• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Acknowledgement
 Table of Contents
 Abstract
 Introduction
 Equilibrium beach profile
 RPCWAVE model
 DNRBS model for calculating longshore...
 Shoreline change considering...
 Example application of the model...
 Some general results for idealized...
 Summary and conclusion
 Reference














Title: Effect of offshore dredge pits on adjacent shorelines considering wave refraction and diffraction
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00091402/00001
 Material Information
Title: Effect of offshore dredge pits on adjacent shorelines considering wave refraction and diffraction
Series Title: Effect of offshore dredge pits on adjacent shorelines considering wave refraction and diffraction
Physical Description: Book
Language: English
Creator: Tang, Yuhong
Publisher: Coastal & Oceanographic Engineering Dept. of Civil & Coastal Engineering, University of Florida
Place of Publication: Gainesville, Fla.
 Record Information
Bibliographic ID: UF00091402
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Page i
    Acknowledgement
        Page ii
    Table of Contents
        Page iii
        Page iv
    Abstract
        Page v
        Page vi
    Introduction
        Page 1
        Page 2
        Page 3
    Equilibrium beach profile
        Page 4
        Page 5
        Page 6
        Page 7
    RPCWAVE model
        Page 8
        Page 9
        Page 10
        Page 11
    DNRBS model for calculating longshore sediment transport
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
    Shoreline change considering geometry
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
    Example application of the model for an actual case
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
    Some general results for idealized cases
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
    Summary and conclusion
        Page 63
        Page 64
        Page 65
    Reference
        Page 66
        Page 67
Full Text



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
page

ACKNOWLEDGMENTS ....................................................... ................................... ii

A B STR A C T ................................................................................................................... v

CHAPTERS

1 IN TR O D U CTION ................................................................................................... 1

Problem Statem ent.................................................................................................. 1
O objectives and Scope.............................................................................................. 2

2 EQUILIBRIUM BEACH PROFILE .............................................................................4

3 R CPW A V E M OD EL............................................................................................... 8

Introduction .............................................................................................. . ............ 8
B background of R CPW A V E ....................................................................................... 8
Assumptions and Limiations................................................................................. 9
G 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 RCPWAVE ............................................................................ 27
Adding Second Term in "CERC" Equation and Comparing the Results ................... 39


7 SOME GENERAL RESULTS FOR IDEALIZED CASES ......................................41

Introduction ........................................................................................................... 4 1








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, ox and oa, 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 (-,) and the greater the standard deviation in the longshore

direction (a-y), the smaller the shoreline changes. The shoreline changes are largest when

the pit shape is approximated by a circular pit (cr = o-, ). Thus the best pit shape is one

with small oc and large ay, 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 length 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 D (d) may be representative of the magnitude of

the destructive force per unit volume.

l dF
D(d)= (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

F 1 pgH2 (2.3)
8

The breaking waves are considered to decay throughout the surf zone according to:

H = Kh (2.4)

Where K is a dimensionless breaking wave constant, usually taken as 0.78. Equation (2.2)

can now be written:

d( pgK2h2 gh)
D,(d) = h -(2.5)
hdy

Taking the derivative and simplifying:


D (d)= 5 2pg2 h2 dh (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,

S24D(d) y = AyY (2.7)
5pggK2

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 = 0.067w044 (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, + ( A)(y y,) (2.9)
Yn+1 Yn


SEDIMENT FALL VELOCITY, w (cm/s)
0 01 0.1 1.0 10.0 100.0
Et 1.0 Suggested Empirical
E Relitionshlp A va. D7
(Moorn) O0
From Hughsrs / Aj0 *
S on Individual Field Field R lsults
E Profiles Where a Rang
S Slland Szes was Glv l
< 0.10
DB oA an' ranstftming
a A v.DCu veUslling



n 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,,-,. 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 yn+, is calculated as follows:


hn, = {hK + 2 [A -A5]
5m,,


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


(A,,, A)
mn =(1 -A)
Yn+, Y,


(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 m3 ) (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
0210


0.01
0.0672
0,103
0.127
0.1466
0.1622
0.1742
0.1859
0.1948
0.2028
0.2108


__


e


~


~-~--


.~..













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 bottom-

induced 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


(CC )+ -(CC )+ K2CC = O (3.1)
ax ax y 3 ay









where x and y are two orthogonal horizontal coordinate directions; C is wave

celerity; Cgis group velocity; K is wave number and 0 is the complex velocity

potential.

The velocity potential function is

S= ae (3.2)

where a is a wave amplitude function (a=gH/2 c), 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 12 2
-{ +- + -C -[Va V(CC )]} + K2 -Vs 0 (3.3)
a Q2X Q y CCg

a a
(Vs sin )-- (Vs cos0) = 0 (3.4)
ax ay

-(a2CCg, Vs cos0)+-a2(a2CCg Vs sinO) = 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.

KP,
Q KP= (4.1)
(p., p)g( 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, = F cosOsinO = pgH2C, sin 20b (4.2)

where Ob 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 = gh) and = Hb/h, where Hb is the

breaking wave height and K is the breaking index, the CERC equation becomes:

KH Y% gK sin(l ab) cos( ab) )
8(s --1)(1-- p)

where the subscript 'b' denotes breaking conditions, s is the sediment specific gravity

(p, p p 2.65) of the water in which it is immersed, P 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 a,,, p/ and









/ in which p/ is the azimuth of general alignment of the shoreline as defined by a

baseline, and


xr x
p =/u -- tan ( )
2 ay


0

Q


Reference
Base Line


-Shoreline





+Q


(4.4)


Figure 4.1, Definition sketch (for waves and shoreline orientation)
(Dean and Grant, 1989)


The conservation of sediment equation is

8Q 8v
OQ = a- (4.5)
By 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 =A (4.6)
h. +B

Substituting Equation (4.6) into (4.5), the conservation of sediment equation then

becomes

6x 1 Q
-+ -= 0 (4.7)
at h. +B oy

Assuming energy conservation and Snell's law, Equation (4.3) can be expressed in

terms of deep water conditions as follows

KH.4 C.g2 0.4 cos1.2(0 -ao)sin(,0 -a.)
Q 0 (4.8)
8(s 1)(1 p)C.ICK04 Cos(,0 ab)

and

C*
a. = ,o -sin-'[-sin(f0 a)] (4.9)
Co

where the subscript "0" denotes deep water conditions and C. is the wave celerity in

water depth, h,.

Because cos(0o -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)
2G

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

KHYJ2 K
G= KH-gb K (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) (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 C,,

3. The equation is more physically clear.































FRF












.. DUCK, NC
Wa'sRftraction Diagr
: ., ,.- "'' Period (reC) 2
Angle (deg)- -20






Figure 5.1, Wave rays at Duck, North Carolina
(Ebersole, Cialone and Prater 1986)









Y-AXIS


X-AXIS DUCK PIER. NORTH CAROUNA BATHYMETRY
DEPTHS ARE METERS BELOW MSL


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

1100

1000 -

900 8027

800 2.50062 2

c 700 .303
1.9 2
600 17

500 -
0
400
S. 4 8 0 2 7
300
2.2 156
200

100
0 I ,I I I IrI 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, ao =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


GULF OF MEXIX)I /









GRAND ISLE, LOUISIANA
SCALE
) 5BOU I0m0oe zm0


*4IU ,q2.40.









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
















1885


Figure 6.2, Pit geometry at Grand Isle





27



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)













-* ..















(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
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












12000

11000

10000

9000

, 8000

7000

6000

5000

4000

3000

2000

1000

0


I I


I I I


I I I I I


-10 0 10
Shoreline Change (m)


Figure 6.6 Shoreline changes for a normal incident wave before 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)


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


~c-





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

-10


Pit Centerline


`-------~_ ----_
<^^" ~______-~~


I I I I i i


I I I I I I I I I I


-5 0 5 11
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


ai = 1/ 3(a,_ + a, + a,,)





32



diffraction and possibly other processes. In the RCPWAVE 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












, I , I


0.4 0.6 0.8
Breaking Wave Height (m)


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 1 1 ,,1 ,,,


IIIIHII


ri l l ll.l.l l T


2


I









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,j = 1/ 8(h,_-1 + 4h,, + hi+, + h,_j- + h,,J) (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

S7000

5 6000

0
S5000

= 4000

3000

2000

1000


Pit Centerline


I I I


3


f


? I I I I I I r I I I T I


. I, I . I 1 , ,


I I


%0


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

S7000

5 6000

5000

=. 4000
CO
3000

2000

1000


nt1


Pit Centerline

<"-_


SI


. .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













12000

11000

10000

9000

E 8000

r 7000

S6000


0
S5000

. 4000

3000

2000

1000

0


MM


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)


i n I I I I I I I


SI


I















12000

11000

10000

9000

8000

S7000

a 6000

5000 o

4000

3000

2000

1000

-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



7000


0 a (Positive)
6000
6. a (Negative)



5000



4000

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,









KH5 glc sin(O-ab)cos(O-a) K2Hb,5 g/Kcos(O -ab) dHb
8(s 1)(1- p) 8(s 1)(1 p) tan(7) 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

S8000

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-xo)2 (y-yo)2
h(x, y) = h + h e 2<'x 2y2

In which 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, yo is the distance from the center of pit to the X axis (offshore

direction) and o, and ay 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
S9000 1
,S 8000 i I __ a (Positive)
a 7000 -
S7000 a (Negative)
6000 -
o 5000
4000
3000 xo-
2000
1000 -

5000 10000 15000
Offshore Distance X (m)




Figure 7.1 Sketch for normal distribution pit
(ox = 400 m, o-=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 P 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, -x = 200 m, r-,= 1,200 m and y = 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 m and

3,600 m.

Figure 7.2 shows the shoreline changes for x0=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 x0 =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 x0 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

10000

e 8000

o 6000

4000

2000


---S .



Vy/t

r


I I I I i i I i i i


I I I II


U
-3 -2 -1 0 1 2
Shoreline Change (m)


Figure 7.2 Shoreline changes at x0 =1400 m, pit centerline at y=9000 m
(h= 8 m, Ah= 6 m, o- = 200 m, -y= 1,200 m, T=10 s, H =1 m)














18000

16000

14000

12000 -


S 000

S8000

o 6000
C,,
4000

2000 -


-0.4 -0.2 0 0.2
Shoreline Change (m)


Figure 7.3 Shoreline changes at x0 =2200 m, pit centerline at y=9000 m
(h= 8 m, Ah=6m, = 200 m, a-= 1,200 m, T=10 s, H =1 m)
















0 -








-1*
-0.5







S-1.5

-,
0

E -2

0/


-2.5 -


3 I I l I i lI i l i Il i i I , I , , I ,

0 500 1000 1500 2000 2500 3000 3500
Offshore Distance, X (m)



Figure 7.4 The largest shoreline recession for different x0
(h= 8 m, Ah= 6 m, = 200 m, o-= 1,200 m, T=10 s, H =1 m)















1.5











S0.5
E






0 500 1000 1500 2000 2500 3000 3500
Offshore Distance, X (m)


Figure 7.5 The largest shoreline advancement for different x0
I-









0 500 1000 1500 2000 2500 3000 3500
Offshore Distance, X (m)


Figure 7.5 The largest shoreline advancement for different x0
(h= 8 m, Ah= 6 m, o- = 200 m, o-= 1,200 m, T=10 s, H =1 m)

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, cr and o, 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 1V
Depth of Pit (m)



Figure 7.6 The maximum shoreline recession versus pit depth
(h = 8 m, cr = 200 m, o = 600 m, T=10 s, Ho =1 m)












10-

9 -

-8

E 7
) 6


5

0 4

E -







0 5 10 15
Depth of Pit (m)


Figure 7.7 The maximum shoreline advancement versus pit depth
3-: y/
)4- /
S- /
I /






0 5 10 15
Depth of Pit (m)


Figure 7.7 The maximum shoreline advancement versus pit depth
(h= 8 m, = 200 m, o-= 600 m, T=10 s, H =1 m)

7.2.3 Effect of Pit Size and Shape on Shoreline Changes

The borrow pit size and shape will affect the shoreline changes. By changing o-x and

ay for several cases, basic trends can be obtained showing the effect on shoreline change

due to different pit size and shape. For the numerical model, the base conditions for water

depth and wave criteria are the same as previous cases. x0 = 3600 meters, Ah equals 6

meters. Seventy different cases are calculated with cx ranging from 200 m to 800 m, and









C, 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 ac equals 800 m, ac equals approximately 600 m and 200 m.

Beach recession is largest for o, larger than ay,. Figure 7.9 shows that there are two

maximum shoreline advancement peaks located on x = 800 m and oy =700 m and


1200

1100

1000

900

800

700

600

500

400

300

200


500 1000
o (m)


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









a,=400 m. Again shoreline advancement is largest if o, is larger than oy. For ox

less than 200 m and cr greater than 800 m, the associated beach recession and

advancement are quite small. Therefore the best pit shape is one with small Cx and

large o-, ie a pit that is elongated with its major axis parallel to the coastline.






1200 -

1100 -

1000 -

900

800
z 700 14"
2:!* IP INV
700


500

400

300

200
500 1000
ox (m)


Figure 7.9 The maximum shoreline advancement versus the sizes of the pit in the x and y
dimensions (x = 3600 m, h= 8 m, Ah= 6 m, T=10 s, H =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 ox = 400 m and ca,=1,100 m, and Case 2 is ox= 800 m

and ca,=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 y .






15000
14000
13000
12000
11000
E 10000
8 000

S8a (Positive)
7000 a (Negative)
S6000
0
o 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, xo= 3600 m, a,= 400 m and a,=1,100 m, T=10 s, H0=1 m)












15000
14000
13000
12000
11000
E10000 -
S9000

. 8000
S7000
S6000
o
S. 5000
4000
3000
2000
1000
0-1
-1.5


Pit Centerline


-1 -0.5 0 0.5 1 1.i
Breaking Wave Angle (degree)


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



















K


-------------------------------


15000
14000
13000
12000
11000
E10000

1 9000
C
a 8000
S7000
S6000
o
.. 5000
4000 -
3000
2000
1000

.15


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, xo= 3600 m, o,= 400 m and o-=1,100 m, T=10 s, H =1 m)


jj


(



I I i I


Pit Centerline


I I I I I


1.45 1.5


I I I I I


i l li i i i i i iil i- i il . . . .











15000
14000
13000
12000
S11000
'10000
9000




o 5000 -
4 4000
3000
2000
1000

0 5000 ) U-2

3000
2000
1000
0
-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= 6 m, xo= 3600 m, o-= 400 m and o-=1,100 m, T=10 s, H =1 m)












15000
14000
13000 i
12000 Il,l


I10000 375 551'
12000
11000 -. . 0


S70000
S6000 .

L-
5 8000 0

3000
2000
000 5 10 0
4000 i 102625
3000
2000 !
1000

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, x0= 3600 m, o-= 400 m and oy=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
>--
S9000
2 8000
a 7000
S6000
o 5000
S4000
3000
2000
1000
0
-5


-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 cry=1,100 m, T=10 s, H =1 m)













9000

8000

7000

6000

. 5000 a-~ (Positive)
0 :a (Negative)
4000

C) 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, x= 3600 m, o-,= 800 m and o =600 m, T=10 s, H0=1 m)















9000


8000

7000
E
6000


.T 5000


- 4000
o
c 3000


2000


1000


, I ,. , I .


--~-~-~-c~-~~'-~


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


. i i r i l l l. l l lr. Ir.i l l l l r l l


Pit Centerline


I . . I . . I I I


-15


On


-5 0 5
Breaking Wave Angle (degree)













9000

8000

7000 -

a 6000 -

. -5000 f Pit Centerline

= 4000

S3000

2000

1000


%.2 0.4 0.6 0.8 1 1.2 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
(h= 8 m, Ah= 6 m, x = 3600 m, o, = 800 m and o,=600 m, T=10 s, Ho =1 m)













9000

8000 -


7 000 .

6 4000

5000 -



3000
u,
2000 ..


1000


-30 -20 -10 0 10 20 30
Shoreline Change (m)


Figure 7.19 Shoreline change for Case 2
(h= 8 m, Ah= 6 m, x = 3600 m, o,= 800 m and coy=600 m, T=10 s, H =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 (rx)

and the greater the standard deviation in the longshore direction (a,), 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 ox and

large cry, 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 I-2150-A, pp. 2-7.




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs