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OCR for page 151
c
Shore Response
Modeling Methods
INTRODUCTION
This appendix reviews the characteristics and capabilities of
several shore response models. Development and implementation of
the {onger-term recommended methodology for predicting shoreline
change would be based on improvements to and extensions of these
and possibly new models.
The presentation below is organized in terms of "Iongshore" and
"cross-shore transport models, consistent with the general pattern
of individual model development to represent shore response to one
or the other of these transport components.
[ONGSHOR1: TRANSPORT MODELS
Longshore transport models include analytical models (applica-
ble to limited situations of interest) and numerical models. Both
analytical and numerical models can represent one contour (usually
at the mean sea level) or several contours of interest.
Analytical Models
The one-line analytic mode! was developed by Peinard-Considere
(1956) and applies to a number of cases of interest. The governing
151
OCR for page 152
152
APPENDIX C
equation Is the combined result of the linearized sediment trans-
port equation and the continuity equation. Le Mehaute and Soldate
(1978) and Larson et al. (1987) have summarized many of the avail-
able analytical solutions. Two examples of application of the model
to problems of interest are presented below and will serve to illustrate
the general capabilities of analytical models.
The interruption of longshore sediment transport by a littoral
barrier wiD cause sed~rnent accumulation on the uplift side and
erosion on the downdrift side. According to this model, bypassing
does not commence until the shoreline reaches the tip of the struc-
ture. Following that tune, sediment transport around the structure
commences and approaches the ambient value. Figure C-1 compares
the analytical mode} to experimental results obtained from tests in a
wave basin. As Is evident, good agreement was found.
A second example of interest is the planform evolution following
placement of a rectangular beach nourishment project. Figure C-2
presents one example based on the solution of the PeInard-Considere
equation. This solution demonstrates that the longevity of a nour-
ishment project varies directly as the square of the project length
and inversely as the 2.5 power of the representative wave height.
Numerical ModeLs
A number of investigators have developed one-~me numerical
models to represent beach planform evolution as a result of natural
effects or human-~duced alterations (Le Mehaute and Soldate, 1978
and 1980~. These models include the GENESIS model now used by
the U.S. Army Corps of Engineers. Because one-line representations
have inherent limitations, treatment of cross-shore transport, where
necessary, must be by an ad hoc procedure.
CROS~SHORE TRANSPORT MODELS
A primary motivation for cross-shore transport models (also
called onshore-offshore transport models) is associated with the es-
tablishment of a zone of impact caused by elevated storm tides and
high waves occurring during a severe storm. Some earlier models,
based primarily on geometrical considerations, wiD not be discussed.
Various models are reviewed briefly below.
OCR for page 153
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154
APPENDIX C
Swart (1976)
This empirical method is based on large-scale wave tank tests.
The procedure is complex and involves numerous empirical expres-
sions that, when programmed, make the method relatively straight-
forward to apply. The only known application of Swart's theory to
field conditions is by Swain and Houston (1984a,b) for storm erosion
at Santa Barbara, California, and near Oregon Inlet, North Car-
olina. Their modifications provided for time-varying tide and wave
conditions.
Vellinga (1983)
This profile response mode! was developed to evaluate the in-
tegrity of the Dutch dikes against storms and is based on a series of
wave tank tests. The required parameters include wave height, storm
tide, and grain size. The method predicts the profile for a storm du-
ration of 5 hours; procedures are presented for storms differing from
this duration.
:Eriebe] and Dean (1985)
This model allows time-varying input of storm tide and wave
height and solves the equations governing cross-shore sediment trans-
port and continuity using an efficient numerical method. The cross-
shore sediment transport equation is based on the profile disequilib-
rium caused by elevated storm tide and wave height conditions. The
mode] has been evaluated against Hurricane Eloise (1975) for Bay
County, Florida. A simplified modification of this method is cur-
rently in use by the Florida Department of Natural Resources in its
implementation of the Coastal Construction Control Tine program.
Balsillie (1986)
This is an empirical method that models relationships for the
average and maximum expected erosion caused by a storm based on
storm tide rise time raised to the 0.8 power and peak storm tide
raised to the 1.6 power. Balsillie's approach provides encouraging
correlation with numerous field data.
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OCR for page 156
156
APPENDIX C
[arson et al. (1988)
This mode] is based on extensive correlations of wave, sediment,
and profile characteristics. The beach/nearshore profile is subdi-
vided into four zones, each with different transport rate properties.
The model has been applied to erosion of natural and seawalled pro-
files. It is capable of predicting single and multiple bar formations.
Comparisons/evaluations have been conducted with wave tank data
and with field data from Duck, North Carolina. The model also was
compared with the Kriebe} and Dean (1985) model. Good agreement
was found with the laboratory case and the Kriebel/Dean model, but
only fair agreement was obtained with the field data.
Federal Emergency Management Agency (FEMA) Method
The method adopted by FEMA (Hallermeier and Rhodes, 1988)
for the 100-year storm event references all eroded volumes to the
portion of the dune above the 100-year still water flood level (SWFL).
The method is illustrated graphically in Figure ~3. The first step
evaluates whether at least 50 m3/m of sand per meter of beach length
is contained in the dune reservoir above the SWFL and seaward of
the dune crest (Figure ~3A). If this reservoir contains at least 50
m3/m, then the dune is considered to not erode through and the
geometry of the eroded profile is as follows. The landward portion
of the eroded profile is at a 1:1 slope and extends landward from
the SWFL to intersection with the dune profile. Seaward from the
SWFI., the profile extends seaward at a slope of 1:40. The final
seaward segment of the profile is at a slope of 1:12.5 and extends
downward to intersection with the prestorm profile. The eroded
volume above the SWFI. is 50 m3/m, and the 1:40 slope extends
seaward the required distance to obtain a balance between eroded
and deposited volumes.
We return now to the case presented in Figure C-3C in which
the dune reservoir does not contain the 50 m3/m, and it is therefore
assumed that the dune will be eroded through. The eroded profile
is at a 1:50 slope and extends landward from the dune toe defined
as the slope transition between the seaward limit of the dune and
the milder beach berm. For this case a portion of the eroded sand
is considered to be transported landward; thus, there is no basis (or
requirement) for balancing eroded and deposited volumes.
OCR for page 157
APPENDIX C
A. Cross section to ~
be compared to / /////
50 s uare meters
q / Em/ Frontal ~
/ ~ Dune ~:
~~/~ - SWFL-
(Defined by existing profile and
vertical line from upper limit of
steep rear slope to horizontal
line at stillwater elevation)
B. Eroded profile
/ .
for case of
duneface retreat J
/ 1 on 1
~ Slope
1. Place t on 1 slope for
Som2 erosion above SWFL
2. Determine additional
erosion, shown domed
3. Place 1 on 12.5 slope for
erosion/deposition balance
C. Eroded profile
for case of ;
dune removal /
1. Locate dune toe at lower
limit to steep front slope
2. Remove dune above 1 on 50
slope through dune toe
157
\
\
lon40
Slope
\ SWFL
-
SWFL
Movable I
1 on 12.5 Slope
FIGURE C-3 Treatment of sand dune erosion in l00-year event for a coastal
good insurance study. SOURCE: Hallermeier and Rhodes, 1988.
OCR for page 158
158
APPENDIX C
Brunn Rue
Bruun (1962) was the first to evaluate quantitatively the role
of slowly changing water levels on shore erosion. His formulation is
based on the concept of an equilibrium profile, defined as an average
profile that maintains its form, apart from small fluctuations, at a
particular water level.
The Bruun rule provides a profile of equilibrium with the mate-
rial removed during shoreline retreat transferred onto the adjacent
shoreface, thus maintaining the original nearshore shallow-water pro-
file relative to the increased water level. Hence, the formulation
represents an on/offshore sediment balancing between eroded and
deposited volumes without consideration of longshore transport.
The Bruun rule can be expressed as
dy_ {dS~ ~ w* ~
at \`dtJ \`h*+B)'
where y is the shoreline position, ads represents the average rate of
sea level rise, h* + B is the vertical extent of active profile motion,
and w* is the associated width of active motion. Thus, the milder
the nearshore slope [(h* + B)/w*] of the active profile, the greater
the erosion rate. An offshore limit of sediment activity is assumed,
thus precluding the possibility of shoreward sediment transport.
Bruun's concept is intuitively appearing but difficult to confirm
or quantify without precise bathymetric surveys and documentation
of complex nearshore profiles over a long period of time.
A problem with the Bruun rule is that it always predicts shore
recession with offshore transport through time as sea levels have
gradually risen. However, this is not the case along all shorelines.
For example, some barrier islands along the west coast of Florida
have obviously accreted over the last few thousand years from the
onshore movement of sand (Evans et al., 1985~. Sandy material from
the shallow shoreface and inner shelf have been moved onshore by
waves to form "perched" barrier islands atop of Pleistocene limestone
highs. There is no other source of the beach sediment, indicating a
reverse product from that predicted by a cursory application of the
Bruun rule. The Dutch also have argued that large-scare coastal
accretion (thousands of feet of beach and dune) has occurred dur-
ing the late Holocene (last 6,000 years) during a period of ostensible
sea level rise. Finally, there are direct indications of onshore sediment
OCR for page 159
APPENDIX C
159
transport by using natural tracers. Millions and Meisburger (1987)
reported that glaucionitic sands, which are only available by wave
quarrying of offshore sediments, are found on the Rockaway beaches
in significant quantities and geographic positions to indicate such a
transport process.
REFERENCES
Balsillie, J. H. 1986. Beach and storm erosion due to extreme event impact.
Shore Beach 54~4~:22-36.
Bruun, P. 1962. Sea level rise as a cause of shore erosion. J. Waterways Harbors
Division, ASCE 88:117-130.
Dean, R. G. 1988. Sediment interaction at modified coastal inlets: Processes
and policies. In Hydrodynamics and Sediment Dynamics of Tidal Inlets, D.
Aubrey, ed. Woods Hole, Mass.: Woods Hole Oceanographic Institution.
Evans, M. W., A. C. Hine, D. F. Belknap, and R. A. Davis, Jr. 1985. Bedrock
controls on barrier island development: West-central Florida coast. Marine
Geol. 63:263-283.
Hallermeier, R. J., and P. E. Rhodes. 1988. Generic Treatment of Dune Erosion
for 100-Year Event. Proceedings, Twenty-First International Conference on
Coastal Engineering, ASCE, pp. 1121-1197.
Kriebel, D. L., and R. G. Dean. 1985. Numerical simulation of time-dependent
beach and dune erosion. Coastal Eng. 9:221-245.
Larson, M., H. Hanson, and N. C. Kraus. 1987. Analytical Solutions of
the One-Line Model of Shoreline Change. Technical Report CERC-87-15,
U.S. Army Engineer Waterways Experiment Station, Coastal Engineering
Research Center.
Larson, M., N. Kraus, and T. Sunamura. 1988. Beach Profile Change: Morphol-
ogy, Transport Rate and Numerical Simulation. Proceedings, Twenty-First
International Conference on Coastal Engineering, ASCE, pp. 1295-1309.
Le Mehaute, B., and M. Soldate. 1978. Mathematical Modelling of Shoreline
Evolution. Proceedings, Sixteenth International Conference on Coastal
Engineering, ASCE, pp. 1163-1179.
Le Mehaute, B., and M. Soldate. 1980. A Numerical Modelling for Predicting
Shoreline Change. U.S. Army Corps of Engineers, Coastal Engineering
Research Center (CERC), No. 80-6.
Pelnard-Considere, J. 1956. Essai de Theorie de ['Evolution des Formes de
Rivate en Plages de Sable et de Galets. 4th Journees de l'Hydraulique, Les
Energies de la Mar, Question III, Rapport No. 1.
Swain, A., and J. R. Houston. 1984a. Onshore-OfEshore Sediment Transport
Numerical Model. Proceedings, Nineteenth International Conference on
Coastal Engineering, ASCE, pp. 1244-1251.
Swain, A., and J. R. Houston. 1984b. Discussion of the Proceedings Paper
17749 by Richard J. Seymour, The Nearshore Sediment Transport Study.
ASCE, Port, Coastal and Ocean Engineering Division.
Swart, D. H. 1976. Predictive Equations Regarding Coastal Transports. Proceed
ings, Fifteenth International Conference on Coastal Engineering, Honolulu
ASCE, pp. 1113-1132.
,
OCR for page 160
160
APPENDIX C
Vellinga, P. 1983. Predictive Computational Modelling for Beach and Dune
Erosion During Storm Surges. Proceedings of ASCE Specialty Conference
Coastal Structures '83, pp. 806-819.
Williams, S. J., and E. P. Meisburger. 1987. Sand sources for the transgressive
barrier coast of Long Island, New York—evidence for landward transport
of shelf sediments. Pp. 1517-1532 in Proceedings, Coastal Sediment. New
York: ASCE.
Representative terms from entire chapter:
coastal engineering
