30.00 175 -30.00 176 -30.00 177 -30.00 178 -30.00 179 -30.00 180 -30.00 LCUR = 10 PCT(LCUR) = .69 LCUR = 11 PCT(LCUR) = .68 LCUR = 12 PCT(LCUR) = .68 LCUR = 13 PCT(LCUR) = .67 LCUR = 14 PCT(LCUR) = .67 LCUR = 15 PCT(LCUR) = .67 LCUR = 16 PCT(LCUR) = .67 LCUR = 17 PCT(LCUR) = .66 LCUR = 18 PCT(LCUR) = .66 LCUR = 19 PCT(LCUR) = .66 LCUR = 20 PCT(LCUR) = .66 LCUR = 21 PCT(LCUR) = .66 LCUR = 22 PCT(LCUR) = .65 LCUR = 23 PCT(LCUR) = .65 LCUR = 24 PCT(LCUR) = .65 LCUR = 25 PCT(LCUR) = .65 LCUR = 26 PCT(LCUR) = .65 LCUR = 27 PCT(LCUR) = .65 LCUR = 28 PCT(LCUR) = .65 LCUR = 29 PCT(LCUR) = .65 TIME = 30 YEARS 1 -30.00 2 -29.92 3 -29.84 4 -29.75 5 -29.67 6 -29.58 7 -29.50 8 -29.40 9 -29.31 10 -29.20 11 -29.10 12 -28.98 13 -28.86 14 -28.73 15 -28.60 16 -28.45 17 -28.29 18 -28.13 19 -27.95 20 -27.76 21 -27.56 22 -27.34 23 -27.11 24 -26.86 25 -26.60 26 -26.31 27 -26.01 28 -25.70 29 -25.36 30 -25.00 31 -24.61 32 -24.21 33 -23.78 34 -23.32 35 -22.84 36 -22.33 37 -21.80 38 -21.23 39 -20.63 40 -20.00 41 -19.34 42 -18.65 43 -17.92 44 -17.16 45 -16.36 46 -15.52 47 -14.65 48 -13.73 49 -12.78 50 -11.78 51 -10.74 52 -9.66 53 -8.54 54 -7.37 55 -6.16 56 -4.91 57 -3.60 58 -2.25 59 -.85 60 .59 61 2.09 62 3.63 63 5.22 64 6.87 65 8.56 66 10.31 67 12.11 68 13.96 69 15.86 70 17.82 71 19.82 72 21.89 73 24.00 74 26.17 75 28.40 76 30.68 77 33.02 78 35.41 79 37.86 80 40.37 81 42.94 82 45.57 83 48.27 84 51.05 85 53.93 86 56.89 87 59.96 88 63.15 89 66.45 90 69.88 91 73.44 92 77.14 93 81.00 94 85.01 95 89.19 96 93.54 97 98.07 98 102.80 99 107.63 100 114.06 101 -200.54 102 -194.06 103 -189.14 104 -184.31 105 -179.64 106 -175.14 107 -170.79 108 -166.61 109 -162.59 110 -158.72 111 -155.00 112 -151.44 113 -148.02 114 -144.74 115 -141.61 116 -138.62 117 -135.76 118 -133.03 119 -130.43 120 -127.95 121 -125.59 122 -123.35 123 -121.23 124 -119.21 125 -117.30 126 -115.49 127 -113.78 128 -112.16 129 -110.64 130 -109.20 131 -107.85 132 -106.57 133 -105.38 134 -104.25 135 -103.20 136 -102.21 137 -101.29 138 -100.42 139 -99.61 140 -98.86 141 -98.16 142 -97.51 143 -96.90 144 -96.33 145 -95.81 146 -95.32 147 -94.87 148 -94.46 149 -94.07 150 -93.72 151 -93.39 152 -93.09 153 -92.81 154 -92.55 155 -92.32 156 -92.10 157 -91.90 158 -91.72 159 -91.56 160 -91.41 161 -91.27 162 -91.14 163 -91.02 164 -90.92 165 -90.82 166 -90.73 167 -90.65 168 -90.58 169 -90.51 170 -90.45 171 -90.39 172 -90.33 173 -90.28 174 -90.24 175 -90.19 176 -90.15 177 -90.11 178 -90.07 179 -90.03 180 -90.00 LCUR = 30 PCT(LCUR) = .65 153