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Effect of offshore dredge pits on adjacent shorelines considering wave refraction and diffraction

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Effect of offshore dredge pits on adjacent shorelines considering wave refraction and diffraction
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Effect of offshore dredge pits on adjacent shorelines considering wave refraction and diffraction
Creator:
Tang, Yuhong
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Gainesville, Fla.
Publisher:
Coastal & Oceanographic Engineering Dept. of Civil & Coastal Engineering, University of Florida
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English

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University of Florida
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University of Florida
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UFL/COEL-2002/008

THE EFFECT OF OFFSHORE DREDGE PITS ON ADJACENT SHORELINES CONSIDERING WAVE REFRACTION AND DIFFRACTION
by
Yuhong Tang
Thesis

2002




THE EFFECT OF OFFSHORE DREDGE PITS ON ADJACENT SHORELINES
CONSIDERING WAVE REFRACTION AND DIFFRACTION
By
YUHONG TANG

A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA

2002




ACKNOWLEDGMENTS
I would like to express my sincere gratitude to those individuals who have helped me accomplish this work. I would like to thank my advisor, Dr. Robert G. Dean, for providing me with the opportunity to pursue this work. He has afforded me tremendous support, guidance and freedom of work environment in which to pursue my goals. His suggestions and ideas were of substantial assistance. I also express my appreciation to my committee members, Dr. Daniel M. Hanes and Dr. Robert J. Thieke, for their excellent lectures and help in my research and studies. I thank Helen Twedell and Kimberly Hunt in the Archives, and Becky Hudson for their help and friendship. I appreciate all my colleagues for helping making my endeavors at the University of Florida both productive and enjoyable.
The study on which this thesis is based was funded by the Bureau of Beaches and Wetland Resources of the Florida Department of Environmental Protection, its support for this work is appreciated greatly.
I would like to thank my husband for his love, support and encouragement, and my daughter for her lovely smiles. Finally I would like to thank my parents for their endless love and my friends for their encouragement.




TABLE OF CONTENTS
ACKNOWLEDGMENTS ......................................................................1
ABSTRACT ..................................................................................... v
CHAPTERS
1 INTRODUCTION .........................................................................1.
Problem Statement .........................................................................1.
Objectives and Scope ........................................................................ 2
2 EQUILIBRIUM BEACH PROFILE........................................................ 4
3 RCP WAVE MODEL......................................................................... 8
Introduction .................................................................................. 8
Background of RCP WAVE ................................................................. 8
Assumptions and Limiations ................................................................ 9
Governing Equations ........................................................................ 9
4 DNRBS MODEL FOR CALCULATING LONGSHORE
SEDIMENT TRANSPORT ................................................................ 12
Introduction................................................................................ 12
Governing Equation for DNRBS .......................................................... 12
5 SHORELINE CHANGE CONSIDERING GEOMETRY............................... 17
6 EXAMPLE APPLICATION OF MODEL FOR AN ACTUAL CASE ............... 23
Geographic Description of Grand Isle .................................................... 23
Borrow Pit Characteristics ................................................................. 24
Results Based on RCP WAVE............................................................. 27
Adding Second Term in "CERC" Equation and Comparing the Results ............. 39
7 SOME GENERAL RESULTS FOR IDEALIZED CASES ............................ 41
Introduction................................................................................ 41




Shoreline Effects Due to Various Pit Parameters ....................................................... 41
Shoreline Changes as a Function of Distance of Pit from the Shoreline .............. 43
Effects of Pit Depth on Shoreline Changes ........................................................... 47
Effects of Pit Size and Shape on Shoreline Changes ............................................ 49
8 SUMMARY AND CONCLUSION ............................................................................ 63
BIOGRAPHICAL SKETCH ............................................................................................. 67




Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
THE EFFECT OF OFFSHORE DREDGE PITS ON ADJACENT SHORELINES
CONSIDERING WAVE REFRACTION AND DIFFRACTION By
Yuhong Tang
August 2002
Chairman: Dr. Robert G. Dean
Major Department: Civil and Coastal Engineering
Wave climates can be modified by offshore dredge pits and thus alter the equilibrium shoreline planform, thereby resulting in erosional hot spots (EHSs). The four wave transformation processes associated with offshore bathymetric changes due to borrow pits can include wave refraction, diffraction, reflection and dissipation.
Computational models have been used to simulate wave transformation and shoreline evolution based on the equilibrium beach profile, the RCPWAVE model, and the DNRBS model. These models account for wave refraction and diffraction only, and can predict the shoreline change for arbitrary bathymetry of mild slope, including the case of offshore contours which are not straight and parallel. An actual case at Grand Isle is used to examine this model and the results from this simulation are opposite to the observations in nature. Thus, it is not adequate to predict realistic shoreline changes accounting only for wave refraction and diffraction.




Several cases with a bathymetric anomaly (pit), described by a bivariate normal distribution with the pit dimensions in the cross shore and longshore directions represented by the associated standard deviations, o-, and oy, respectively, are examined using these models. It is found that the shoreline changes decrease with dredge pit distance from the shoreline and increase with pit depth. The smaller the pit dimension in the cross shore direction (o-,) and the greater the standard deviation in the longshore direction (o-y), the smaller the shoreline changes. The shoreline changes are largest when the pit shape is approximated by a circular pit ( cr = ory ). Thus the best pit shape is one with small o-. and large -y i.e. a pit that is elongated with its major axis parallel to the shoreline.




CHAPTER 1
INTRODUCTION
1.1 Problem Statement
Beaches serve as recreational resources and provide protection to upland structures from damage by hurricanes and other storms. However beaches are dynamic and many suffer erosional pressure leading to shoreline retreat. A number of methods have been employed to prevent the effects of erosion including "hard" structures, such as seawalls, revetments, groins and offshore breakwaters, thus reducing potential damage due to hurricanes and wave attack. However, this armoring of the shoreline can interrupt the longshore transport of sand and adversely impact adjacent beaches. "Softer" approaches, such as beach nourishment restore the beaches, provide shore protection and possibly environmental benefits and thus have grown in acceptance.
Beach nourishment typically comprises the placement of sand on eroding beaches to compensate for erosion, with the nourishment sand source from an offshore or onshore borrow area. Most beach nourishment projects designed to reduce coastal erosion are successful. However some beaches can experience local erosional hot spots (EHSs) that erode more rapidly than anticipated in design or more rapidly than neighboring portions of the nourished projects. Some of these EHSs can be related to the offshore borrow pits associated with the project.
A possible linkage between borrow pits and EHSs is that the pits can modify the wave climate and thus affect shoreline stability. There are four wave transformation




processes including wave refraction, wave diffraction, wave reflection and wave dissipation which can be caused by altering the offshore bottom topography due to offshore borrow pits. Therefore one approach to mitigating or avoiding EHSs is to understand the reasons and physical mechanisms associated with their formation. Toward this goal, this thesis uses available numerical models to simulate the effects of the borrow pits on wave transformation, the resulting alongshore sediment transport and formation of EHSs.
1.2 Objectives and Scope
Horikawa, Sasaki and Sakuramoto (1977), and Motyka and Willis (1974) evaluated the effects of dredge pits on the shoreline using numerical and physical models. The numerical model included refraction, but not wave diffraction, reflection or dissipation. However diffraction effects were clearly visible in the lee of borrow pits of oblique aerial photography at Grand Isle, LA. After beach nourishment, two large cuspate features formed in the lee of the two borrow pits and resulted in a narrow beach adjacent to the cuspate feature (Combe and Soileau, 1987). This outcome was probably due to the combination of transformation processes as affected by the borrow pit bathymetry, causing sand to be transported to and deposited in the lees of the two borrow pits.
The purpose of this thesis is to evaluate the wave refraction and diffraction mechanisms using available numerical models in an attempt to determine the causes of the EHSs due to offshore pits. If the causes can be determined, it should be possible to design the borrow pits to minimize their adverse effects. Comparing the results with the shoreline changes at Grand Isle, the usefulness of numerical models in predicting shoreline changes can be evaluated. Using this numerical approach to investigate a range




3
of idealized pit geometries, some general shoreline change results are developed for the effects of offshore dredge pits due to different pit locations, shapes and depths.




CHAPTER 2
EQUILIBRIUM BEACH PROFILE
One useful tool in coastal engineering studies is the equilibrium beach profile that was proposed originally by Bruun (1954). The nearshore profile from the closure depth (h&,) to the shoreline can be obtained by using equilibrium beach profile (EBP) theory if the sand sizes are known. In some of present application, EBP methodology will be employed to represent profile landward of and outside the influence of the borrow pits. The profiles for a wide variety of beaches can be represented reasonably well by the simple relation
2
h(y = Ay3 (2.1)
In which h is the depth at a distance y seaward of the shoreline and A is an empirical coefficient termed the "profile scale parameter", having the dimensions lengthy'. Dean (1977) showed that A is related to the wave energy dissipation per unit water volume in the surf zone and is based on the median sand size. It is assumed that the turbulence in the surf zone, created by the breaking process, is the dominant destructive force. Thus, the energy dissipation per unit volume DA (d) may be representative of the magnitude of the destructive force per unit volume.
D* () = 1 dF(2.2)
h dy




Where F is wave energy flux per unit crest length, and y is the shore-normal coordinate directed offshore. From linear shallow water wave theory, energy flux can be expressed as
8pgH2 gh (2.3)
The breaking waves are considered to decay throughout the surf zone according to:
H = Kch (2.4)
Where r, is a dimensionless breaking wave constant, usually taken as 0.78. Equation (2.2) can now be written:
d(8 pc2 h 2 gh)
D(d) = h (2.5)
hdy
Taking the derivative and simplifying:
D (d) = 5 pg32 /C2 h yy (2.6)
16 dy
Which is directly dependent on the beach slope and the square root of the water depth h. Integrating Equation (2.6), we obtain, h 24D,(d) IY=3 Ay Y (2.7)
5pg 21
It is intuitively clear that larger sand particles can withstand greater destructive forces and are more stable under the influence of turbulence and bottom friction. Sediments of larger sizes would be associated with steeper profiles.
The relationship between the scale parameter A and median sediment size has been developed by Moore (1982) (see Figure 2.1). Later, Dean (1987) simply transformed




Moore's relationship of A versus d (diameter) to w, the fall velocity, and found a linear
(on a log-log plot) relationship as shown in Figure 2.1, and given by
A = 0.067w0.44 (2.8)
In which w is in cm/s and A is in m A realistic beach comprises a range of sand sizes,
with the sand sizes usually becoming finer in the offshore direction. Dean and Charles
(1994) developed a relationship representing nonuniform sand sizes based on the
assumption of a linearly varying sediment scale parameter A between adjacent sampling
locations.
A, -A
A(y) = A,, + ( ,,. )(y_- y,) (2.9)
yn+1 yn
SEDIMENT FALL VELOCITY, w (cm/s)
0.01 0.1 1.0 10.0 100.0
tE 1.0 Suggested Empirical
E Relstionship A V.
from Hughes' At A0.08tw ** rofndividulsl Field Fld ResultsR
E Nottles Where a Rang
t Sand Sizes wasl Giv y
0.10
D.~ Bsed on' transforming
Uiy A Va.D0CuVSeUsing
... Fall Veloci Relationship
0)0
.,I
Lii
J From Swart's
ELaboralDry Riasults
o 0.01
0.01 0.1 1.0 10.0 100.0
SEDIMENT SIZE, D (mm)
Figure 2.1, Variation of beach profile scale parameter, A, with sediment size, D, and fall
velocity, w.. Dean (1987)
Which is applicable for y,, < y < y,-1. The A values were determined from Table 1 which
range from a sediment size D from 0.1mm to 1.09mm (Dean 1994) based on the median




sediment size. Given the calculated depth h, at one sampling location, y,, the depth at the next sampling location y,,, is calculated as follows:

h+, = {hn32 + 2 [A -A ]} 2
5mn n,, +

In which m,, is the slope of the A vs y relationship between y,, and y,,+ i.e.

m (A+1 A)
yn,, yn
.+1 .

(2.10)

(2.11)

Thus, the equilibrium beach profile theory can be used to predict the beach profile for both uniform sand sizes and sand sizes which vary across the nearshore zone.
Table 1: Summary of Recommended A Values (Dean)

0.02 0.03 0.04
0.Q714 0.0756 0.0798 0.106 0.109 0.112
0.129 0.131 0.133
0.1482 0.1498 0.1514 0.1634 0.1646 0.1658 0.1754 0.1766 0.1778 0.1868 0.1877 0.1886 0.1956 0.1964 0.1972 0.2036 0.2044 0.2052 0.2116 0.2124 0.2132

0.05 0.084 0.115 0.135 0.153 0.167 0.179 0.1895 0.198 0.206 0.2140

0.06 0.07
0.0872 0.0904 0.117 0.119 0.137 0.139 0.1546 0.1562 0.1682 0.1694 0.1802 0.1814 0.1904 0.1913 0.1988 0.1996 0.2068 0.2076 0.2148 0.2156

0.08 0.09
0.0936 0.0968 0.121 0.123 0.141 0.143 0.1578 0.1594 0.1706 0.1718 0.1826 0.1838 0.1922 0.1931 0.2004 0.2012 0.2084 0.2092 0.2164 0.2172

(Units of A Parameter are m Y3 ) (To convert A values to feet units, multiply by 1.5)

D(mm)
0.1 0.2 03 0.4 0.5
0.6 0.7 0.8 0.9 1.0

0.00 0.063
0.100 0.125
0.145 0.161
0.173 0.185 0.194 0.202 0.210

0.01 0.0672 0.103 0.127
0.1466 0.1622
0.1742 0.1859
0.1948 0.2028 0.2108




CHAPTER 3
RCPWAVE MODEL
3.1 Introduction
The Regional Coastal Processes Wave (RCPWAVE) Propagation Model (Ebersole, et al. 1986) is a short-wave numerical model specifically designed for predicting linear plane wave propagation over arbitrary bathymetry of mild slope. RCPWAVE adopts linear wave theory to solve wave propagation problems, and refractive and bottominduced diffractive effects are included in the model. However, this model does not consider wave reflection and energy losses outside the surf zone, nonlinear effects, nor a spectral representation of irregular waves. RCPWAVE is the numerical model employed in this thesis to investigate wave propagation and transformation over borrow pits. The output of RCPWAVE was later combined with a shoreline change model to investigate the impact of the borrow pit on shoreline stability.
3.2 Background of RCPWAVE
Classical wave ray refraction theory fails to yield adequate solutions in regions of complex bathymetry where waves are strongly convergent or divergent. Often due to complexities in the bottom topography, wave tracing diagrams may have intersecting wave rays which cause interpretation difficulties, as this theory predicts infinite wave heights at these locations. Combining refraction and bottom-induced diffraction effects, Berkhoff (1972, 1976) derived an elliptic equation that can represent the complete wave




transformation process for linear waves over an arbitrary bathymetry limited only by the assumption of mild bottom slopes. The model is more efficient than traditional wave ray models because the governing equations are solved directly on the bathymetric grid in the horizontal plane rather than by ray shooting and interpolation to the grid.
3.3 Assumptions and Limitations
Application of any model requires a clear understanding of its physical basis and capabilities of the model to simulate the processes of interest. If the model foundation is appropriate for the problem of interest, the results produced should be much more realistic.
RCPWAVE is a linear, monochromatic, short wave model. Therefore, nonlinear effects and irregular waves cannot be modeled. Model applications are restricted to a mild bottom slope. Time-dependent effects are not modeled since RCPWAVE is a steady-state model. Wave reflection is assumed negligible, and energy losses due to bottom friction or breaking outside of the surf zone are also assumed negligible.
These assumptions and limitations are common in many numerical models. The results from the model are sufficiently accurate to be used in the prediction of longshore sediment transport rates and shoreline change if wave reflection and energy losses can be neglected.
3.4 Governing Equations
The mild slope equation is
9 (CC .)+ -(CC -)+K2CC9=O (3.1)
ax a (3.1




where x and y are two orthogonal horizontal coordinate directions; C is wave celerity; Cg is group velocity; K is wave number and q5 is the complex velocity potential.
The velocity potential function is
0 = ae s (3.2)
where a is a wave amplitude function (a=gH/2 a), H is wave height, o- is angular wave frequency and s is the wave phase function. Substituting the velocity potential into Equation (3.1) to obtain real and imaginary parts and combining the irrotationality of the wave phase function gradient (V x (Vs) = 0), three equations were developed (Berkhoff 1976),
1 02a 2a 1 2 2
-x + + C [Va.V(CCg)]}+ 0 (3.3)
a CC
a (Vs sinO)-a (Vs cos 0) = 0 (3.4)
-x ay
a (a2CCgVslcosO)+-a(a2CCg Vs sin9) = 0 (3.5)
and form the basis for RCPWAVE.
Numerical solution of the above equations can yield the wave field outside the surf zone. The wave breaking model (Dally, Dean and Dalrymple 1984) is used to calculate wave parameters inside the surf zone. Although the model RCPWAVE includes some assumptions ---- mild bottom slope, negligible wave reflection and energy losses, the model is efficient and very stable. Because the wave height, wave angle and water depth are represented directly on a grid, these results are easily linked to other engineering




11
models in particular the longshore sediment transport model as described in the following chapter.




CHAPTER 4
DNRBS MODEL FOR CALCULATING LONGSHORE SEDIMENT TRANSPORT
4.1 Introduction
The waves and the longshore currents that are generated by breaking waves and arrive at the coast at an oblique angle may move considerable amounts of sand in the longshore direction. The gradients in longshore sediment transport cause beach erosion and accretion at various longshore locations. A beach nourishment project constructed on a long straight beach will spread out along the shoreline due to waves.
Dean and Grant (1989) developed a numerical model called DNRBS to simulate longshore sediment transport. This model is a one-dimensional model based on an explicit solution scheme. The model assumes straight and parallel bathymetric contours and ignores energy losses from deep water to wave breaking.
4.2 Governing Equations for DNRBS
The DNRBS model is based on the equations of longshore sediment transport and continuity. The longshore sediment transport equation is an empirical energy flux model.
One relationship for representing longshore sediment transport is based on the longshore wave energy flux at wave breaking. The simplest and still one of the most successful relationships is known as the CERC-formula (Coastal Engineering Research




Center, 1984) and is based on an empirical correlation between the longshore component of energy flux P in the longshore direction and the longshore sediment transport Q.
Q KP (4.1)
(P., -p)g(1- p)
Equation (4.1) is dimensionally correct longshore sediment transport and was developed by Inman and Bagnold (1963). In Eq. (4.1) P is the alongshore energy flux per unit length of beach at breaking and is defined as
P = FcosOsinO = 1 pgH2Cgsin20b (4.2)
16 b C
where 0b is the angle the wave ray makes with the onshore (-X) direction, p is the porosity of sediment, typically about 0.35 to 0.4, the dimensionless parameter K is 0.77, (Komar and Inman 1970) p, and p are the densities of sand and water, respectively.
Equations (4.1) and (4.2) can be combined to yield a simplified form of the CERC equation. Considering shallow water (Cg = h ) and c = Hb/h, where Hb is the breaking wave height and Kc is the breaking index, the CERC equation becomes:
Q KH 2 g-K sin(fl-ab)cos(,8-a) (4.3)
8(s 1)(1 p)
where the subscript 'b' denotes breaking conditions, s is the sediment specific gravity (p, /p 2.65) of the water in which it is immersed, 8J represents the azimuth of the outward normal to the shoreline, and ab represents the azimuth of the direction from which the breaking waves originate. Figure 4.1 presents a definition sketch for ab ,p and




/8, in which p is the azimuth of general alignment of the shoreline as defined by a baseline, and

/3 =/u- ---tan-)
2

0
0
Q

Reference Base Line

(4.4)

Figure 4.1, Definition sketch (for waves and shoreline orientation) (Dean and Grant, 1989)
The conservation of sediment equation is
Q av (4.5)
oy at
In which Q is the alongshore transport rate of total volumetric sediment transport integrated across the surf zone and V is the volume of sand per unit beach length. It is




assumed 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, Ax, associated with a volumetric change, AV, can be expressed as
Ax- AV (4.6)
h. +B
Substituting Equation (4.6) into (4.5), the conservation of sediment equation then becomes
a-+I a 0 (4.7)
at h.+ B o'y
Assuming energy conservation and Snell's law, Equation (4.3) can be expressed in terms of deep water conditions as follows
KH 2.4cl .2 gO.4 ,(6
- 0 Go0 cOs12(f0 a0) sin(f0 -a.)
- 8(s 1)(1 p)C 04 cos(J0 ab)
and
C*.
a = ,0 -sin-1[-sin(f30 -ao)] (4.9)
CO
where the subscript "0" denotes deep water conditions and C. is the wave celerity in water depth, h,.
Because cos(,80 -ab) is approximately unity, this longshore transport equation depends almost entirely on deep water parameters. However, the complex problem of longshore sediment transport is not represented completely by this relationship due to the lack of an overall description of essential parameters, for instance sediment grain size and bed morphology which affect longshore sediment transport. An offshore dredged area




affects the wave climate and thus the alongshore sediment transport which is of special concern here.
To assure numerical stability using DNRBS which solves the transport and continuity equations explicitly, the following criterion must be satisfied,
1 Ay2
At <- (4.10)
2 G
where Ax is the longshore grid space and At is time step, the longshoree diffusivity" G can be expressed in term of breaking condition as
G- KH g/ (4.11)
8(1 p)(s 1)(h. + B)
where ( h. + B ) represents the vertical dimension of the active profile.
A grid definition sketch is presented in Figure 4.2, where i is a spatial index.

Figure 4.2 Grid definition sketch used in computational method




CHAPTER 5
SHORELINE CHANGE CONSIDERING GEOMETRY
Chapter 4 discussed the DNRBS model which employs the assumption that the bathymetric contours are straight and parallel. In many applications, the offshore contours can be considered as straight and parallel which allows computation of wave refraction from deep to shallow water by Snell's law. However, for the case of interest here, it is necessary to use a numerical model, which can consider the effects of irregular bathymetry, refraction and diffraction, to determine the nearshore wave conditions. The linear-wave transformation model RCPWAVE can be used to provide such detailed wave information and this information can be used in DNRBS to obtain more accurate results for longshore sediment transport. The RCPWAVE model has the following advantages:
1. The computation is very stable and efficient,
2. The refraction and diffraction effects caused by irregular bathymetry are included,
3. The wave variables are calculated at the grid intersection points and are easy to
output.
In the DNRBS model, the energy flux at the wave breaking point is used to calculate the longshore sediment transport, Q,
- K(ECg cos 0 sin O) (5.1)
pg(s )( p)
It is difficult to establish directly, the wave conditions at the breaking point, so the equation is converted to one expressed in deep-water conditions (Chapter 4). In this




conversion, the bathymetry is considered to be straight and parallel and the energy losses from deep water to the wave breaking line are neglected.
Figure 5.1 shows the computated wave rays for the irregular bathymetry in Figure 5.2 (Ebersole, B. A., Cialone, M. A. and Prater, M. D., 1986, using RCPWAVE). The data are from Duck, North Carolina. From Figure 5.1, it is seen that the wave rays are affected by bathymetry and are not parallel to each other. Thus the waves arrive at the wave breaker line, with directions which vary in the longshore direction.
Figure 5.3 shows the computed wave height contours at Duck, North Carolina. It can be seen that the wave breaking position would vary with distance from the shoreline.
These figures have shown the effect of bathymetry on wave breaking characteristics at different locations. These wave climates then will determine the longshore sediment transport. To express the sediment transport, Q, we need to use the wave climates at the breaking line instead of those in deep water.
In our calculations, Equation (5.1) is used at the wave breaking locations to calculate Q. It has several advantages over the deep-water version.
1. More accurate, because at different positions, the different wave angles, heights,
and water depths are used to obtain Q,
2. It is not necessary to use the deep water direction to find Cb,
3. The equation is more physically clear.




.PIER
DUCK, NC Wv e Refrction Diagram Angle deg) -20
48
se.Ine) so L~-4.60
Figure 5.1, Wave rays at Duck, North Carolina
(Ebersole, Cialone and Prater 1986)




Y-A S

X-AXIS DUCK PIER. NORTH CAROUNA BATHYMETRY
DEPTHS ARE METERS BELOW MSI.
Figure 5.2, Bathymetric contours at Duck, North Carolina (Ebersole, Cialone and Prater 1986)
All the terms in Equation (5.1) can be determined from the results of the RCPWAVE model. A flowchart of the computations is presented in Figure 5.4.
When the shoreline changes due to gradients in longshore sediment transport, the entire bathymetry will also change and it will affect the wave field determined by RCPWAVE. Thus, an iteration is required to update the RCPWAVE and DNRBS model. In the DNRBS model, the time step is relatively small due to the stability requirement (Eq. (4.10)). At every time step (1000s), the shoreline change is very small and its effect on RCPWAVE is negligible. Besides the RCPWAVE model computations are time consuming, it is not reasonable to run RCPWAVE model every time step of DNRBS. Therefore in the computations we can set a key value 1/2 Ax where Ax is the cell size in the cross-shore direction for shoreline change. When the shoreline change exceeds that value, the RCPWAVE model is run once and then the wave characteristics are maintained constant until the shoreline change equals the specified value again.




1200
2.500 162 1100
1000
900 ~ 8027
800 2.500b' 'b 21
S700 .303 2o
1.9 2
600
500
0
S400 300 .48027
300
2.2 156
200
100
0 I f I I I I r I I I I I i
200 400 600 800 1000 1200
Offshore distance (m)
Figure 5.3, Wave height contours at Duck, North Carolina (T=12 s, H=2 m, cao0 =20 degrees)




Figure 5.4: Computational flowchart




CHAPTER 6
EXAMPLE APPLICATION OF THE MODEL FOR AN ACTUAL CASE
6.1 Geographic Description of Grand Isle
Grand Isle is located on the Gulf of Mexico in Jefferson Parish, Louisiana, (See Figure 6.1), and is about 60 miles south of New Orleans, 45 miles northwest of the Southwest Pass of the Mississippi River (Gravens and Rosati, 1994). Grand Isle is part of the Bayou Lafourche barrier system that forms the seaward geologic framework of eastern Terrebonne and western Barataria basin in Terrebonne, Lafourche, and Jefferson parishes (Penland et al. 1992). Grand Isle is a lateral migration of the flanking barrier islands developed by recurved spit processes. It is a low-lying barrier island with natural ground elevations ranging between 3 and 5 ft above National Geodetic Vertical Datum (NGVD). Its length is nearly 7.5 miles and its width is approximately 0.75 miles (Gravens and Rosati, 1994 and Combe and Soileau, 1987). Based on data for a 100-year period (McBride et al. 1992), the shoreline of Grand Isle has retreated on its western end, kept relatively stationary at its middle part, and advanced on its eastern end.
Recently, a 2600 ft revetment and jetty system has been built at the western end of the island to try to halt the rapid beach erosion commencing in this area near the end of the 1960's and the beginning of the 1970's. Although these structures achieved the expected objectives stabilizing the shoreline on the western end, storms had caused large amounts




of sand transport from the beach face with offshore deposition. Due to erosion of this island, a beach nourishment project was undertaken in 1978.

Figure 6.1, Grand Isle vicinity map (Gravens, and Rosati, 1994)
6.2 Borrow Pit Characteristics
As noted previously, borrow pit locations can interact with waves and lead to a modification of the wave patterns along the shoreline. A man-made beach and dune 7.5 miles long with a crest elevation of 7 feet NGVD was built in 1976 along the gulf shore at Grand Isle. For controlling beach erosion and reducing hurricane wave damage, a beach renourishment project was initiated in September 1983, and was completed one year later. This project comprised the placement of 5,600,000 cubic yards of sand in the

GRAND ISLE, LOUISIANA ~~~SCALE ''
SE112 ~ 5~O I0~0 Z _J
*4IU 2640M




beach and dune system. The dune dimensions were 10-foot crown at elevation 11.5 feet NGVD, with side slopes equal to 1 vertical to 5 horizontal extending to a natural ground elevation on the protected side and to elevation 8.5 feet NGVD where it intersected the beach berm (Combe and Soileau, 1987). Sand was obtained from two offshore borrow areas located about 3000 feet Gulfward. The original water depth in the vicinity of the borrow pit was 15 feet, the depth of excavation below the sea bed was 20 feet near both ends and 10 feet at the center. As a consequence, the borrow areas are described as a "dumbbell" shape with the centroids of the bells located about 4,500 feet apart and considerably deeper than the middle portion (see Figure 6.2). After a short time, a series of shoreline changes became evident. By August 9, 1985, the two large cuspate features along the nourished beach, which had formed landward of the ends of the primary borrow areas adjacent to the center of the island were clearly visible as shown in Figure 6.3. The sand in these features was drawn from the neighboring beaches, leaving these areas quite narrow. Gravens and Rosati (1994) examined this situation using the numerical models RCPWAVE and GENESIS which was used to compute longshore sediment transport rates and shoreline change, and have concluded that wave refraction led to lower wave energy at the shoreline directly landward of the pits and higher wave energy adjacent to the pits. This results in larger wave setup at the shoreline on the sides of two dredged pits which could drive currents into the sheltered area result in sediment transport and localized deposition which forms the salients. Thus, the offshore borrow pits at Grand Isle were likely the cause of the observed shoreline changes.
Because long-term wave measurements were not available in the vicinity of Grand Isle, Gravens and Rosati (1994) used a 20-year hindcast for the Gulf of Mexico coast that




t88'i

Figure 6.2, Pit geometry at Grand Isle




was summarized in the U.S. Army Corps of Engineers Wave Information Study database. The average incident wave conditions in deep water conclude that the representative wave height, wave angle and wave period, are 1.5 ft, 6.5 degrees west of shore-normal and 5.6 seconds respectively. A contour plot of the bathymetry grid that causes an irregular longshore breaking wave field produced by the borrow pit is indicated in Figure
6.4. (Gravens and Rosati, 1994)

Figure 6.3, Aerial photograph at Grand Isle in 1985
(Combe and Soileau, 1987)




Figure 6.4, Contour plot of Grand Isle nearshore bathymetry grid (Gravens, and Rosati, 1994)
6.3 Results Based on RCPWAVE
The Grand Isle borrow pit geometry and shoreline were used to evaluate the methodology described in this thesis (RCPWAVE and DNRBS). The sediment size is 0.2mm and the base conditions for the following cases are a water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet and a period of 5.6 seconds. The profile landward of borrow pit was represented as an equilibrium beach profile. The initial computational domain is shown in Figure 6.5. The length in the longshore direction encompasses 343 cells, 35 m each of length, for a total of 12,005 m, and the modeled length in the cross-shore direction comprises 80 cells, 28.75 m width each, for a total of




2300 m. The time step is 1000 seconds. Two cases with different wave angles were examined.
1. Wave angle =0.0 degree

2. Wave angle=6.5 degree

z
Y
x

Figure 6.5 Computational domain for bathymetry and wave direction
The length in the longshore direction encompasses 343 cells, 35 m each of length, for a total of 12,005 m, and the modeled length in the cross-shore direction comprises 80
cells, 28.75 m width each, for a total of 2300 m at Grand Isle




-10 0 10
Shoreline Change (m)

12000 11000 10000 9000 8000 7000 6000 5000
4000 3000
2000 1000
0

I I I

I I I I I

Figure 6.6 Shoreline changes for a normal incident wave before smoothing (Pit centerline at 6000 rn offshore)
(Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet and a period of 5.6 seconds at Grand Isle)
Figure 6.6 shows the calculated shoreline evolution with time for a normally incident wave. It is seen that the shoreline changes are quite irregular and this irregular pattern remains even for large time. Comparison with the real shoreline demonstrates that this result is not physically correct. To examine the cause of this effect, the breaking wave conditions were examined. Figure 6.7 shows the wave angle change at the breaker line where is seen that the wave angle varies smoothly, thus this is not the source of the




31
irregularity. The wave angle here has been averaged using three points to reduce any oscillations, i.e.

(6.1)

12000 11000 10000 9000 8000 7000 6000 5000
4000 3000 2000
1000 0
-10

Pit Centerline

I I I I I I

I I I I I I I I I I

-5 0 5
Breaking Wave Angle (degree)

Figure 6.7 Wave angle at the breaker line before smoothing
(Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet and a period of 5.6 seconds at Grand Isle) Figure 6.8 shows the wave height at the breaking line where it is evident that the wave height varies significantly over small longshore distances. This type of oscillation is believed to be physically unrealistic, because the large gradients will be smoothed by

aj = I/ 3(ai-I + ai + ai+,)




32
diffraction and possibly other processes. In the RCP WAVE model, there is no smoothing although diffraction is represented. This character suggests that to obtain correct results, these large gradients should be smoothed.

12000 11000 10000
9000 8000 7000 6000 5000
4000 3000 2000
1000

Pit Centerline

0.4 0.6 0.8
Breaking Wave Height (in)

Figure 6.8 Breaking wave height before smoothing at Grand Isle
(Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet
and a period of 5.6 seconds at Grand Isle)

.1 ........ .. .....I .............

i i i .

2




Figure 6.2 shows the pit geometry used to conduct the computations. There are sharp changes in the beach bathymetry and these sharp changes may cause large gradients in the solution. To verify this possibility, the beach bathymetry is smoothed using the following equation
h = 1/ 8(h,._ + 4h,1 + hi+,,j + h,j_ + hij+,1) (6.2)
To obtain smoother results, the original bathymetry is averaged 100 times using Equation (6.2). This equation will not change the total amount of sand excavated from the pit; however, the maximum depth is decreased.
Figure 6.9 shows the computational domain after the smoothing and Figure 6.10 shows the wave height at the breaker line where it is seen that the wave height is much smoother than in Figure 6.8. Figure 6.11 shows the wave angle at the breaker line which is very similar to that in Figure 6.7. It is quite interesting that smoothing the bathymetry seems to have a considerable smoothing effect on the breaking wave height but a relatively small effect on the wave angle. Figure 6.12 shows the calculated shoreline change. Because the RCPWAVE model only includes the effects of wave refraction and diffraction, and not wave reflection and dissipation, this result is opposite to that appearing in Figure 6.3 for Grand Isle. Figure 6.13 shows the shoreline change for an incident wave angle equal to 6.5 degrees which is also opposite to the actual case which has two erosional cold spots and three erosional hot spots.
Figure 6.14 depicts wave directions and wave rays in the vicinity of the smoothed pit. It can be noted that in the center of pit the direction of wave rays is towards inside which associated with an erosional cold spot and the direction of wave ray near the ends of pit is toward outside which related to forming erosional hot spots.




z
x

Figure 6.9 Bathymetry after smoothing at Grand Isle
The length in the longshore direction encompasses 343 cells, 35 m each of length, for a total of 12,005 m, and the modeled length in the cross-shore direction comprises 80 cells, 28.75 m width each, for a total of 2300 m




12000 11000 10000
9000 E 8000
(.)
j5 7000 53 000 = 5000
CO)
3000
2000 1000

Pit Centerline

I I I

3

I

. I I I I 1 1 1 1 1

0.5
Breaking Wave Height (m)

Figure 6. 10 Breaking wave height after smoothing at Grand Isle
(Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet and a period of 5.6 seconds)




12000 11000 10000
9000 E 8000 7000
5 6000 5 6000
0
= 4000
3000
2000 1000

17

Pit Centerline

i i i

I I I I I I I I I

-10 -5 0 5 10
Breaking Wave Angle (degree)
Figure 6.11 Breaking wave angle after smoothing at Grand Isle
(Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet and a period of 5.6 seconds)

I I I




MM'

I

12000 11000 10000
9000 E 8000 (D
7000 j5 6000
5000
0
4000 3000
2000 1000
0

0
Shoreline Change (m)

Figure 6.12 Shoreline change for a normal incident wave after smoothing
(Pit centerline at 6000 m offshore)
(Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet
and a period of 5.6 seconds at Grand Isle)




12000 11000 10000
9000 go 8000
7000 j5 6000 5000
0 :
.~4000 CO,
3000
2000 1000
0 rl il I Iii I I I I li il I I
-15 -10 -5 0 5 10
Shoreline Change (m)
Figure 6.13 Shoreline change for incident wave angle equal to 6.5 degree after smoothing (Pit centerline at 6000 offshore) (Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet and a period of 5.6 seconds at Grand Isle)




8000
E 7000
0 (a (Positive)
a)i6000
.- a (Negative)
0
co
5000
4000
- I I I I i i I , I r I ,
0 1000 2000 3000 4000 5000
Offshore Distance (m)
Figure 6.14 Wave rays for smoothed pit at Grand Isle and definition sketch for wave angle direction at Grand Isle (Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet and a period of 5.6 seconds)
6.4 Adding Second Term in "CERC" Equation and Comparing the Results
Chapter 4 presented a form of the CERC equation which included only one term which represents sediment transport due to obliquely incident breaking waves. However, a second term represents the transport contribution produced by longshore currents resulting from a gradient in wave-setup if breaking wave heights vary in the longshore direction (Ozasa and Brampton, 1980). The full CERC transport equation as follows,




K1Hh / gcsin(O-a)cos(O-a) K2HbS g/K cos(O- ab) dHh (6.3)
8(s 1)(1 p) 8(s 1)(1 p) tan(y) dx
where K2 is the sediment transport coefficient of the second term and tan y is the slope from nearshore to depth of closure. Figure (6.15) presents shoreline change results of applying Equation (6.3) with K2= 0.77, K1=0.78 and tany,= 0.02. The resulting shoreline changes including the second term are only slightly smaller than that with only the first term included.

12000 11000
10000 9000 8000 7000 6000 5000
4000 3000 2000 1000

Including First Term Only Including First and Second Terms

Shoreline Change (m)

Figure 6.15 Comparing the results of simplified CERC and full CERC equations normal incident waves at Grand Isle (Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet and a period of 5.6 seconds)




CHAPTER 7
SOME GENERAL RESULTS FOR IDEALIZED CASES
7.1 Introduction
As much as 90 percent of the sand for beach nourishment projects is obtained from offshore sources. In these areas, sediment sizes are often reasonably compatible with the beach that is to be nourished. These offshore areas can be located small or large (tens of kilometers) distances from the beach to be nourished. The excavated depths of borrow pits are also different. Regardless of their geometries and locations, borrow pits can affect shoreline stability. Because borrow pits can change the offshore bathymetry significantly, the bathymetric pattern will impact the shoreline due to wave refraction, diffraction reflection and dissipation. To obtain generalized effects of offshore borrow areas, a series of idealized pit geometries represented as a bivariate normal distributions were calculated using the numerical simulation methods described in the previous section.
7.2 Shoreline Effects Due to Various Pit Parameters
Chapter 3 has discussed the requirement of a mild bottom slope for the model RCPWAVE. For purposes here, we represent the pit geometry by an idealized bivariate normal distribution as follows,
--[ (x-x)2 + (Y-Y)2]
h(x, y)=h +Ah e 2,'2 2'-y2
In which h is the water depth without the pit, Ah is the maximum depth of offshore borrow pit relative to the ambient depth, x0 is the distance from the shoreline base line to




the center of pit, y0 is the distance from the center of pit to the X axis (offshore
direction) and o-, and (7 are the distances from the center of pit to the respective
standard deviation distances, respectively (see Figure 7.1). The profile landward of the pit
is represented by equilibrium beach profile based on a sand size of 0.2 mm.
15000 14000 13000 12000
-~11000
10000
9000 /1.
,'800i x (Positive)
19 8000 >
7000 x (Negative)
6000
0 5000
CO4000L.
OYx
3000 X0ON2000 1000
i I I I i I I i I i
5000 10000 15000
Offshore Distance X (m)
Figure 7.1 Sketch for normal distribution pit (oru = 400 m, oY =1100 m and x0=3600 m)
7.2.1 Shoreline Changes as a Function of Distance of Pit from the Shoreline
Beach nourishment is less costly if the borrow pits are located near the shoreline.
However, the shoreline will be affected more for small distances of the pit from the




shoreline. In the present study, we examine the general effect on shoreline changes as related to the distance from the pit to the shoreline. Thus in these cases, all the parameters are kept constant except for x,, which is the distance from the center of the pit to the shoreline. The computational domain is 320 by 300, ie 300 cells in longshore direction
(y) and 320 cells in cross shore (x) direction. The grid sizes in the x and y directions are Ax = 20 meters and Ay = 60 meters. The base incident wave parameters for the following trials are that the relative wave angle ,6 a seaward of the pit is equal zero, the wave height HO is one meter and the wave period equals 10 seconds. In the simulation, h 8 m, Ah = 6 m, o-x = 200 m, ay, = 1,200 mn and yo = 9,000 m. Eight different cases are calculated at x0 = 1,400 m, 1,600 m, 1,800 m, 2,000 m, 2,200 m, 2,400 m, 2,600 mn and 3,600 m.
Figure 7.2 shows the shoreline changes for xO =1,400 m. It is seen that the largest shoreline accretion occurs at y= 12,000 m and y=6,000 m and the maximum erosion occurs at y= 9,000 m, ie directly landward of the pit. Figure 7.3 shows the shoreline change for xO =2,200 m. From Fig. 7.2 and 7.3 it is seen that although for this different x0,. the position of largest erosion is not changed, the maximum shoreline changes decrease with increasing pit distance from the shoreline.
The largest shoreline recession and advancement for different xO are plotted in Figures 7.4 and 7.5 respectively. These results indicate the principal trends of shoreline change which are that the greater the distance from the shoreline base line to the center of pit, the smaller the effect on the shoreline. The trend of shoreline change is nearly linear




when the pit is close to the shoreline. It is interesting to note that there is a small region where the effect of the pit on the shoreline dramatically decreases with increasing distance from the pit to the shoreline. If the borrow pit is sufficiently far from the shoreline, very small shoreline changes result.
18000 16000
14000
E
'12000
06000/ K
CO
4000 2000
0 I I
-3 -2 -1 0 1 2
Shoreline Change (in)
Figure 7.2 Shoreline changes at x0 =1400 m, pit centerline at y--9000 m
(h =8 m,Ah= 6m, o-_,=200 m, o-y1,200 m, T=10s, HO =lM)




18000
16000 14000 '12000
8000
0 6000
4000
0
-0.4 -0.2 0 0.2
Shoreline Change (m)
Figure 7.3 Shoreline changes at xo =2200 m, pit centerline at y=9000 m
(h= 8m, Ah=6m,o- = 200 m, o-Y= 1,200 m,T=10 s, H0 =1 m)




0 .7. ...
/
/
--0.5/
0
=-15
,
E -2 E
.,
~/ 2 /
/
-2.5
0 500 1000 1500 2000 2500 3000 3500
Offshore Distance, X (m)
Figure 7.4 The largest shoreline recession for different x0
(h=8m, Ah=6m, cra=200 m, o-,= 1,200 m, T=l0 s, H0=l m)




1.5
E
>1
0 Cf)
E
= 0.5
E
06 500 1000 1500 2000 2500 3000 3500
Offshore Distance, X (in)
Figure 7.5 The largest shoreline advancement for different x0
( = 8 m, Ah =6m,c,,= 200 m, c=1,200 m, T=10 s, H, =1m)
7.2.2 Effects of Pit Depth on Shoreline Changes
The pit depth is related to the shoreline change magnitude. To quantify this effect, in the simulations to be discussed, all other parameters were kept constant except for Ah which is the maximum pit depth. The computational domain is 380 by 380 with 380 grids in both longshore (y) and cross shore (x) directions. The grid size in the x direction, Ax, is 20 meters and Ay is 30 meters. The base conditions as described previously for wave




characteristics and water depth )h were used. In these calculations, o-, and ou, were maintained at 200 m and 600 m, xO and yo were 3,600 m and 5,700 m respectively. Seven different cases are simulated with Ah equals 2 m, 4 m, 6 m, 8 m, 10 m, 12 m and 15 m. Figures 7.6 and 7.7 show the maximum shoreline recession and advancement respectively. It is seen that the shoreline increases with increasing pit depth.

I I I I I

I I I I I I I I I

5 10
Depth of Pit (in)
Figure 7.6 The maximum shoreline recession versus pit depth
(h = 8m, a., =200m, o-Y = 600 m, T= 0 s, H =l m)




10 9
-8
E 7
co/
2 //
1/
0) 5/01
Depthof Pt (m
Figre .7Themaimu shreineadancmen vrsu pt dpt
(h=8ma.) 00m -=60m T1 ,H 1M
7 .2 feto i ieadSaeo hrln hne Th4 borwptsz/n hp ilafc hesoeiecags ycagn n EY fo/eea aebscted a eotindsoigteefc nsoeiecag
deph nd avFigr a .7 teamm shoreies adanceent v0 30 eers it depths
fotr Seventfralt cases aiare calbelotaed howiranng effeon sh0moelinemchane




CY ranging from 200 m to 1200 m. Figures 7.8 and 7.9 show the maximum shoreline recessions and advancement respectively. Figure 7.8 indicates that there are two recessional peaks for cr. equals 800 m, ay equals approximately 600 m and 200 m. Beach recession is largest for c, larger than ay Figure 7.9 shows that there are two maximum shoreline advancement peaks located on o-= 800 m and ory =700m and

1200 1100 1000 900 800 700 600 500
400 300
200

500 1000
a (M)

Figure 7.8 The maximum shoreline recession versus the sizes of the pit in the x and y
dimensions (x0= 3600 m, h= 8 m, Ah= 6 m, T=10 s, H0 =1 m)




cry =400 m. Again shoreline advancement is largest if o-, is larger than ary. For o, less than 200 m and cry greater than 800 m, the associated beach recession and advancement are quite small. Therefore the best pit shape is one with small o, and large oY, ie a pit that is elongated with its major axis parallel to the coastline.
1200 17 /r/
/ / -/ /.'."?,
1100 /
100013 (
900 / / /< -"i
800 141
500700 "
600 (x0 4 3600 m hT
5004!
400 -5 I2<, 167/< /
< ~ 1:21'
200 I
20500 1000
(in)
Figure 7.9 The maximum shoreline advancement versus the sizes of the pit in the x and y
dimensions (x = 3600m, h 8 m, Ah =6 m, T=10s, HO =1 m)




It is instructive to examine in greater detail two of the seventy cases resulting in Figures 7.8 and 7.9. Case 1 is for o- = 400 m and cy=l,100 m, and Case 2 is o-,,= 800 m and o'Y=600 m. In Case 1, the computational domain is 320 by 300, ie 300 cells in longshore direction (y) and 320 cells in cross shore (x) direction. The grid sizes in the x and y directions are Ax = 20 meters and Ay = 50 meters and y. =7,500 m. Figure 7.10 shows wave rays and the wave angle directions. The wave rays diverge slightly as they pass over the pit. Figure 7.11 presents the breaking wave angle which varies between
-1.2 deg. and 1.2 deg. Figure 7.12 presents the breaking wave height which changes from 1.2 m to 1.4 m. Figure 7.13 shows shoreline evolution with a maximum shoreline advancement and recession of 3.1 m and 4.4 m respectively. The maximum erosion occurs immediately landward of the pit, and this result is similar to the results obtained by Motyka and Willis(1974). Figure 7.14 presents wave height contours, and Figure 7.15 presents the final shoreline changes considering the first term in the CERC equation and both terms. It is seen that using the full CERC equation causes smaller maximum shoreline changes, i.e. including this second term causes changes which reduce slightly the differences between these computed results and those at Grand Isle. In Case 2, the computational domain is 380 by 320, ie 320 cells in longshore direction (y) and 380 cells in cross shore (x) direction. The grid sizes in the x and y directions are Ax = 20 meters and Ay 30 meters and y0=4800 m. Figure 7.16 presents the wave rays where it is seen that the deviation due to the pit are much larger than for Case 1. Figure 7.17 shows that the breaking wave angle varies between -11 deg. and 11 deg. Figure 7.18 presents breaking wave height which varies from 0.6 m to 2.6 m. Figure 7.19 shows shoreline




evolutions with a maximum shoreline advancement of 30 m and a maximum recession of 29 m. These plots show large variations in breaking wave angle and wave height which result in large shoreline changes, the shoreline changes are even larger if o-. is smaller
than cy
15000 14000 13000 12000
11000 ----- 7 X -s,,
1000
8000
.La 8000 ... (MI-X IE- I (Positive)
70 a (Negative)
= 6000
0
5000 4000 -
3000 2000 1000
5000 10000 15000
Offshore Distance (m)
Figure 7.10 Wave rays and wave angle direction for Case 1
(h-= 8 m, Ah= 6 m, x0= 3600 m, cr= 400 m and -y=l,100 m, T=10 s, H0=1 m)




15000 14000 13000 12000 11000 E10000 o 9000 8000 0 7000 6000
0
= 5000
co
4000 3000 2000 1000
0-~
-1.5

Pit Centerline

11
-1 -0.5 0 0.5 1 1.,1
Breaking Wave Angle (degree)

Figure 7.11 Breaking wave angle for Case 1
(h=8 m, Ah= 6 m, xo =3600 m, a,- =400 m and ory=1,100 m, T=10 s, H0 =1 m)




\
----------------

15000 14000 13000 12000 11000 E10000 CD
o 9000 a 8000 7000 6000
co
..c: 5000
4000 3000 2000 1000
Y

1.2 1.25 1.3 1.35 1.4
Breaking Wave Height (m)

Figure 7.12 Breaking wave height for Case 1
(h=8 m, Ah= 6 m, x. = 3600 m, o-,= 400 m and o-y=l,100 m, T=10 s, H, =1 m)

//
j)

(
I I i I

Pit Centerline

I I I I

1.45 1.5

I I I I I

i l I I |I!| I I [II . . . .




15000 14000 13000 12000
,..11000
'10000 ...).
a 9000 8000
07000 \
6000 5~ 000
S40003000 2000 1000
0 F
-5 -4 -3 -2 -1 0 1 2 3 4
Shoreline Change (m)
Figure 7.13 Shoreline change for Case 1
(h=8 m, Ah=6m, xo= 3600m, or,=400 mand oy=1,100 m, T=10 s, Ho=l m)




15000
14000
13000
12000
11000 M ............. 1o2
E10000 "375 1.55 )
9000 ~'~
: 7000
6000 f "
5000 ,.
C0 /~ 1.04'/
4000 _11.02625
3000 (
2000
1000 .
0 ,I .... I .... I 1l111 iii i 1i I 1 ,
0 2000 4000 6000 8000 10000 12000 14000 16000
x
Figure 7.14 Wave height contours for Case 1
(h=8 m, Ah= 6 m, xo= 3600 m, o- = 400 m and cry=1,100 m, T=10 s, Ho=1 m)




- Including First Term Only
- -Including First and Second Terms

15000 14000 13000 12000 '.,11000
E
-10000
9000 2 8000 o 7000 (D
6000 O 5000 4000
3000 2000 1000
05

-2 -1 0 1 Shoreline Change (m)

Figure 7.15 Comparing the results of simplified CERC and full CERC equations normal incident waves for Case 1
(h= 8 m, Ah= 6 m, x0 = 3600 m, o-,= 400 m and cy=1,100 m, T=10 s, H0 =1 m)




9000 8000
7000 < ..
6000 /
5000 a (Positive)
_ .. (Negative)
4000
CO) 3000 __ _ _ _ _ _
2000 1000
0 2000 4000 6000 8000 10000
Offshore Distance (m)
Figure 7.16 Wave rays and wave direction for Case 2
(h=8 m, Ah= 6 m, xo= 3600 m, o-,= 800 m and -y=600 m, T=10 s, H0=1 m)




9000 8000 7000
E
6000 .T 5000
0
c 3000
2000 1000

, I . I I .

Figure 7.17 Breaking wave angle for Case 2
( = 8 m, Ah = 6 m, xo = 3600 m, ax = 800 m and o- =600 m, T=10 s, Ho =1 m)

. i r r lil l l l l l l r i r.l l l l l l l r l l l i

Pit Centerline

I . . I . . I I . I

-15

On

-5 0 5
Breaking Wave Angle (degree)




9000
8000 7000
6000 /
- 5000 f Pit Centerline
= 4000
0
e- 3000
2000
1000
%. 0.4 0.6 0.8 1 12 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8
Breaking Wave Height (m) Figure 7.18 Breaking wave height for Case 2
(=8 m, Ah = 6 m, xo = 3600 m, a-, = 800 m and o-Y=600 m, T=10 s, Ho =1 m)




9000
8000
- 7000 E M
' 6000 ... >f-'t 'Z---.C I "
6000
5000
4000
S3000 -I -7-k~
2 3000
1000
I I I I I t I I I I I I I I I
-30 -20 -10 0 10 20 30
Shoreline Change (m)
Figure 7.19 Shoreline change for Case 2 (h = 8 m, Ah= 6 m, xo = 3600 m, cr= 800 m and cr-Y =600 m, T=10 s, Ho =1 m)




CHAPTER 8
SUMMARY AND CONCLUSION
A computational model for beach planform evolution as affected by offshore borrow pits has been developed based on the equilibrium beach profile, RCPWAVE model and DNRBS model. This new method presented here can predict the shoreline change for arbitrary bathymetry of mild slope including the case of offshore contours which are not straight and parallel. The model described in this study accounts for wave refraction and diffraction only and does not account for wave reflection or dissipation which can affect shoreline changes significantly. In this model, shoreline changes were predicted based on equilibrium beach profiles which depend on the sand size and the basic borrow pit geometry, which served as input data for the RCPWAVE model. After obtaining the wave conditions from the RCPWAVE model, the DNRBS model is used to calculate shoreline change. The RCPWAVE model and DNRBS model have been incorporated into one code, and data exchange between the RCPWAVE model and the DNRBS model occurs inside the code. In simulating shoreline change, the wave conditions at the wave breaking points are used, which differs from the general way in which DNRBS was developed originally which used deep water conditions as input. This change was required because of the lack of straight and parallel bottom contours as required by the original DNRBS model. To avoid unnecessary oscillations in this model, averaging of the wave height and angle at breaking has been applied.




A test for Grand Isle conditions, used to qualitatively evaluate the present model, shows that the shoreline change results from the present method are opposite to the actual case, (see Chapter 6) probably because the RCPWAVE model does not consider wave reflection or dissipation. It is worth mentioning that a smoothing procedure is necessary for Grand Isle bathymetry to obtain reasonable results. The full CERC equation (adding the second term) was introduced to simulate shoreline change, and the effect is reasonably small for the conditions examined.
To systematically study the effect of pits on shoreline change, different cases with bathymetric anomalies represented by a bivariate normal distribution were investigated using the present method. Conditions varied included the distance from the pit center to the shoreline, the pit depth, and the size and shape of the pit. It was found that the shoreline changes attributable to the pit decrease with increasing pit distance from the shoreline and increase with pit depth. The pit shape also affects shoreline recession and advancement. The smaller the pit standard deviation in the cross shore direction (0-x) and the greater the standard deviation in the longshore direction (0o), the smaller the effect on shoreline change. When the pit shape is approximated by circular contours, shoreline changes become large. Therefore the best pit shape is one with small 0-, and large orY ie a pit that is elongated with its major axis parallel to the coastline.
Future investigation of the effect of borrow pits on shoreline changes should include the effects of wave reflection and dissipation.




65
The results presented in this thesis demonstrate conclusively that for pits of realistic geometry, the combination of wave refraction and diffraction are not sufficient to predict realistic shoreline responses.
Additional field data relating shoreline response to borrow pit geometry and wave characteristics will assist in evaluating present capabilities and contribute to the development of improving future predictive procedures.




REFERENCES

Berkhoff, J.C.W., 1972, "Computation of Combined Refraction-Diffracion," Proc. 13th
Inl. Conf. Coastal Engineering, ASCE, Vancouver, pp. 471-484.
Berkhoff, J.C.W., 1976, "Mathematical Models for Simple Harmonic Linear Water
Waves, Wave Diffraction and Refraction," Publication No. 1963, Delft
Hydraulics Laboratory, Delft, the Netherlands.
Bruun, P., 1954, "Coast Erosion and the Development of Beach Profiles," Technical
Memorandum No. 44 Beach Erosion Board.
Combe, A. P. and Soileau, C. W., 1987, "Behavior of Man-made Beach and Dune at
Grand Isle, Louisiana," Coastal Sediments 1987, American Society of Civil
Engineers, New Orleans, pp. 1232-1242.
Dally, W. R., Dean, R. G., and Dalrymple, R. A. 1984, "Modeling Wave Transformation
in the Surf Zone," Miscellaneous Paper CERC-84-8, US Army Engineer
Waterways Experiment Station, Vicksburg, Miss.
Dean, R. G., 1987, "Coastal Sediment Processes: Toward Engineering Solutions,"
Proceedings, Coastal Sediments, ASCE, pp. 1-24.
Dean, R. G. and Charles, L., 1994, "Equilibrium Beach Profiles: Concepts and
Evaluation," Technical Report UFL/COEL-94/013, Department of Coastal and
Oceanographic Engineering, University of Florida.
Dean, R. G. and Dalrymple, R. A., 2002, Coastal Processes with Engineering
Applications, Cambridge University Press, Cambridge, England.
Dean, R. G. and Grant, J., 1989, "Development of Methodology for Thirty-year Shoreline
Projections in the Vicinity of Beach Nourishment Projects," Technical Report
UFL/COEL-89/026, Division of Beaches and Shores, Tallahassee, FL.
Dean, R. G., Liotta, R., and Simon, G. 1999, "Erosional Hot Spots," Technical Report
UFL/COEL-99/021. University of Florida
Ebersole, B. A., Cialone, M. A., and Prater, M. D., 1986, "RCPWAVE-A Linear Wave
Propagation Model for Engineering Use," Technical Report CERC-86-4, U.S.
Army Engineer Waterways Experiment Station, Vicksburg, MS.




Gravens, M. B., Kraus, N. C., and Hanson, H., 1991, "GENESIS: Generalized Model of
Simulating Shoreline Change, Report 2, Workbook and System User's Manual,"
Technical report CERC-89-19, U.S. Army Engineer Waterways Experiment
Station, Vicksburg, MS.
Gravens, M. B. and Rosati, J. D., 1994, "Numerical Study of Breakwaters at Grand Isle,
Louisiana," Miscellaneous Paper CERC-94-16, Vicksburg, MS, U.S. Army Corps
of Engineers.
Horikawa, K., Sasaki, T., and Sakuramoto, H., 1977, Mathematical and Laboratory
Models of Shoreline Change due to Dredged Holes," Journal of the Faculty of
Engineering, the University of Tokyo, Vol. XXXIV, No. 1, pp. 49-57.
Inman, D. L. and Bagnold, R. A., 1963, "Littoral Processes," in The Sea, ed. M. N. Hill,
3, 529-533, New York, Interscience.
Komar, P.D. and Inman, D. L., 1970, "Longshore Sand Transport on Beaches," J.
Geophys. Res., 75, 30, 5914-5927.
McBride, R. A., Penland, Shea, and Hiland, M. W., 1992, "Analysis of Barrier Shoreline
Change Louisiana from 1853 to 1989," U.S. Geological Survey Miscellaneous
Investigations Series 1-2150-A, pp. 36-97.
Moore, B., 1982, "Beach Profile Evolution in Response to Changes in Water Level and
Wave Heights," M.S. Thesis, University of Delaware, Newark, DE.
Motyka, J. M. and Willis, D. H., 1974, "The Effect of Wave Refraction over Dredged
Holes," Proc. 14th International Conference on Coastal Engineering, ASCE,
Copenhagen, 1, pp. 615-625.
Ozasa, H. and Brampton, A.H., 1980, "Mathematical Modeling of Beaches Backed by
Seawalls," Coastal Engineering, Volume 4, No. 1, pp. 47-64.
Penland, Shea, Williams, S. J., and Davis, D. W., 1992, "Barrier Island Erosion and
Wetland Loss in Louisiana," U.S. Geological Survey Miscellaneous
Investigations Series 1-2150-A, pp. 2-7.