UFL/COEL-86/019

SEDIMENT BUDGET
PRINCIPALS AND APPLICATIONS

By

Robert G. Dean

November, 1996

SEDIMENT BUDGET

PRINCIPLES AND APPLICATIONS

BY

R.G. DEAN

PUBLISHED IN DYNAMICS OF SAND BEACHES, INTERNATIONAL

CONFERENCE ON COASTAL ENGINEERING (ICCE) 20th TAIPEL,
R.O.C. NOV., 1986.

TABLE OF CONTENTS

CHAPTER PAGE
SEDIMENT BUDGET PRINCIPLES AND APPLICATIONS..................... 3
INTRODUCTION................................................. 3
GOVERNING EQUATIONS.......................................... 3
Integrated Form of the Governing Equation................. 4
Application..... ......................................... 6
EQUILIBRIUM BEACH PROFILES........... ...................... 11
Introduction.............................................. 11
Equilibrium Beach Profile Characteristics................. 11
Applications of Equilibrium Beach Profiles................ 19
Required Beach Nourishment Volumes..................... 19
Response to Sea Level Rise................................ 22
Volume of Sediment Transported Offshore to Various
Depths Due to Sea Level Rise........................... 22
Additional Applications of Equilibrium Beach Profiles..... 26
ADDITIONAL USEFUL APPROXIMATIONS IN SEDIMENT BUDGET
CALCULATIONS............................................... 26
Volumetric Changes Associated with Shoreline Changes...... 26
APPLICATIONS... .......................... .................. 27
South Shore of Long Island. .............................. 27
Brevard County, Florida................................... 30
Ocean City Inlet, Maryland................................ 37
Cross-Shore Distribution of Longshore Sediment Transport.. 40
Entrance to St. Andrews Bay, Florida...................... 44
Rudee Inlet, Virginia..................................... 48
SUMMARY ................................................ ..... 48
REFERENCES................................................... 51

CHAPTER

SEDIMENT BUDGET

PRINCIPLES AND APPLICATIONS

by

R. G. Dean

INTRODUCTION

The framework of sediment budget concepts provides a formalized procedure

to account for the various components of sediment flux and the changes of

volume that occur within a given region. Sediment budget methodology can be

useful in a number of coastal engineering and research applications,

including: inferring the amount of onshore sediment transport for a nearshore

system that contains an "excess of sediment", determining sediment deficits to

downdrift beaches as a result of engineering works at navigational entrances,

evaluating the performance of a beach nourishment project, inferring the

distribution of longshore sediment transport across the surf zone, etc.

This chapter reviews briefly the governing equations for sediment budget

calculations, considers various measurement and other bases for determining

the sediment flux components necessary to apply the sediment budget concept

and finally for illustration purposes, applies the sediment budget concept to

several examples.

GOVERNING EQUATIONS

The governing differential equation for a sediment budget expresses

conservation of sediment volume as

-+ j q S (1)

CHAPTER

SEDIMENT BUDGET

PRINCIPLES AND APPLICATIONS

by

R. G. Dean

INTRODUCTION

The framework of sediment budget concepts provides a formalized procedure

to account for the various components of sediment flux and the changes of

volume that occur within a given region. Sediment budget methodology can be

useful in a number of coastal engineering and research applications,

including: inferring the amount of onshore sediment transport for a nearshore

system that contains an "excess of sediment", determining sediment deficits to

downdrift beaches as a result of engineering works at navigational entrances,

evaluating the performance of a beach nourishment project, inferring the

distribution of longshore sediment transport across the surf zone, etc.

This chapter reviews briefly the governing equations for sediment budget

calculations, considers various measurement and other bases for determining

the sediment flux components necessary to apply the sediment budget concept

and finally for illustration purposes, applies the sediment budget concept to

several examples.

GOVERNING EQUATIONS

The governing differential equation for a sediment budget expresses

conservation of sediment volume as

-+ j q S (1)

in which z is the vertical coordinate of the bottom, q is the sediment

transport vector with components (qx, qy) and S represents a source of sand

per unit area, see Figure 1. Eq. (1) can also be expressed in terms of the

water depth, h, referenced to a fixed datum,

-h S (2)

or in expanded form

ah x q+ -S (3)
3t ax Sy

Integrated Form of the Governing Equation

In some cases, it is possible to apply Eq. (2) directly; however, usually

the data available for use in the conservation equation or information

required from application of the equation are such that an integrated form is

more useful. Integrating Eq. (2) across the beach from xl to x2,

x2 x2 x2
--f h dx = q -x +x qy dx f S dx (4)
X 1 1 ax x1

in which qx x2 and qx Ix represent the transport per unit width in the

offshore direction at the seaward and shoreward ends of the control volume

respectively. The first integral term represents the water area, A, between

the sand level and the vertical datum, z=0. If onshore transport occurs at

the seaward limit of the control volume, then qx x2 < 0 and if landward

transport of sand occurs due to overwash processes or wind blown sand,

then qxxl < 0. If fill were added to the profile, then S > 0. Equation (4)

may be useful to apply in this form. However, in some applications, it is

helpful to integrate Eq. (4) in an alongshore direction between coordinates yl

and y2; the result is

Figure 1. Definition Sketch for Sediment Transport Considerations.

S(Y2 1 y x xI -x x2 y y + (5)

in which Qy(y2) and Qy(Y1) represent the total longshore fluxes of sediment

passing through the control volume boundaries at y = yl and y y2. The

quantity represents the total sand volume (referenced to some vertical

datum) within the control volume and *A is the amount of volume added.

Finally, since volume changes are usually observed over some time period

At(= t2 tl), in these applications it is appropriate to integrate Eq. (5)

over time interval, At, which yields

= (Y2- y1) At [q xx2- qx xl] [Q(Y2) (y1)] At + AVA (6)

Application

Prior to proceeding further it may be useful to illustrate an immediate

application of Eq. (6).

The Nearshore Sediment Transport Study (NSTS) included a field program at

Santa Barbara, California to provide data to calibrate the total longshore

transport equation,

Qy K P2s (7)

in which PIs is the so-called longshore energy flux factor at the wave

breaking line and Qy is the associated total longshore sediment transport.

The field site including the location of the directional wave gage used

in the correlation and the survey lines are presented in Figure 2. In this

example, the survey lines extended sufficient distances offshore and upland to

East Beach

S 50 meter Nominal Spacing

+ = Sxy Wave Array

0 250 500
scale in m

Santa Barbara Survey Plan and Location of Sxy Wave Gages.
xy

Figure 2.

encompass the entire limit of profile change; thus qx xl -x qx x2 0.

Additionally, the navigational channel at the east end of the spit was

considered (and believed to be) a complete barrier to longshore sediment

transport (Qy(Y2) = 0) and there were no sediment additions or removals to the

system (AVA) = 0. Therefore Eq. (6) simplifies to

A = Q(yl)At (8)

which simply expresses that the change in volume is due to the influx of

sediment at an average rate Qy(y1), where yl is the location of the wave

gage. Thus, the coefficient K can be determined by combining Eqs. (7) and

(8).

t2 t2
I Qydt = f K Psdt
t t
1 1

t2
J Qydt
K =-2 (9)
t2 t
SPsdt f Psdt
t t

such that the numerator is determined from the field surveys and the

denominator from the directional wave gage. The results from this study are

presented in Table I and Figure 3.

Prior to presenting more examples, it may be useful to review various

approaches to augmenting limited data to provide the necessary components in

the sediment budget expressions. Because so many useful results can be

obtained from equilibrium beach profile concepts, a summary will be presented

in the next section.

Santa Barbara Field Results

Net Onshore
Immersed Net Longshore Flux of
Weight Component of Longshore K* I/Sxy
No. Total Transport Wave Energy K It/Pts Component of
Intersurvey of Dredging Volume Rate Flux at Breaking Momentum (m/s)
Perioo Days Event Change(m3) I (N/s) P.s (N/s) Sxy (N/m)

Oct. 13, 1979- 48 No 32,820 85.3 52.2 1.63 27.8 3.06
Nov. 30, 1979

Dec. 1, 1979- 31 Yes, 65,070 159.1 101.4 1.57 45.4 3.50
Jan. 20, 1980 Major

Jan. 21, 1980- 35 Yes, 82,810 295.0 352.4 0.84 119.6 2.47
Feb. 25, 1980 Minor

Apr. 11, 1980- 53 No 10,290 24.2 76.6 0.32 37.9 0.64
June 3, 1980

June 4, 1980- 82 No 22,220 33.8 31.7 1.07 17.6 1.91
Aug. 25, 1980

Aug. 26, 1980- 57 No 38,760 84.8 63.8 1.33 32.6 2.60
Oct. .23, 1980

Oct. 24, 1980- 54 Yes, 35,640 84.6 64.4 1.31 34.2 2.47
Dec. 17, 1980 Major

Table I

- Summary of

100
P (N/S)

1000

Data from Santa Barbara (*) and Rudee Inlet (o) Field Experiments.
I, vs Pts, Present and Past Correlations.

Figure 3.

EQUILIBRIUM BEACH PROFILES

Introduction

Beach profiles in nature are continuously evolving under the varying

action of waves, currents, tides and sediment supply which here will be termed

the "forcing functions". If the "forcing functions" were maintained constant,

the profile would stabilize into a so-called "equilibrium beach profile",

although the equilibration time could be very long. A knowledge of

equilibrium beach profiles is useful both in interpreting natural beach

conditions and in engineering applications. Problems which can be addressed

through equilibrium beach profiles include: beach restoration with a sand of

arbitrary size, response of natural or seawalled shorelines to storms and

tides, the effects of changes in wave characteristics and thus the seasonal

variations in beach profiles, response to sea level rise, and finally through

a knowledge of equilibrium beach profiles, it is possible to formulate and

test hypotheses on the response of profiles out of equilibrium. One

limitation of most presently available equilibrium profile forms is that they

are monotonic whereas many profiles in nature are seasonally or perennially

barred.

Equilibrium Beach Profile Characteristics

Studies, encompassing several thousand beach profiles from nature and

laboratory (with by far a predominance from nature) have demonstrated that

most beach profiles can be represented well by the monotonic form

h(x) Ax2/3 (10)

in which h(x) is the water depth at a distance, x, offshore and A is a so-

called "scale parameter". It is noted that the parameter A has dimensions of

length to the one-third power (i.e., ft1/3 or m1/3). It can be shown from

linear wave theory that Eq. (10) is consistent with uniform wave energy

dissipation per unit water volume in the surf zone. Figure 4 shows the origin

of one set of field profiles exceeding 500 in number. This set extended from

the eastern end of Long Island to the Texas-Mexico border.

Figures 5, 6, 7 and 8 present examples of the fits to various averaged

and individual profiles that were used in an assessment to determine the scale

parameter. Figure 7 is of special interest in that the sizes of the "sand

grains" ranged from 10 to 30 cm in diameter, approximately the size of bowling

balls!

Most engineering applications require knowledge of the scale parameter

"A" in Eq. (10). The analyses carried out have shown that A depends primarily

on the sediment size and only secondarily on wave conditions. Figure 9

presents A vs D which was the first relationship developed and is recommended

if no information is available describing the particular wave height

characteristics. It is evident from this figure that beaches composed of

larger diameter sediments are steeper, i.e., characterized by larger A values

whereas finer grained beaches are characterized by smaller A values and thus

are milder in slope. The second representation of A is presented in Figure 10

and includes effects of both sediment size, here represented as the fall

velocity, w, and waves, i.e., the breaking wave height, Hb, and wave period

T. Examination of Figure 10 will demonstrate the following variation of beach

slope with various parameters.

Location Map of the 502 Profiles Used in the Analysis (From Hayden,
et al.).

Figure 4.

DISTANCE OFFSHORE (ft)
400 600 800

Data Group I
N =35
h = 0.398 x0533

Data Group II
N =43
h = 0.079xO822

Data Group I
N = 38 0762
h = 0.095 x

O0 Data Group "Z

h = 0.128 XO709

10 -
Data Group Z
N=14
h = 0.243 x.523
Average Profile for Group
Reference Profile (Average of All 502 Profiles)
& A Computed Profile from Given Equation of Form: h= Axm

Figure 5. Comparison of Beach Profiles .for Data Groups I-V (From Dean, 1977).

DISTANCE OFFSHORE (ft)
400 600 800

1000

1200

U I-I- III
Data Group I
N =234
h =0.255x0.594
0-

0(O------- I^ ^ ^c '-^

Data Group 3II
N= 10

Data Group =3ZI
N=34
h = 0.277x0.554

Data Group IK
N =38

Data Group I
N = 27

Average Profile for Group
-- Reference Profile (Average of All 502 Profiles)
A a Computed Profile from Given Equation of Form: h= Ax

Figure 6. Comparison of Beach Profiles for Data Groups VI-X (From Dean,
1977).

I
I-
a-
w
0
LJ
Q

f

200

DISTANCE OFFSHORE(m)
25.00

- Least Squares Fit
Actual Profile

Profile P4 (From Zenkovich, 1967).
Kamchatka. Sand Diameter: 150 mm -
of A = 0.82 m1/3 (From Moore, 1982),

A Boulder Coast in Eastern
300 mm. Least Squares Value

DISTANCE OFFSHORE (m)
60.00

---Least Squares Fit
Actual Profile

Profile P10 (From Zenkovich, 1967). Near the End of a Stit in
Western Black Sea. Whole and Broken Shells. A = 0.25 m173
(From Moore, 1982).

50.00

Figure 7.

Q,
E

w

w
!LJ
3.5

Figure 8.

E

i--

Ln
_J

U
1-
z

0

Beach Profile Factor, A, vs Sediment Diameter, D, in Relationship h = Ax2/3 (Modified From Moore,
1982).

1.0-

0.10-

0.01-
0.01

0.1 1.0 10.0 100.0
SEDIMENT SIZE, D(mm)

Figure 9.

,Normal Profile I Storm Profile,

cr
w
H

0

U
_1
<

6-
LIJ

w
Co

0.5-
SHb= Breaking Wave
Height
T = Wave Period
Sw = Sediment Fall
Velocity

0.10

0.05

0.01
.01

(No Bar)

- V ..........N-

I I I I III

Bar Present

I I I I lI II* _

Recommended
Relationship

From Hughes'
Field Results

___________________________________ 4

I I

I u I sI ll

From Swart's
Laboratory Results

I I

I I I j l ,

I I I I 'I I l l

.10 1.0 10.0

FALL VELOCITY/ WAVE CHARACTERISTICS
(Hb/wT)

Figure 10.

PARAMETER,

Correlation of Equilibrium Beach Profile Scale Parameter, A, with Combined Sediment/Wave
Parameter, Hb/wT.

h(x)= Ax/3

(2) A < AN

In this case, with a finer sand placed in the nourishment process than is

naturally present on the beaches, the nourished profile will be characterized

by a milder slope than the native. The required volume per unit length of

beach is

[AN (Ax + W,513 AB (W,)5/3] + B Ax (12)

it is seen that Eq. (A-3) reduces to Eq. (A-2) for the case of AN = AB.

(3) AB > AN

In this case, with the placed material being coarser than the native, the

two profiles may or may not intersect, depending on the geometry. Thus

consideration of two sub-cases is required.

In the first sub-case, the two profiles do not intersect. In this case,

the volume required per unit length of beach is the same as for Case 2, in

which the profiles do not intersect, i.e.,

S=I [AN (Ax + W,)5/3 A (W,)5/3] + B Ax (13)

In the second sub-case, the profiles intersect at h', so sand is only required

shoreward of this location, see Figure 11.

The required volume is

V 3 h'W' + B Ax (14)
5

where h' is determined by solving the following equation, first for W'

h' AN (Ax +W')2/3 '2/3 (15)

which yields

1 Ax (16)
A 2/3
---) -1
AN

20

Large fall velocities (large diameter sediment)

Steep Slopes Small wave heights

Long wave periods

Small fall velocities (small diameter sediment)

Mild Slopes Large wave heights

Short wave periods

It is noted that all of the above interrelationships are in accord with

observations in nature of the variation of wave profiles with wave and

sediment characteristics.

Applications of Equilibrium Beach Profiles

Some of the applications of equilibrium beach profiles will be developed

below.

Required Beach Nourishment Volumes This problem must be considered for three

separate cases: (1) AB = AN, (2) AB < AN and (3) AB > AN, where the subscripts

"B" and "N" denote "borrow" and "native", respectively and A is the profile

scale parameter discussed earlier.

(1) AB=AN

For this case, the native and nourished profiles would be of the same

form. The required volume, I-, per unit length of beach would be
3A [(Ax + W,5/3 5/3
S= -- [(x + W)53 3] + B Ax (11)

in which Ax = shoreline advancement
h, = effective depth of limiting motion
B = berm height
W, = width of the nourished surf zone (i.e., out to h*).

h-6x

a) Sub-Case in which Two Profiles do not Intersect, h* > h'.

W i

b) Sub-Case in which Two Profiles Intersect, h' < h*.
Figure 11. Two Sub-Cases of AB > AN.

and h' can thus be determined as

h' -A [ (17)

() -1

and h' < h*, Profiles do not intersect Eq. (13)

h' > h,, Profiles intersect Eq. (14)

Response to Sea Level Rise

It can be shown that with no additions to or losses of sand from a

profile, a rise of sea level, S, will cause a retreat, R, given by the

implicit equation,

R S 3 h* 5/3
S B B [1 (1 ) ] (18)
W* B 5B W*

It can be shown that for retreat magnitudes, R, which are small compared

to the surf zone width, W*, Eq. (18) simplifies to

W,*
R = S h + B (19)

which is recognized as the so-called "Bruun Rule" presented by Bruun in 1962

to represent this phenomenon.

Volume of Sediment Transported Offshore to Various Depths Due to Sea Level

Rise The case just considered results in an offshore transport of sediment

due to sea level rise. However, if there are no longshore gradients of

sediment transport, there is no loss of sediment along a profile and accurate

consecutive surveys encompassing the entire region of profile change

referenced to the same vertical datum should result in the same total volume.

Of relevance to the present study is the case in which the profiles do

not extend a sufficient distance offshore to encompass the entire region of

profile change. For example, if the surveys extended only out to the profile

intersection point, the apparent volumetric loss would be the hatched area

above the intersection point in Figure 12.

It can be shown that the non-dimensional apparent volume loss is

approximately

3/2
VE (B/h, + h /h) h 3/2
= (B/h + ) ( (20)
WS (B/h, + 1) h

in which hS is the offshore depths to which the surveys are conducted. The

profile intersection depth, hl, referenced to the datum before the sea level

rise is approximately

hi 4 1 (21)
h2 9(21)
h* 9 (1 + B/h)2

In Eq. (20), the quantity W*S is the nominal amount usually referenced as the

volumetric erosion due to sea level rise.

To examine Eq. (20) further, Figure 13 presents the non-dimensional

apparent volumetric erosion VE/(W*S) vs hS/h* for ratios B/h* of 0 and 0.25.

It is seen that the greatest volume of apparent erosion possible (and only if

the surveys were carried out precisely to the intersection point) are 15% and

20% of the nominal value respectively for B/h* values of 0 and 0.25. The

reason for this can be determined by examining the effects of shifting a

profile vertically upward (due to sea level rise) and landward (to conserve

Portion of Profile
over which Erosion
Occurs

Portion of Profile over
which Deposition Occurs

Figure 12.

Definition Sketch Showing Portions of Profile over which Erosion and Deposition Occue Due to a
Landward and Upward Profile Translation.

___ CS ___

Rwa
(... ---F- W .
"I; ^ _
^T

NON-DIMENSIONAL

Figure 13.

SURVEY DEPTH, hs/ h.

Relationship of Non-Dimensional Apparent Eroded Volume to
Non-Dimensional Survey Depth.

sediment). The apparent total erosion due to a vertical displacement S is

clearly W*S; however, when the profile is also shifted landward not only is

the net erosion reduced (indeed to zero), but the local erosion (landward of

the limit of offshore motion) is reduced substantially relative to W*S.

Additional Applications of Equilibrium Beach Profiles

Additional applications of equilibrium beach profiles that will only be

mentioned here include: the response of natural and seawalled profiles to

storms and sea level rise and providing a basis for examining the transient

response of profiles, i.e., profiles that are not in equilibrium. The reader

is referred to Dean (1983) for additional information.

ADDITIONAL USEFUL APPROXIMATIONS IN SEDIMENT BUDGET CALCULATIONS

This section presents a number of useful approximations and aids in

supplementing limited data in order to carry out sediment budget calculations.

Volumetric Changes Associated with Shoreline Changes

In many cases, there may be data available for shoreline changes, but not

volumetric changes. If the profile remains unchanged as the profile advances,

the associated volume change, per unit length of beachfront, AV, is

A- = (h, + B) Ax (22)

such that an advancement (retreat) of the beach would be associated with a

gain (loss) of volume. In the case in which an entire barrier island is

advancing (retreating) without change of form, then the change of volume is

(Figure 13)

A = (h, h* ) Ax (23)
o b

in which the subscripts "o" and "b" denote ocean and bay, respectively.

APPLICATIONS

One application of the sediment budget concept was presented

previously. This section presents several additional specific examples.

South Shore of Long Island

The south shore of Long Island is 134 km in length and due to the impact

of a number of major storms, several surveys have been conducted since 1933,

although the quality of the more recent data is much better than the earlier

data.

Briefly, referring to Figure 14, the net transport along the shoreline is

from east to west and shoreline surveys indicate that there is not sufficient

erosion to provide the quantity of sediment transport documented at Fire

Island Inlet (approximately 350,000 m3/yr). This strongly suggests an onshore

transport of sediment of considerable magnitude. Two time periods of

reasonably high quality are available: 1940-1955 and 1955-1979. The onshore

sediment transport, qx(x2), is inferred from Eq. (6) as

x 2 y)- (t2- t) I xl 2 y) + Oyly1 Oyjy -A* (24)

Applying the above equation to the data presented in Table II from the two

time periods results in a substantial variation of the onshore sediment

transport, i.e.

sediment). The apparent total erosion due to a vertical displacement S is

clearly W*S; however, when the profile is also shifted landward not only is

the net erosion reduced (indeed to zero), but the local erosion (landward of

the limit of offshore motion) is reduced substantially relative to W*S.

Additional Applications of Equilibrium Beach Profiles

Additional applications of equilibrium beach profiles that will only be

mentioned here include: the response of natural and seawalled profiles to

storms and sea level rise and providing a basis for examining the transient

response of profiles, i.e., profiles that are not in equilibrium. The reader

is referred to Dean (1983) for additional information.

ADDITIONAL USEFUL APPROXIMATIONS IN SEDIMENT BUDGET CALCULATIONS

This section presents a number of useful approximations and aids in

supplementing limited data in order to carry out sediment budget calculations.

Volumetric Changes Associated with Shoreline Changes

In many cases, there may be data available for shoreline changes, but not

volumetric changes. If the profile remains unchanged as the profile advances,

the associated volume change, per unit length of beachfront, AV, is

A- = (h, + B) Ax (22)

such that an advancement (retreat) of the beach would be associated with a

gain (loss) of volume. In the case in which an entire barrier island is

advancing (retreating) without change of form, then the change of volume is

(Figure 13)

A = (h, h* ) Ax (23)
o b

in which the subscripts "o" and "b" denote ocean and bay, respectively.

APPLICATIONS

One application of the sediment budget concept was presented

previously. This section presents several additional specific examples.

South Shore of Long Island

The south shore of Long Island is 134 km in length and due to the impact

of a number of major storms, several surveys have been conducted since 1933,

although the quality of the more recent data is much better than the earlier

data.

Briefly, referring to Figure 14, the net transport along the shoreline is

from east to west and shoreline surveys indicate that there is not sufficient

erosion to provide the quantity of sediment transport documented at Fire

Island Inlet (approximately 350,000 m3/yr). This strongly suggests an onshore

transport of sediment of considerable magnitude. Two time periods of

reasonably high quality are available: 1940-1955 and 1955-1979. The onshore

sediment transport, qx(x2), is inferred from Eq. (6) as

x 2 y)- (t2- t) I xl 2 y) + Oyly1 Oyjy -A* (24)

Applying the above equation to the data presented in Table II from the two

time periods results in a substantial variation of the onshore sediment

transport, i.e.

Montouk
Point

Shinnecock
Inlet

Moriches
Inlet

t f %

Fire Island
Inlet

Figure 14.

0 10 20km
I I I I I I I I I I I

The South Shore of Long Island and the Questions of the Magnitude of Net Onshore Sediment
Transport.

Table II

SUMMARY OF SEDIMENT BUDGET ANALYSIS
MONTAUK POINT TO FIRE ISLAND INLET

(4) (5) (6)

STime Span

Number
of Years

Net Change
Change
(yd /yr)

Fill
Additions
(yd3/yr)

Washover
Aeolian
Transport
(yd /yr)

Inferred
Allowance For Transport Transport
Sea Level Rise Past Democrat Onshore.
(yd3/yr) Point (yd3/yr) (yd3/yr)

1940-1955 15.4 1,356,929 313,032 94,330 64,606 0 1,.359,349

1955-1979 24.5 7,501 420,444 32,825 64,606 400,000 294,710

1940-1979 39.9 528,333 378,987 56,564 64,606 245,614 705,622

Inferred Onshore Transport Rate (Column (8)) = Column (3) 0.5 x Column (4) + Column (5)
+ Column (6) + Column (7).

Inferred Onshore
Time Period Sediment Transport

1940-1955 1,040,000 m3/yr

1955-1979 225,000 m3/yr

Based on these results, it was concluded that the onshore sediment

transport was episodic and possibly the result of infrequent storm conditions

or highly varying storm seasons. Also, the representative annual onshore

sediment transport, based on a weighted average of the above two values is

540,000 m3.

In applying and interpreting the sediment budget approach, it is always

useful to question the reasonableness of the results and the inferred large

magnitudes of sediment transport at Long Island is no exception. The

continental shelf off Long Island is a glacial outwash plain composed of

poorly sorted sediments. Comparison of a representative profile with two

equilibrium profiles for sediment of the appropriate size (Figure 15)

indicates that indeed the profile is probably "out of equilibrium" with an

excess of sediment which would tend to result in onshore sediment transport

due to the milder bottom slopes (compared to equilibrium). Moreover, the size

of the sediment is such that it tends to be transported only by the larger

waves associated with infrequent storms.

Brevard County, Florida

This example provides a good case study illustrating the application of a

sediment budget analysis to determine the effect of a channel entrance. Port

Canaveral entrance was cut in 1951 and is therefore a relatively young

entrance. Figure 16 presents a location map for this entrance on the east

30

OFFSHORE (m)

00

Actual Profile

\ 17
'0o \

SIdealized
Profiles

Figure 15.

Comparison of Actual and Idealized Profiles.
Sinnecock and Moriches Inlets.

Actual Profile Approximately Midway between

DISTANCE

-sO - k

Atlantic
Ocean

Port Canaveral
Entrance

a.*.
.

Location Map of Brevard County and Port Canaveral Entrance.

Gulf of Mexico

Figure 16.

coast of Florida. Shoreline change results are available for this area

commencing in 1855. Table III presents a chronology of events relevant to

changes in the shoreline.

TABLE III

CHRONOLOGY OF SIGNIFICANT EVENTS AT PORT CANAVERAL ENTRANCE

Entrance Cut 1951

Jetties Constructed 1953-1954

Beach Nourishment Project 1974

The longshore sediment transport is predominantly toward the south at

rates estimated up to 270,000 m3/yr although there is substantial uncertainty

in this estimate. The shoreline changes following construction of the inlet

coupled with a sediment budget analysis provide a basis for improving this

estimate.

Figure 17a presents the pre-entrance shoreline change rates. The

abscissa represents distance toward the south with the total length shown

representing a distance in excess of 66 km. The ordinate represents shoreline

change rate. It is seen that in the time period 1877-1951, which is

dominantly pre-entrance, the shoreline was accreting over more than 80% of the

shoreline. The average shoreline change rate over this 78 year time period is

approximately 0.3 m/yr. During the 19 year period (1955-1974) subsequent to

the cutting of the entrance, erosion had commenced with the maximum erosion

existing immediately downdrift (south) of the entrance. The maximum erosion

rate was approximately 5 m/yr over this 19 year period and the effect extended

some 5.5 km south of the entrance.

a)Effects of Channel Entrance on Down Drift Beach Stability

SPort Canaveral Entrance

Sebastian Inlet

Entrance I

20 40
DISTANCE SOUTH FROM PORT CANAVERAL
ENTRANCE (km)

Figure 17.

b) Shoreline Changes Following 1974 Nourishment Project

Effects of Establishment of Cape Canaveral Entrance and Subsequent
Nourishment Project on Downdrift Beaches.

1974- 1986 (Post Nourishment)

- %... --- ^ ^

I

*--1955- 1974 (Post-Entrance, Pre-Nourishment)
I
I
/

I I I I I I

_ __

c
~~C~c

50

In order to apply a sediment budget approach to determine the longshore

transport rate, it would be desirable to have available volumetric changes

downdrift of the entrance. However, lacking volumetric data, it is possible

to utilize Eq. (22) which relates volumetric change to plan area change.

Integrating the plan area in Figure 17b to determine the plan area rate of

change between the pre-entrance and post-entrance rate of change yields

approximately 15,000 m2/yr. Considering a vertical dimension of 8 m over

which the profile is shifted landward in the erosion process with the form

remaining unchanged and making the assumption (probably quite true) that there

is no cross-shore transport outside the shoreward or seaward limits accounted

for here, Eq. (6) simplifies to

= Qy (y Qy(Y2) (25)

in which Qy(y1) and Qy(Y2) represent the longshore transport at the jetty and

that outside the region affected by the entrance. The quantity Qy(Y2) of

course is the unaffected net longshore sediment transport and is the transport

of interest. If it is assumed that the south jetty is impermeable, then

Qy(Yi) 0, and

Q (y2) =- 15,000 m2/yr (8 m)

= 120,000 m3/yr

It is of interest to examine the effect of the south jetty if it were not

impermeable. It is clear that if the jetty is permeable, that sand would be

lost into the entrance through the jetty, i.e. Qy(Yi < 0), and

Y -i -y(Y1) (26)

Thus a leaky jetty would tend to overemphasize the amount of longshore

sediment transport if it were assumed to be sand tight.

Ideally one would have available other data indicating whether or not the

permeability of a jetty could result in significant transport through the

jetty. In particular the orientation of the shoreline relative to the jetty

can serve as a qualitative indication of permeability. For example, if the

shoreline is aligned perpendicular to the jetty, there is probably little

sediment transport through the jetty. If the shoreline forms an acute angle

with the jetty, the jetty is clearly "leaky" and significant transport over or

through the jetty is probably occurring. In the case of Port Canaveral

Entrance, inspection of the south jetty demonstrates that it is "leaky";

however, the shoreline orientation is such that this transport component is

not considered to be significant.

Having explored the net longshore sediment transport through analysis of

the erosional phase of the shoreline south of Port Canaveral Entrance, it is

useful to examine the shoreline changes subsequent to a relatively substantial

nourishment project. In 1974, a nourishment project consisting of

approximately 2 million cubic meters was placed along a 3,400 m segment of

shoreline immediately south of the south jetty. The shoreline changes from

1972 to 1986 are presented in Figure 17b. This figure is based on an entirely

different data source and over a completely different time period, yet it is

of interest to note that outside the region of influence of the entrance the

shoreline change rates are very similar to those based on the period 1877-

1951. This figure clearly shows qualitatively that the erosive "wave" has now

moved some 27 km south of the entrance and that it is being followed by an

accretional wave resulting from the 1974 beach nourishment project. It is of

interest to attempt to separate the erosional and accretional waves. At

present, this can only be accomplished in an approximately manner.

Ocean City Inlet, Maryland

Ocean City Inlet was caused by a hurricane in 1933. Within the next few

years, jetties were constructed to maintain the channel navigable. Major

changes that occurred in the vicinity included impoundment at the north jetty,

severe erosion of the shoreline south of Ocean City Inlet and the development

of a substantial shoal offshore and slightly south of the entrance centerline.

Additionally, substantial erosion of the ocean shoreline occurred with

landward migration. Figure 18 presents map showing the location of Ocean City

Inlet.

This example describes a field effort to explain the cause of erosion to

the northern portion of Assateague Island and also presents the results of an

attempt to compute a sand budget.

The sand budget components were determined by a combination of field and

computational procedures. The net longshore sediment transport was based on a

combination of impoundment measurements against the north jetty after it was

constructed and wave observations. The computational results are presented in

Figure 19 and are to be compared to the impoundment results against the

updrift jetty of 120,000 m3/yr. The computed values based on wave

observations exceed the impoundment values by a factor of 6, however, the

observations were made at a distance of 13 km south of the inlet and it is

known that transport increases to the south. The volumes lost and gained by

migration of the barrier island were based on Eq. (23) and even though the

I *

Approsomote Sector
Sneiterea From
'I

S Northeast waves By
60 1 Deon Contour

I. r

,. ,' ,0o o N
Z -T--OO' .

' '7500,W

'' : '" Legend
Pa ./I---- 60 f Contour
~6 tt Contour
o--'

0 10 20 30
Scote Inoui. m )

Figure 18. Location of Ocean City Inlet and Influence of Bathymetry in
Reducing Wave Action Along Northern Segment of Shoreline Cape
Henlopen to Fishing Point.

C-

.5

/,

II I I I 1 I I I

SNo I: Figures 17 & IS Bosod On The
LorngAhore Tronsport neroy

in The Shore Protection Monuol

I t I I I I I I I I I

J F M A M J J

A SO ND

Month

Figure 19. Averages and Ranges of Net Longshore Transport, Assateague Island,
Based on LEO Data for the Years 1973, 1974 and 1975.

60

400-

200

0

-200

FIL

'w

island basically retained the original width, the volumes lost exceeded those

gained by 38,000 m3/yr due to ho > hb* of Eq. (23).

Field observations of the south jetty demonstrated that it was both low

and porous allowing considerable sediment to flow from north Assateague Island

into the entrance channel from where it was jetted to partially account for

the growth of the offshore shoal. Field measurements were conducted with a

"swash trap" constructed of reinforcing rod and porous plastic mesh, see

Figure 20. Deployment of this trap quantified the flux of sediment through

the south jetty and these results extrapolated to account for the variable

wave and tide conditions resulted in an estimated flux of 31,000 m3/yr over

and through the south jetty. As support for the concept of the low and

permeable south jetty "draining" sand off Assateague Island's north beach,

beach profiles showed a trend of decreasing berm height from the natural

elevation of 2.4 m MSL-several thousand meters south of the south jetty to the

1.4 m crest elevation of the south jetty, see Figure 21.

Finally, Figure 22 presents a best attempt to account for all the

components of the sediment budget. It is seen that there is a residual or

"mismatch" of 38,000 m3/yr out of a total of 680,000 m3/yr, or a discrepancy

of about 11%

Cross-Shore Distribution of Longshore Sediment Transport

A knowledge of the cross-shore distribution of longshore sediment

transport is important in a number of engineering applications, including weir

jetty design. Several methods have been explored for inferring the cross-

shore distribution of longshore sediment transport, including tracers, local

traps and in situ point measurements of suspended sediment, longshore currents

and bed load traps.

^/ Reinforcing Rods

Filter Cloth

Uprush Direction

Figure 20.

Sediment Trap Used in Measurements of Sand Transported by Wave
Swash.

Distance From Boseline (ft)

a) Beach Profiles Approximately 200 ft. South of South Jetty.

w Beach Profile: Sept.,I 1976 (post -Belle)-
S" Beoch Profile: June I. 1977

4

g6 "~ PProfile of South Jeltty \'
0 Projected on a Line Normal
S2 to Main Beach Alignment

w 0 -_J L 1_JL
0 50 100 150 200 250 300 350 400 450

Distance From Baseline (ft)

b) Beach Profiles Approximately 2700 ft. South of South Jetty.

Figure 21.

Comparison of Elevations of South Jetty and Beach Profiles at Two
Locations South of Jetty.

Legend

1972
1931

Boy Shools
(+ 1.0 x 106 yd3)
-Total-

0 5000
Scale (ft)

:,
,

.*

Upword Growth Of Assoteogue
Island Due To Seo Level Rise
Over A Distance Of 32,000 ft
(+0.8 x 106 yd3)

N

Fillet Impoundment
At North Jetty Over
A 7000 ft Distance
(+ 2.8 x 10 yd )

L Ebb Shoal
/ (+8.0 10 yd5)

;-Recession of Eastern
I Shore Of Assoteogue
I Island Over A 32,000 ft
S Distance.
(-18.8 x 10 yd )

I

Westward Migration Of
Assoteoge Island Boy
Shoreline Over A Dis-
tonce Of 32,000 ft.

(+8.2 x 106 yd )

NET FROM SEDIMENT BUDGET ANALYSIS = +2.0 x 106 yd

Figure 22. Results of Sediment Budget Analysis.

The method described here is based on Eq. (3), rewritten below

ah 9qx + qy
at x ay

in which the source term, S, has been set equal to zero. Consider a barrier

placed instantaneously across the surf zone such that at the barrier,

q E 0. Also, consider that profile measurements are conducted before the

near-barrier profiles steepen to the degree that cross-shore transport is

induced. Thus if the profile is initially in equilibrium and remains so, the

cross-shore transport Qx = 0.

Integrating Eq. (3) along a contour from the barrier to a location, y2,

unaffected by the presence of the barrier,

qy(Y2,h) = q y(Ylh) + j Ah(h)dy
Y1

Fulford (1975) has applied this method in the laboratory. Bodge (1986) has

applied this method in the laboratory and field and has presented a method to

remove the first-order time-varying effects of the tide. Figure 23 presents

an example from Bodge of the cross-shore distribution for plunging waves.

Entrance to St. Andrews Bay, Florida

This situation is somewhat similar to Brevard County, Florida. The

entrance was cut across a barrier island in 1934 and thus in geological time

scale is a fairly young inlet.

Shoreline change data are available for the period 1855-1934 as shown in

Figure 24a. There were areas of erosion and accretion; however, for the 36 km

section presented in Figure 24, the average shoreline change was one of

44

b
IA

Xb

0.01

0

Figure 23. E
T

0.5
x/xb

examples of the Cross-Shore Distribution of Longshore Sediment
transportt (Bodge, 1986)

5

-51 1 1 1

DISTANCE

10
EAST FROM

BAY COUNTY

LINE (km)

a) Shoreline Change Rates
1855-1934 (79 Years).

5

E

0
z
I
u

z
Li

0
= 1 1

Prior to Cutting Entrance to St. Andrews Bay,

DISTANCE EAST FROM BAY COUNTY LINE (km)

b) Comparison of Shoreline Change Rates Prior to Cutting Entrance to
St. Andrews Bay, 1855-1934 (79 Years) and Subsequent to Cutting
Entrance, 1934-1984 (50 Years).

Figure 24. Effect of Cutting Entrance to St. Andrews Bay in 1934 on Downdrift
Shoreline.

0O

accretion, averaging approximately 0.3 m/yr. The average shoreline change for

the period 1934 to 1984 is presented in Figure 24b. It is seen that

immediately downdrift (west) of the entrance, the shoreline change rate had

been altered from one of accretion of approximately 1 m/yr to one of erosion

in excess of 2.5 m/yr, i.e. a differential erosion in excess of 3.5 m/yr. In

this 50 year period, the shoreline immediately downdrift of the inlet eroded

by more than 125 m whereas under natural conditions, the projected accretion

would have been approximately 50 m.

In the case of St. Andrews Bay Entrance, there were three contributing

factors to the downdrift erosion:

(1) Approximately 7.5 million cubic meters of sand was dredged from the

entrance channel and spoiled in deep water,

(2) After the inlet was cut, the ebb tidal shoal developed accumulating

approximately 3,000,000 cubic meters, and

(3) The jetties were extremely leaky which contributed to the necessary

dredging in (1), above.

As a verification that the leaky jetties contributed to the required

shoaling (and thus the downdrift erosion), the net longshore sediment

transport is estimated as 60,000 cubic meters per year whereas the downdrift

erosion was in excess of 160,000 cubic meters/yr.

Offshore bathymetry is insufficient to estimate the downdrift volumetric

erosion rate. However, as before, it is possible to estimate this based on

planform changes and Eq. (22). The average annual differential planform

changes are 20,300 m2 erosion which when combined with a profile change of

8 m, yields an annual volumetric erosion rate of 160,000 cubic meters or a

total erosion over the 50 year period of 8,100,000 cubic meters.

Rudee Inlet, Virginia

Rudee Inlet, Virginia was a second field location in the Nearshore

Sediment Transport Study program where transport rates were studied to

investigate the longshore sediment transport equation. The net longshore

sediment transport is toward the north. The south jetty of the inlet includes

a weir section which allows sediment to enter a deposition basin from which

the sediment is dredged and transported by pipeline across the entrance to

Virgin Beach, see Figure 25.

When the experiment was planned, it was assumed that the weir allowed the

net longshore transport to pass over the weir during transport toward the

north and that sediment transported during reversals was relatively small.

Fortunately, the survey plan included a substantial portion of the updrift

beach as shown in Figure 26.

It was found that the net longshore sediment transport toward the north

was a small fraction of the gross transport. During periods of northerly

transport, relatively large volumes of sediment are transported and deposited

updrift of the north jetty whereas only a small quantity enters the deposition

jetty. During periods of sediment reversal, the volumes stored updrift of the

jetty is diminished, but sand continues to be carried across the weir section.

Thus in order to obtain the appropriate volume for correlation with the

longshore wave energy flux factor, it is necessary to include the volume

accumulated in the deposition basin and that either deposited or eroded from

the updrift (south) beach during the intersurvey period.

SUMMARY

The formalized framework provided by a sediment budget analysis is useful

in many general and specific coastal engineering applications, including

Virginia
Beach

I I II I I I I

100

Scale (m)

mber Sheet Pile
Weir Section

Figure 25. Rudee Inlet, Showing Weir Jetty and Impountment Basin (Adapted
From Needham and Johnson, 1972).

200

..
..

..

..
..
..

- Kitt0 tT tl S-- u.4 ;-so t ltt t -.--
INtItVL

SCALt I' et a o o00 to

Figure 26. Rudee Inlet Survey Plan and Location of SX Wave Gage.
Ky

interpreting natural and altered systems, inferring onshore (or offshore)

sediment transport for a system that is out of equilibrium, determining

sediment transport rates from volumetric measurements, estimating the cross-

shore distribution of longshore sediment transport, and many others. This

frameword should be developed and applied by all practicing coastal engineers

confronted by the difficult problems of understanding a system, many times

with inadequate data available.

REFERENCES

Bodge, K. R., "Short Term Impoundment of Longshore Sediment Transport," Ph.D.

Dissertation, Coastal and Oceanographic Engineering Department,

University of Florida, Gainesville, FL, 1986.

Dean, R. G., "Shoreline Erosion Due to Extreme Storms and Sea Level Rise,"

Report No. UF/COEL-83/007, Coastal and Oceanographic Engineering

Department, University of Florida, Gainesville, FL, 1983.

Fulford, E. T., "Distribution of Longshore Sediment Transport Across the Surf

Zone," Master's Thesis, Department of Civil Engineering, University of

Delaware, Newark, DE, 1982.

Rudee Inlet, Virginia

Rudee Inlet, Virginia was a second field location in the Nearshore

Sediment Transport Study program where transport rates were studied to

investigate the longshore sediment transport equation. The net longshore

sediment transport is toward the north. The south jetty of the inlet includes

a weir section which allows sediment to enter a deposition basin from which

the sediment is dredged and transported by pipeline across the entrance to

Virgin Beach, see Figure 25.

When the experiment was planned, it was assumed that the weir allowed the

net longshore transport to pass over the weir during transport toward the

north and that sediment transported during reversals was relatively small.

Fortunately, the survey plan included a substantial portion of the updrift

beach as shown in Figure 26.

It was found that the net longshore sediment transport toward the north

was a small fraction of the gross transport. During periods of northerly

transport, relatively large volumes of sediment are transported and deposited

updrift of the north jetty whereas only a small quantity enters the deposition

jetty. During periods of sediment reversal, the volumes stored updrift of the

jetty is diminished, but sand continues to be carried across the weir section.

Thus in order to obtain the appropriate volume for correlation with the

longshore wave energy flux factor, it is necessary to include the volume

accumulated in the deposition basin and that either deposited or eroded from

the updrift (south) beach during the intersurvey period.

SUMMARY

The formalized framework provided by a sediment budget analysis is useful

in many general and specific coastal engineering applications, including

interpreting natural and altered systems, inferring onshore (or offshore)

sediment transport for a system that is out of equilibrium, determining

sediment transport rates from volumetric measurements, estimating the cross-

shore distribution of longshore sediment transport, and many others. This

frameword should be developed and applied by all practicing coastal engineers

confronted by the difficult problems of understanding a system, many times

with inadequate data available.

REFERENCES

Bodge, K. R., "Short Term Impoundment of Longshore Sediment Transport," Ph.D.

Dissertation, Coastal and Oceanographic Engineering Department,

University of Florida, Gainesville, FL, 1986.

Dean, R. G., "Shoreline Erosion Due to Extreme Storms and Sea Level Rise,"

Report No. UF/COEL-83/007, Coastal and Oceanographic Engineering

Department, University of Florida, Gainesville, FL, 1983.

Fulford, E. T., "Distribution of Longshore Sediment Transport Across the Surf

Zone," Master's Thesis, Department of Civil Engineering, University of

Delaware, Newark, DE, 1982.