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APPENDIX
CPrediction of
Beach Nourishment Performance
INTRODUCTION
Beach nourishment is the placement of relatively large quantities of good-
quality material on a beach to advance the shoreline seaward and to provide an
elevation to adequately protect the upland area. Usually, beach nourishment is
carried out in areas where the shore protection beach, the recreational beach, or
both are inadequate to fulfill the intended function or functions. Beach width and
elevation inadequacies can occur because the shoreline is retreating or by impru-
dent location of upland construction. Erosion can be either natural or human
induced. In the latter instance, it is important to attempt to remove or reduce the
cause of erosion whenever possible.
Beach nourishment material is usually placed on a steeper-than-equilibrium
slope; it also represents a planform perturbation. These disequilibriums in both
the planform and profile induce sediment flows that, over time, will reduce the
disequilibrium, thereby approaching the equilibrium state. Retention structures
can be employed to increase the longevity of the project, but in many situations
they can also increase erosion on adjacent shorelines. Performance can be pre-
dicted with simple, relatively rapid, inexpensive methods and also through the
use of numerical models. The time scales associated with project equilibration
are of considerable design interest and are critical to the economic viability of a
project. Figure C-1 illustrates the complicated three-dimensional sediment trans-
port patterns associated with various phases of project evolution.
Although beach nourishment projects have been carried out actively for
several decades, there is still not an adequate methodology to predict their de
167
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168
l
BEACH NOURISHMENT AND PROTECTION
Increasing Time
~ :=~3
I ~ Profiles !
(a) Offshore Transport on Over- (b) Onshore Transport on Flattened (c) Onshore Transport in Zone of
steepened Profiles and Long- Profiles and Longshore Transport Flattened Profiles Due to Long
shore Transport Due to Wave Due to Wave Obliquity. shore Transport Distribution
Obliquity. Across the Surf Zone.
FIGURE C-1 Three Phases of observed sediment transport in the vicinity of nourished
projects. Note: cross-contour transport due to profile disequilibrium (from Dean et al.
19931.
tailed performance. This is due in part to the complicated alongshore and cross-
shore transport processes, the near uniqueness of every setting for such projects,
and the generally inadequate monitoring of both the forces on and responses of
past projects to provide a basis for assessment of available methodologies and
guidance for their improvement.
This appendix reviews simple analytical and numerical procedures available
for prediction of beach nourishment project performance, introduces some less-
well-known behavioral characteristics affecting performance, and provides esti-
mates of predictability under various nourishment scenarios.
METHODS FOR PREDICTING
BEACH NOURISHMENT PROJECT EVOLUTION
Simple Analytical Procedures
The simple analytical prediction procedures are best suited for the less com-
plex geometries and for preliminary design in the early phase and scoping of the
volumes, costs, and renourishment intervals. More complex geometries, includ
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APPENDIX C
169
ing the effects of structures, require the use of numerical models and are dis-
cussed later.
Evolution of a beach nourishment project is a result of both cross-shore and
alongshore sediment transport. For the simple case of a long nourishment project
on a long straight beach, the time scales for cross-shore and planform equilibra-
tion are disparate. The cross-shore and alongshore time scales are on the order of
2 to 3 years and decades, respectively. This discussion will assume that the
profile adjustment occurs instantaneously. For this adjustment, predicting the
equilibrium width of dry beach is the principal focus. For the alongshore equili-
bration, the focus is on the time scales and evolutionary behavior. The disparity
of time scales is fortunate because current knowledge of alongshore sediment
transport has been developed over a period of 4 or 5 decades. The knowledge of
alongshore sediment transport is much more advanced than for cross-shore trans-
port, which has been studied actively for only about a decade.
Equilibrium Dry Beach Width
In cases in which the nourishment material is similar to the native beach
material, the additional dry beach width after equilibration, /\yO, can be shown to
be approximately
V
° h* + B
(C-1)
in which V is the volume of fill added per unit beach length and h* + B represents
the dimension of the active vertical profile, where h* is the depth of active motion
(depth of closure) dependent on the upper ranges of wave height experienced, as
given by Hallermeier (1978) and Birkemeier (1985), and B is usually selected as
the height of the active natural berm but may exceed this elevation for flood
control purposes.
Dean (1991) has shown that for the general case in which the native and fill
materials differ the additional dry beach width can differ substantially from that
given by Equation (C-11. In this case, the best approach is to use the equilibrium
beach profile concept, in which the simplest profile form is
h=Ay
where h is the depth at a distance y from the shoreline.
(C-2)
Equation (C-2) represents the ideal profile that occurs naturally and cannot
represent bar features or effects of rock outcrops, hard bottoms, or coral reefs.
Use of these idealized assumptions in applying Equation (C-2) has been criticized
by Pilkey et al. (1993~. Equilibrium beach profile forms other than Equation (C-
2) have been proposed by Bodge (1992), Komar and McDougal (1993~; and
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170
-
tr:
UJ
~ 0.10
LL
I:
J
o
0.01
BEACH NOURISHMENT AND PROTECTION
SEDIMENT FALL VELOCITY, w (cm/s)
0.01
1.0
From Individual
Field Profiles
Where a Range
of Sand Sizes
was Given
From Swartz's ~
Laboratory Results
0.1
I Suggested Empirical
Relationship A vs. D
(Moore)
1.0 10.0 100.0
From Hughes'
FiRId Results
~;p ~~
Based on transforming
_0- ~ A vs. D Curve Using
Fall Velocity Relationship
ff-'
'0 ~~ A=0.067w0~44
0.01 0.1
1.0 10.0 100.0
SEDIMENT SIZE, D (mm)
FIGURE C-2 Variation of sediment-scale parameter, A, with sediment size and fall
velocity (from Dean, 1987~.
Inman et al. (1993), however, these authors provide no guidance for applying
these forms in cases where only the grain size is known.
In order to apply Equation (C-2) to beach nourishment, a relationship is
needed between the sediment-scale parameter, A, and the grain size, D, or equiva-
lent sediment fall velocity, w. Such a relationship, originally developed by Moore
(1982) and modified by Dean (1987), is shown in Figure C-2. In applying Equa-
tion (C-2) the parameters for the native and fill materials will be indicated by
subscripts N and F. respectively. In general, three types of nourished profiles can
occur, depending primarily on the relative A parameters and the amounts of fill
placed. These types, intersecting, nonintersecting, and submerged, are illustrated
in Figure C-3.
It can be shown that the nondimensional dry beach width, l~yO/W*, is a
function of the three nondimensional variables:
/\YO ~ V AF
W* ~ BW* AN B
h* = ~V', A,, hB ~
(C-3)
where V is the volume added per unit beach length and B is the berm height. W*
is the width of the active profile (to h*) on the native profile, that is, from
Equation (C-2~:
W*=
h :312
~AN)
(C-4)
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Representative terms from entire chapter:
sediment transport
APPENDIX C
171
(a) Intersecting Profile APA;N
(b) Non-lntersecting Profile
Ay<0
. .
B
Added Sand 2~
-
`,~_
. . . ~ . _
.... . .~
1' W* ~
~ Aye
Adds ////
h*
t
h*
:~7,)t
:__ vv. ~
Virtual Origin of~ `;~ |
Nourished Profile~ `_
1 'an; ~
(c) Submerged Profile AF
72
To
W*
on
10.0
0.001
. 1 1 1 _
AW = AVIBW,* = 10.0,
T
N1
=~:Z
. I /
=~
=:
_ _
_ _
__ ~
1
'1
At ymptot as' I
toy= _
1. 1 w
I ~ _ 1
o~W-t
i=
SIB
46
-
Definition Sketch
. ~
\], s o.O
~ i tS on-lot `;,^ -~
_q',!~_
~, ~
Em-.
, 1, :
. ~-
W
ll ~'
Mel
... ,
. l ~
h* - ,_.
!
'
0 1.0
A = AF/AN
BEA CH NO URISHMENT AND PR O TECTI ON
v~=0.5
1
V. = 0.2
--r-r~
V. = 0.1 .
a.
1 1 .
V* = 0.05-
i.
T T
T I
_Y*=0.02 _
--t-T-
V. = 0.01
_ ~ 1 -
. l l
1 1
~ = 0.005
-' 1 - 1 '-
1 1
= V/BOO. = 0.002
. __ .
2.0
FIGURE C-4 Variation of nondimensional shoreline advancement, /\yOIW*, with A' and
results shown for h*lB = 2.0 (from Dean, 1991).
Figures C-4 and C-5 present graphical solutions to Equation (C-3) for values of
hJB of 2 and 4, respectively.
Planform Evolution
Planform evolution is influenced by the general morphology of the system to
be nourished; the simplest case is a long straight beach. The planform of the
nourishment can influence the performance; however, the initial discussions here
will address the case of an initially rectangular planform for which analytical
solutions exist.
0.1
0.01
0.001
0.~01
. .
= Non-lotomocting - .
._ - ~
=~=~
/
~ /]
#~7 ~
-
_ ^symp~tes J
_ ~~=~=
~
.
if-.
~ ~-
`~ ~
. ~ ~-
,# ~ ~
. 'a.,, - :~
Dandy Sag n
_ . _
'If -- _ ~
~ ~ .
~ 1 ~
~ ~
loterse~ng
Profile
~J-~-
- i'=°1
= _
go
- go
'' R1'
. ~ = 0~1 _
=
~ + ~
~ I 1
V'= 0.002
. 1 1
~=~0~1
~ __ ~
'- i 1 I
. - ~ hi. AF ~ ~
~=~ sw.) 1
,.0 2.0
A'-A ~
F N
FILMY C-5 V~adon of nondimensional sborobno advancement #0/^, Cab at' and
results sbo~D for A~ = 4.0 (hoary Dean, 19917
7~
174
BEACHNOURISHMENT AND PROTECTION
Pelnard-Considere (1956) combined the linearized equation of sediment
transport and the equation of continuity, considering the profiles to be displaced
without change of form, to yield
=G Y
At~x2
(C-S)
in which G is the so-called alongshore diffusivity and can be expressed in terms
of breaking or deepwater wave conditions, respectively, as
- ~¢ - ~(~ Ah B' (for breaking conditions) (C-6)
KHo COO g
8~5 - 11~1 - p)C*K (h* + B)
(for deepwater conditions) (C 7)
in which K is a sediment transport factor usually taken as 0.77 but is probably a
function of sediment grain size or other characteristics, H is the wave height, and
K iS the ratio of breaking wave height to local water depth (usually taken as 0.781.
CG is the wave group velocity, C* is celerity at the depth of closure, s is the ratio
of the specific gravity of the sediment to that of the water in which it is immersed
(a 2.65), p is the porosity (a 0.35), and g is the acceleration of gravity. The
subscripts b and 0 denote breaking and deepwater wave conditions, respectively.
Project Longevity for Simplest Case
It can be shown that in the absence of background erosion the fraction of
material remaining, M, in the region where fill is placed depends only on the
parameter ~/~1{, in which His the length of the initially rectangular project and
t is time (see Figure C-6~. For values of M between 0.5 and unity, it can be shown
that within a 15 percent error band in M an approximate expression for the
relationship in Figure C-6 is
M=1- ~
(C-8)
A useful result developed from Equation C-8 is the time (t50%) for 50 percent of
the placed volume to be transported from the original project limits:
e2
tSo% = K s/2
Hb
(C-9)
in which tSo% is expressed in years, and K'= 0.172 years m5/2/square kilometer for
he in kilometers and Hb in meters.
APPENDIX C
1.0
:~ IL
~ o
· Z Us
'A o
o lL ~
Z C' 0 0 5
~-<(
G G
-
175
0.0 0.5 1.0
I I I I I rl ~ ~ T
-
1 ~1 1 1 1 1 1 ~1 1 1 1 1 1 1 1 1 1 1
to Rime After Placement
-\ ~ _ G ~ Alongshore Diffusivity
- \
Asymptote 2
M = 1 - `
0.0
1 1 1 1 1 1 1 1 1
Initial Fill
Planform
T
L
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 T
0 1
2 3 4 5 6
,~
FIGURE C-6 Proportion of material remaining, M, in region placed as a function of the
parameter.
Fill Performance with a Uniform Background Recession Rate, E
For the case in which a uniform background shoreline recession rate, E, is
present, it can be shown that for values of
W' <0.5
the time required for a fraction (1-M) of the material placed to be removed from
the project area (or equivalently for a fraction M of the material placed to remain
in the project area) is
tM =
2a
-b + ~b2 _ 4ac
in which
and
a = (EI ~yO)2,
b = 2E(M- 1) 4 G_
/\YO 7r £
c= (1 _My2
in which l\yO is the initial dry beach width, as defined earlier.
(C-10)
76
BEACH NOURISHMENT AND PROTECTION
Effect of Wave Refraction Around the Project
It can be shown, consistent with intuition, that waves refract, wrapping
around the nourishment planform and thereby tending to prolong its life. Equa-
tion (C-6), applied in conjunction with Figure C-6, does not include the refraction
effects, but they can be approximated simply by multiplying the G value in
Equation (C-6) by the fraction Cb/C.*, in which C is the wave celerity and the
subscripts b and ~ denote values at breaking and depth of closure h*, respectively.
Since this ratio is generally less than unity, the effect is a greater project longevity
with reduced G values. In some applications in Florida the effect of this correc-
tion results in a t50% that is 40 percent greater than without this factor.
Residual Bathymetry
In contrast to the usual assumption that the entire placed beach profile moves
without change of form during evolution of the project planform, in some cases
the beach nourishment may extend to greater depths than will be mobilized, at
least during the first few years following nourishment. If the initial placement is
irregular, this can affect the quasi-equilibrium planform. In an idealized fashion
the upper portions of the placed profile are "planed off'' by the alongshore trans-
port, leaving the placed material below this level of activity as "residual bathym-
etry." Although this residual bathymetry is not active in the transport processes, it
does influence the wave transformation, in particular wave refraction. The effect
of the wave refraction is to cause the quasi-equilibrium planform to remain
irregular rather than to be straight, as would be the case if the entire placed
planform moved in response to gradients in the alongshore sediment transport.
The equilibrium shoreline planform will be a somewhat damped form of the
offshore residual bathymetry. Denoting the celerity of the waves at the outer
depth of the placed bathymetry as Cob and that at the depth of limiting motion, ha,
as C2 (C~ > C2), it can be shown that the project-related transport, Qp, is
KEoCGo cos(>o ° b :( - -i)~i + §2] (C ll)
Eggs - 13~1 - P)C2
in which the ~ variables represent the azimuths of the outward normals of the
various contours as depicted by their subscripts, and the /\13n are defined bY/~pn =
13n -130 p is the mass density of the water, and or is the azimuth from which the
wave Is propagating In deep water.
This result can be interpreted intuitively as the onshore contours "mimick-
ing" those offshore. This phenomenon, as represented by Equation (C-ll), may
explain why some beach nourishment projects experience erosional hot spots at
which the beach erodes faster than the average for the project. Other possible
causes of some erosional hot spots are a break in the offshore bar and wave
refraction over an offshore mound, which allow wave energy to impact the shore
APPENDIX C
177
line. Returning to the case in which the erosional hot spots are explained by
Equation (C-ll), if for some unintended reason the placed material along the
shoreline is not distributed uniformly and if the sediment at the deeper portions of
the profile does not move at the same rate as that at the upper elevations, Equation
(C-11) may provide an explanation of the cause of erosional hot spots. Regardless
of their cause, Equation (C-11) may provide a basis for remedying such effects.
For example, if the natural contours seaward of the placed material are such that
they cause localized erosion, it may be possible (although not practical in all
cases' to place material seaward of the active zone in a planform to refract the
waves in a manner that balances the tendency for localized erosion. Equation (C-
11) can be used to find the shoreline of approximate planform equilibrium. This
occurs, of course, for Qp = 0 and yields
A~2 =~1-(Cc9-)l
(C-12)
from which it can be seen that if there is no residual bathymetry (C: = C1) the
equilibrium shoreline orientation, p2 is equal to DO. As an example, if the plan-
form relief in the offshore residual contours were 50 m and the celerity ratio C2/
Car = 0.5, the planform relief of the shoreline would be 25 m.
Numerical Models for Predicting Beach Nourishment Performance
Computer Models of Alongshore Shoreline Evolution
An important tool in the design and implementation of many beach nourish-
ment projects is the application of computer models that simulate the processes of
alongshore sediment transport and the resulting evolution of the shoreline plan-
form. Such models incorporate equations that relate sediment movements to the
nearshore waves and currents. They also include a continuity equation that in
essence keeps track of the total volume of beach sediment as it is redistributed
alongshore and permits computations of the resulting patterns of shoreline reces-
sion or advance. Such numerical simulation models have proved to be useful
tools in a number of applications, including analyses of the impacts from con-
struction of jetties and breakwaters on the shoreline configuration and predicting
the patterns of shoreline change. Only in recent years have they been applied to
beach nourishment projects. However, the use of numerical models has become a
standard tool in the design of beach nourishment projects involving the U.S.
Army Corps of Engineers (USAGE), although the application of this tool varies
between USACE districts.
The general approach to computer models of shoreline change involves the
conceptual division of the shoreline into a large number of individual cells or
compartments. Equations relating the alongshore sediment transport rate to the
wave parameters that is, to wave heights or energies and to velocities of
78
BEACHNOURISHMENT AND PROTECTION
alongshore currents are employed to calculate the shift of sand from one cell to
the next. The continuity equation, based on the conservation of sediment, makes
sure that none is unaccountably created or destroyed. But more importantly, it
can convert volumes of sand entering or exiting a particular cell into the resulting
shoreline changes, whether these changes are net advances or recessions. In
general, sand enters a particular cell from one direction and exits in the same
direction, so it is the net volume of these transfers that ultimately governs whether
there is recession or advance of the shoreline as represented by that cell. Such an
analysis involves many computations of sand exchanges between cells and the
resulting net volumes of sand in the many cells, and such a computationally
intensive analysis requires the use of a computer. Furthermore, the model is run
through time so as to simulate the shoreline evolution spanning months to de-
cades. In some cases, the models must be run on large powerful computers if an
extended stretch of shoreline is being analyzed for predicted shoreline changes
spanning many years. Reduced versions of such model analyses are also avail-
able for desktop computer applications.
Early examples of computer models of shoreline change that have a range of
applications are provided by Price et al. (1973), Komar (1973, 1977), and Perlin
and Dean ( 1979~. These early studies established the validity of computer models
and demonstrated their reliability in a number of applications. The study by Price
et al., an analysis of the impoundment of sand by groins, is especially noteworthy
in that it provided the first comparison between the results from a computer
model and a physical model undertaken in a laboratory wave basin.
The most recent advances in numerical models used to simulate shoreline
changes have been incorporated into GENESIS, an acronym for generalized
model for simulating shoreline change. GENESIS was developed by the USACE.
Details of the technical development of GENESIS are given in a report by Hanson
and Kraus (1989), and a report by Gravens et al. (1991) serves as a workbook and
user's manual. One of the chief contributions of the GENESIS model is that it
provides a flexible basis for analyses that can be applied to an arbitrary prototype
situation a basis that calculates wave transformations as they shoal and undergo
refraction and diffraction, calculates the patterns of alongshore sediment trans-
port, and then determines the resulting shoreline changes. One of the principal
modifications of the GENESIS model from earlier models is in the calculation of
alongshore sediment transport rates, an approach that includes the transport
caused by waves breaking obliquely to the shoreline and alongshore variations in
wave breaker heights. This modification enhances the capability of GENESIS to
simulate shoreline changes in proximity to structures such as jetties and groins,
where local sheltering from Offshore waves is a factor. The importance of this
inclusion in numerical shoreline models was first demonstrated by Kraus and
Harikai (1983) in their analyses of Oarai Beach, Japan, where wave diffraction at
a long breakwater is a dominant process, and subsequently in some of the appli-
cations of GENESIS that also include shoreline structures.
APPENDIX C
179
Hanson et al. (1988) applied GENESIS to a simulation of the shoreline
development on Homer Spit, Alaska, and the erosion downdrift from a seawall on
Sandy Hook, New Jersey. The most complex analysis, examined in great detail
by Hanson and Kraus (1991a), was of shoreline changes at Lakeview Park, in
Lorain, Ohio, on Lake Erie. This analysis simulated the shoreline changes ob-
served following the construction of three detached breakwaters in the offshore
and two bounding groins and the addition of sand to create a new beach. The
simulation involved analysis of wave diffraction through the gaps between the
breakwaters and of the resulting readjustment of the shoreline from its original
smooth curvature after sand emplacement. Cusps or salients developed in the
sheltered region behind each breakwater, with intervening bays opposite the gaps
between the breakwaters. The agreement between the measured shoreline and
that computed by GENESIS was excellent. However, the result represents a
calibration of the model that included some adjustment of empirical coefficients
to optimize the fit. After the model had been calibrated and tested versus ob-
served shoreline changes, Hanson and Kraus (1991a) explored alternative project
designs for maintaining the beach fill. This included analyses of the beach reten-
tion for various lengths of the bounding groins and for the absence of any groins.
Such analyses demonstrate the usefulness of numerical shoreline models in gen-
eral and GENESIS specifically, as many alternative designs can be examined at
minimal expense. Hanson and Kraus (1991b) compared GENESIS predictions to
the results obtained in physical models, again for a series of detached breakwaters
such as those at Lakeview Park but also for the impoundment of sand in a series
of groins built across the beach. In all cases, the numerical models closely repro-
duced the shoreline changes that occurred in the physical models.
GENESIS includes analyses of wave refraction in the offshore. Therefore, its
use can incorporate design and implementation aspects involving predictions of
potential impacts that result, for example, from changes in offshore water depths
that are produced by dredging in the source area for sand for nourishment. These
potential impacts are illustrated by the earlier study of Motyka and Willis (1975),
which also developed shoreline simulation models coupled with wave refraction/
diffraction analyses. The necessity for computing wave refraction patterns con-
siderably increases the complexity of the model in that it requires an offshore
array to account for the bottom topography as well as to define the shoreline
position, with the possibility of both evolving through time. The problem ana-
lyzed by Motyka and Willis involved an examination of whether dredging of
sediment from the continental shelf could alter the wave refraction to a sufficient
degree that it induces shoreline erosion.
One example of the model calculations of Motyka and Willis (1975) is the
consideration of the effects of dredging a 4-m-deep hole in water that is 7 m deep
and 500 m offshore. The model used realistic profiles of the beach and offshore
and had a dredged hole inserted. The root-mean-square wave height was 0.4 m,
and periods of 5 and 8 seconds were used. Wave directions were selected so as to
80
BEACH NOURISHMENT AND PROTECTION
yield a net alongshore sediment transport of 30,000 m3/year. The results demon-
strate that the dredged hole would cause recession of the shoreline in its lee and
an advance to either side. The pattern is asymmetrical owing to the superimposed
alongshore sediment transport that results from an overall oblique wave approach.
The shoreline alterations are greater with the 8-second waves than with the 5-
second waves because the longer-period waves undergo more refraction. The
models predict major erosion that results from offshore dredging-a shoreline
retreat of 20 to 35 m that exists over a kilometer of shoreline length. Another
example of shoreline recession induced by offshore dredging for a beach nourish-
ment project can be seen at Grand Isle, Louisiana (Combe and Soileau, 19873.
The dredging there occurred over a wide area about 500 m offshore and lowered
the bottom by 3 to 6 m. The resulting development of an erosional embayment
between accretional cusps is very similar to that obtained in the numerical models
of Motyka and Willis (1975~. Although Combe and Soileau confirmed that the
impact at Grand Isle was due to the effects of the dredged hole on wave refrac-
tion, detailed numerical analyses were not undertaken.
In a somewhat comparable fashion, offshore shoals can focus the wave en-
ergy on specific stretches of shoreline through their effects on the patterns of
wave refraction over the shallower water. In some instances, this process may
account for erosional hot spots in nourishment projects. The process has been
suggested as a cause of the erosional hot spots that have occurred at Ocean City,
Maryland. Analyses using shoreline models such as GENESIS that include wave
refraction have the potential for predicting locations of erosional hot spots and
could be used to analyze whether the focus of erosion might be eliminated by
dredging the offshore shoals to some determined water depth.
Shoreline models such as GENESIS have been discussed here as an aspect of
the design of beach nourishment projects and have been used to predict the
shoreline evolution of the sand fill. They can be equally useful during the moni-
toring phase of a project because the models unite measurements of beach pro-
files that can be used to determine the actual resulting patterns of shoreline
recession and advance. This is illustrated by Work (1993), who analyzed moni-
toring data for the nourishment project at Perdido Key, Florida. The continued
use of numerical shoreline models in the monitoring phase of this project has
provided an additional basis for improvements in the models themselves and a
greater confidence in future projects, especially at this site.
One advantage of computer models is that they allow determination of the
effects of particular placement configurations and wave variability. For example,
Hanson and Kraus (1993) have investigated the effectiveness of transitioning the
ends of a project to reduce total costs, including that of renourishment. The
numerical methods could use actual wave data or a simulation of serial wave data
rather than an equivalent wave height, period, and direction, or a combination of
the three. At present, the prediction of shoreline position by numerical models in
some applications may be limited by the accuracy of available wave information.
APPENDIX C
181
There are at least two options to account for the background erosion rates
with numerical models. In applying GENESIS the model should be calibrated
with historical shoreline changes, so that it can faithfully represent the causes of
the background erosion. A second procedure, recommended by Dean and Yoo
(1992), is that the empirical background erosion be represented as background
sediment transport and be superimposed on the transport induced by the nourish-
ment project. In the absence of nourishment, this method ensures that the back-
ground erosion will be reproduced exactly.
The numerical models of shoreline evolution are based on the same equa-
tions as the analytical method described earlier, except that one of the equations
is linearized in the analytical method. Generally, if the two methods are applied
to the same initial planform and wave conditions, the results are essentially the
same. The numerical models also share many of the uncertainties in applications
with the analytical models discussed earlier. Model predictions are limited by the
ability to predict alongshore sediment transport rates. Any uncertainties in the
transport calculations carry over into the model predictions of the shoreline evo-
lution. The dependence of the alongshore transport on sediment grain sizes is not
well established. This especially affects the ability to model the evolution of a
beach fill where the nourishment material does not fully match the grain-size
distribution of the native beach sand. Although full three-dimensional models
that account simultaneously for cross-shore and alongshore sediment transport
are available, the commonly applied models such as GENESIS deal only with
alongshore evolution of the shoreline, and separate models, such as SBEACH,
analyze the cross-shore sediment transport. The models sometimes need
recalibration for the specific site of the application or verification during the
monitoring phase of a nourishment program because of uncertainties in the trans-
port calculations and because of simplified assumptions that are used in develop-
ing the shoreline evolution models.
Prof le Evolution
Numerical models are also available to represent profile evolution and can,
in principle, be used to simulate the equilibration of a placed profile or the profile
response during a storm. The structure of these models is similar to that described
for planform evolution that is, there is a dynamic or transport equation that
prescribes the sediment flow across the profile and a continuity equation that
conducts the bookkeeping of differences between sediment flows in and out of a
computational cell and equates those differences to changes in profile elevation.
These computational models have been employed and verified to a limited degree
in the equilibration phase of a fill; however, only limited efforts have been de-
voted to the recovery phase following storms.
The earliest profile evolution models include those of Edelman (1972), who
assumed that the profile maintained the same shape as the original while it is
82
BEACH NOURISHMENT AND PROTECTION
translated and that the profile equilibration processes kept pace with the rising sea
level. Swart (1974) developed a complex computational model based on a series
of laboratory tests. Moore (1982), Kriebel (1982), and Kriebel and Dean (1985)
have described a profile response model based on a transport that is proportional
to the difference between the actual and equilibrium wave energy dissipation per
unit of water volume. Limited evaluations of prototype and laboratory data pro-
vide support for this transport relationship. Kriebel et al. (1991) and Kriebel and
Dean (1993) have described an analytical method, based on observations from
numerical models, in which the profile tends to approach the equilibrium in an
exponential manner for a constant water level. Kriebel (1990) has described
modifications to his model that allow the effects of seawalls and overwash to be
represented. The Kriebel and Dean (1985) model (EDUNE) was used to some
extent in the design of the Ocean City, Maryland, beach nourishment project,
although its use was limited because it was not calibrated or verified for erosion
events at Ocean City. The numerical modeling system and storm erosion models
were used to evaluate and compare the relative effectiveness of each plan rather
than to determine the dimensions of the alternative proposed plans.
The profile evolution model employed by the USACE is called SBEACH
(Larson and Kraus, 1989a, 1991) and uses a modified form of the transport
equation described earlier. This model is well documented and is in the public
domain. It differs from the others described earlier in that it can predict the
formation of bars-in the eroding profile. The model has been calibrated and
verified for both laboratory and prototype profiles. Larson and Kraus (1989b,
1990) have compared SBEACH predictions with results from a test using a large
wave tank and field data from Duck, North Carolina. The model was also used to
analyze the design of the Ocean City nourishment project after the storm of
January 4, 1992. It was tested both with and without overwash, a feature that was
added to the model to attempt to represent the processes contributing to profile
changes during the storm (Kraus and Wise, 1993; Wise and Kraus, 1993~.
SBEACH allows the effects of seawalls to be represented. With respect to
SBEACH simulations for the Ocean City project, the model calibration param-
eter was 20 percent below that determined in an earlier publication treating a
lesser storm on a smaller fill section at the same site. For Ocean City, Maryland,
Hansen and Byrnes (1991) quote an SBEACH transport coefficient of 1.0 x 10-6
m4/N, Kraus and Wise (1993) quote 1.5 x 10-6 m4/N, and Wise and Kraus (1993)
quote 1.2 x 10-6 m4/N. The SBEACH simulations were not correlated with the
original application of the Kriebel-Dean model. The present version of SBEACH
(Version 3.0) contains additional improvements not found in the versions used in
either of the previous studies mentioned.
NOURISHMENT IN THE PRESENCE OF STRUCTURES
Coastal structures can be used to increase the longevity of beach nourish-
ment projects. Structures for this purpose include groins, terminal structures, and
APPENDIX C
183
submerged or emergent offshore breakwaters. In addition, some projects will be
carried out in areas where seawalls are present. Due to the complexity of the
interaction of sediment transport processes with coastal structures, prediction of
the performance of beach nourishment projects in the presence of coastal struc-
tures will usually require the use of numerical models. Knowledge of the interac-
tion of coastal structures with beach systems is on the edge of the state of the art.
Retention Structures
The "spreading out" losses due to alongshore sediment transport can be
reduced by placing retention structures near or at the ends of a project. These
structures, also frequently referred to as "terminal structures," increase the lon-
gevity of the project by reducing transport from the project to adjacent areas. In
considering the use of such structures, careful consideration must be given to the
possibility and degree to which they might affect the shorelines adjacent to the
project. The potential for impact is much greater in those cases where a substan-
tial alongshore sediment transport exists. To partially alleviate the early impacts
of transport interruption, a surcharge of sand can be placed on the downdrift side
of the downdrift retention structure.
Seawalls
A limiting effect of mismatch of the native and nourishment materials occurs
when nourishment is placed in front of a shoreline that is backed by seawalls and
has alongshore transport potential but little sediment-to-transport potential. In
this case, it can be shown that the planform evolution is markedly different from
nourishment on a beach of compatible sand. The behavior of the beach planform
has been modeled in GENESIS since its inception and is documented in both the
technical reference and specialized publications (Hanson and Kraus, l991a,b;
Gravens et al., 1991~. Dean and Yoo (1994) have shown theoretically, numeri-
cally, and experimentally that the planform evolution is critically dependent on
the transport characteristics near a project's end, in particular for those portions
of the project where the "active" profile does not extend up to the free surface.
The general differences include a downdrift migration of the planform centroid,
with initially increasing and later decreasing speed, and a spreading of the plan-
form, which can be significantly less or greater than would occur on a beach with
compatible sand. The behavior of the beach planform in front of seawalls was
previously incorporated into GENESIS (Hanson and Kraus, 1985, 19893.
Figure C-7 presents an example of a calculated planform and volumetric
evolution for the case of nourishment in front of a seawall and under the action of
oblique waves. The upper panel shows the shoreline displacement and the lower
panel the volumetric distributions. The "threshold volume" is that associated with
an incipient dry beach; that is, sufficient sand is present to just fill the profile to
the water line at the seawall. The planform migrational tendency shown in the
184
120
100
-
z
80
~60
In
cat
IIJ
z40
up
o
I20
Oh
1 200
1 000
800
by600
LL
400
o
200
O
BEACH NOURISHMENT AND PROTECTION
a) Planforms at Years: 0, 1, 3, 5, 10, 15
0 5000 10000 15000 20000 25000 30000 35000 40000 45000
Longshore Distance, (m)
b) Volume Densities at Years: 0, 1, 3, 5, 10, 15
- ~;~ Threshold Volume
tt:405 m' ~
0 5000 10000 15000 20000 25000 30000 35000 40000 45000
Longshore Distance, (m)
FIGURE C-7 Calculated planform and volumetric evolution of an initially rectangular
beach nourishment project fronting a seawall. Deepwater waves at 10° to shore normal
(from Dean and Yoo, 19941.
APPENDIX C
TABLE C-1 Beach Nourishment Invariants
185
Description of Invariant
Initially symmetric planforms remain nearly
symmetric even under oblique wave attack
(Note: this implies that wave direction is
relatively unimportant)
Planform evolution at any time is independent Same as above
of the sequencing of the previous waves
causing the evolution
Good-quality sand remains in the active beach
profile
Conditions
Nourishment on a long, straight
beach with compatible sediment
Good-quality sand has the same
general size characteristics as
that originally present on the beach
figure can be interpreted as due to the oblique waves "cannibalizing" the sand on
the updrift end of the project and depositing it on the downdrift end. In the case of
nourishment on a shoreline of compatible sand, owing to the small aspect ratio of
the project, the transport patterns can be linearized approximately as the superim-
position of alongshore transport on an unperturbed shoreline and normally inci-
dent waves acting on the nourishment project. This is the reason that nourishment
on a beach of compatible sand will result in little downdrift migration or plan-
form asymmetry. In those cases in which nourishment occurs in front of a sea-
wall, there is a much greater need to establish the directional characteristics of the
waves than for nourishment on a beach of compatible sand.
INVARIANTS
Although there are uncertainties associated with the design of beach nourish-
ment projects, there are also some invariants or performance characteristics that
are insensitive to some physical processes. Three relevant design invariants are
characterized in Table C-1.
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