Ue. Res KORA, re Vea © NOUV A Vy ‘a

U.S. Army :
— Coastal Engineering :
Research Center :

¥

DYNAMIC PROPERTIES OF
IMMERSED SAND AT
VIRGINIA BEACH, VIRGINIA

{

| wee | : |

;

TECHNICAL MEMORANDUM NO. 9

DEPARTMENT OF THE ARMY
' CORPS OF ENGINEERS

O @hbbe?oo TOEO O

IOHM/181N

DYNAMIC PROPERTIES OF

IMMERSED SAND AT
VIRGINIA BEACH, VIRGINIA

by

W. Harrison
and
R. Morales Alamo

TECHNICAL MEMORANDUM NO.9
December 1964

Material contained herein is public property and not subject to copyright. Reprint or re-publication of any
of this material shall give appropriate credit to U.S.Army Coastal Engineering Research Center

LIMITED FREE DISTRIBUTION OF THIS PUBLICATION WITHIN THE UNITED STATES IS MADE BY THE U.S.ARMY
COASTAL ENGINEERING RESEARCH CENTER 5201 LITTLE FALLS ROAD, N. W., WASHINGTON D.C. 20016

FOREWORD

Information is scanty relative to mean settling velocities of sand
samples from natural beaches. Nevertheless, for many studies it is
desirable to obtain measurements of the mean still-water settling veloc-
ities of natural aggregates of sand-sized material because the settling
velocity of an individual particle in quiescent water is the most
fundamental hydraulic characteristic that can be measured. This study
was designed to measure and record the systematic variations in mean
settling velocity of a large number of sand samples taken simultaneously
along three transects across a natural beach and in the area around the
mouth of an inlet associated with the beach.

Results of the measurements of mean settling velocities presented
in this technical memorandum are for quiescent water of the temperature
encountered during sampling and the derived dynamic properties of mean
Reynolds number and mean drag coefficient are also for an infinite column
of quiescent sea water at the natural temperature. The various dynamic
properties are tabulated and a set of curves is presented so that the mean
settling velocities observed for the natural water temperature (6.9°) can
be converted to settling velocities at any water temperature between 0°
and 36° C.

This report was prepared by Dr. Wyman Harrison, Associate Marine
Scientist of the Virginia Institute of Marine Science, in pursuance of
Contract DA-49-055-CIVENG-63-6 with the Beach Erosion Board, and in
collaboration with Mr. Reinaldo Morales-Alamo, a graduate student at the
Institute.

This report is published under authority of Public Law 166, 79th
Congress, approved July 31, 1945, as supplemented by Public Law 172,
88th Congress, approved November 7, 1963.

TABLE OF CONTENTS

LIST OF NOTATIONS

ABSTRACT

INTRODUCTION

REVIEW OF PREVIOUS WORK
DESCRIPTION OF PRESENT INVESTIGATION

Area of Investigation
Methods of Study
Sampling
Determination of Shape Factor
Determination of Mean Settling Velocities and
Nominal Diameters
Determination of Settling Velocity in Nature
Determination of Reynolds Numbers and Drag Coefficients
Mineralogy

RESULTS AND DISCUSSION

Shape Factor

Size Analysis

Reynolds Number and Drag Coefficients
Transects
Rudee Inist Area
Swash-backwash Zone

Mineralogy

Application of Data

Beach Model Comparisons

SUMMARY REMARKS

ACKNOWLEDGMENTS

REFERENCES

LIST OF TABLES
Tables 1 - 8

LIST OF FIGURES

Figures 1 - 10

Page

[oo oa os

26-41

43-52

LIST OF NOTATIONS

Long axis of a particle or boundary reference - axis distance.
Cross-sectional area of an immersed body

Intermediate axis of a particle

Short axis of a particle

A numerical resistance coefficient

Drag coefficient of a particle (for an infinite, quiescent fluid)
Drag coefficient corresponding to a given Ra value.

Nominal diameter of a particle (the diameter of a sphere having the
same volume as the particle).

Diameter of an immersed particle

Diameter of a sand grain as determined from "equilibrium" criterion
Force resisting motion of an immersed body

Buoyancy force

Gravitational force

Fluid resistance force

Gravitational constant

Water depth

Wave height in deep water

Wave number

Effective hydraulic roughness length

Wave length in deep water

Mean settling velocity of sand sample (as measured in settling tube).
Mean size (in nominal diameter) of a sand sample.

Probability level indicated by a statistical test or percentile of output
curve from sand analyzer.

Radius of spherical particle

Reynolds number

R, ~ Reynolds number for mean nominal sphere
S - Slope of energy gradient

i) - Sorting coefficient of sand sample

fo)

ta - Depth of flow

V - Particle velocity

Ue - Mean backwash edge velocity

Vi - Settling velocity of nominal sphere

Me - Terminal settling velocity in quiescent fluid

Ww - Terminal fall velocity of particle. (Equivalent to Wop

GQ - Beach slope

. - Dynamic viscosity

U - Kinematic viscosity
Pe - Fluid density

Ps -Particle (solid) density

§% - Geometric expression of shape

cone
ia

DYNAMIC PROPERTIES OF IMMERSED SAND
AT VIRGINIA BEACH, VIRGINIA

by

W. Harrison
U. S. Coast and Geodetic Survey, Norfolk, Virginia‘ 1) and
Virginia Institute of Marine Science, Gloucester Point, Virginia

and

R. Morales-Alamo
Virginia Institute of Marine Science, Gloucester Point, Virginia

ABSTRACT

On March 25, 1963, 219 sand samples were taken from the
shoaling-wave, breaking-wave, swash-backwash, and foreshore
zones of the beach. The following kinds of measurements were
used to describe the properties of the samples: mean settling
velocity in nature (as determined with a Woods Hole Rapid Sand
Analyzer and a special set of curves for settling velocity as
a function of temperature), mean Reynolds number (in nature),
and mean drag coefficient (for an infinite fluid under natural
conditions). Corey's (1949) shape factor and the Dynamic Shape
Factor of Briggs, et al. (1962) were calculated and compared;
the Corey shape factor was used in calculating mean settling
velocity. Also presented are data for mean and median grain
size (in nominal diameter) and sorting for each sample. For
the natural sea-water conditions (T = 6.9°C, S = 26.7 0/00),
average Reynolds numbers for the various zones were 4.8
(shoaling-wave), 8.1 (breaking-wave), 6.2 (swash-backwash) and
12.0 (swash-berm).

The important effect of kinematic viscosity on the dynamic
properties of the particles and on beach slopes in the shoal-
ing wave zone is considered. Observed trends of mean size and
sorting throughout the dynamic zones are compared with those
predicted by Miller and Zeigiler's (1958) model and the com-
parison is found to be rather poor.

1

aero address: Land & Sea Interaction Laboratory, 439 York St.,
Norfolk, Virginia, Study completed while at the Virginia Institute
of Marine Science.

INTRODUCTION

Fundamental to an understanding of the interaction of a particular
beach with the forces exerted upon it by the impinging water body is an
assessment of the dynamic behavior of the particles that comprise the
beach, under the expectable wave and current forces. To this end it is
necessary, first of all, to undertake the description of the dynamic and
associated properties of the existing spectrum of sand-sized particles.
The method of description chosen here for samples of sand from Virginia
Beach (Figure 1) is based upon the measured dynamic property of settling
velocity. Mean settling velocities of sand samples are determined from
fall-tube settiing velocity curves by statistical methods. From a given
mean settling velocity the derived dynamic properties of mean Reynolds
number, mean drag coefficient,and mean dynamic shape factor are determined
for a sample. Mean grain size, in terms of nominal diameter, and sorting
are also determined.

REVIEW OF PREVIOUS WORK

The significance of the settling velocity of sediment particles in
the study of their dynamic properties has been stressed by many investiga-
tors. Brown (1950) states that many of the hydraulic properties that
control the entrainment, transportation, and deposition of mineral particles
apparently also control the dynamics of the mineral particles falling
through the fluid. Briggs, et al. (1962), consider that settling velocity
is perhaps the most fundamental of these hydraulic properties. The U. S.
Inter-Agency Committee on Water Resources (1958) considers that the settl-
ing velocity of the individual particle in quiescent water is the most
fundamental hydraulic characteristic which can be measured; that the
physical properties of the particles greatly affect their settling velocity
but are not in themselves adequate measures of their behavior in motion in
a fluid; and that studies of transport of sediments in water bodies require
a knowledge of the dynamic properties of the particles.

The settling velocity of a particle through a fluid medium is essen-
tially determined by the force that resists motion of an immersed body.
Newton (1687) considered this resisting force (F) to depend upon the cross
sectional area of the body (A), the mass density of the particle (p,),
and the square of the velocity (V).

2
F = (C) Aps — (1)

The term C is a numerical resistance coefficient which Newton believed to
vary only with the shape of the body and its orientation with respect to

the direction of motion. Rouse (1937) considers Newton's equation dimen-
sionally correct but states that the resistance coefficient depends not only

upon shape and orientation but varies considerably with the viscous char-
acteristics of the motion.

Reynolds (1883) showed that the influence of viscosity depends upon
the dynamic viscosity of the fluid (Uw), the fluid density (p,), the size
of the body (D), and the mean velocity of the relative motion (V). Reynolds
combined these parameters as a dimensionless ratio called the Reynolds
number (Re): vDp
R mp tet, ave, (@2))
e Uw Vv

where V is the kinematic viscosity of the fluid and is equal to U/p¢
The magnitude of the Reynolds number indicates the relative significance
of inertial (VD) and viscous (V)forces affecting the motion.

According to Rouse (1938) viscous action may produce three essentially
different types of resistance: deformation drag at very low Reynolds numbers,
with the effects of viscous stress extending a great distance into the
surrounding flow and causing a more or less widespread distortion of the
flow pattern; surface drag at much higher Reynolds numbers, with appreciable
deformation of the flow limited to a thin fluid layer surrounding the body;
and form drag at still higher Reynolds numbers, arising if the form of the
body is such that separation of the flow from the body occurs. The form
of the body also determines to some extent the magnitude of the other two
types of resistance. Rouse (1938) concludes that the resistance to motion
of an immersed body depends only upon the Reynolds number characterizing
the motion and the geometrical form (or shape) and orientation of the body.

Analytical determination of Newton's coefficient of resistance here
called drag coefficient and represented by Cp for certain basic body forms
has been possible only at very low Reynolds numbers. Stokes (1851) first
determined analytically the drag resistance on a sphere falling through a

fluid at very .low Reynolds numbers (R.<0.1). Rouse (1937) rearranged
Stokes’ relationship into a form similar to Newton's (Equation 1).
2
24 V
E aaRe Als => (3)

obtaining the following relationship between Reynolds number and drag
coefficient for very low values of Re,

Oseen (1927) and Goldstein (1929) were able to extend analytically the

range of Stokes' relationship to approximately Re = 2. Beyond this limit
the study of Cp as a function of Re has remained empirical. Schiller (1932)
plotted the known drag coefficients and Reynolds numbers on a Cp - Re
diagram. Examination of Schiller's diagram shows Cp to be solely a function
of Re up to very high values (Re = 5,000 for discs and Rg = 500,000 for
spheres).

The shape of the immersed body determines significantly the drag
resistance of the fluid at Reynolds numbers much higher than those at
which Stokes' relationship is valid. At Reynolds numbers greater than
50 the drag coefficients for discs and spheres diverge noticeably in
Schiller's diagram. Rubey (1933) and Zegrzda (1934) were among the first
to recognize the effect of particle shape on drag resistance. The manner
in which shape affects settling velocity can be expressed in terms of
drag coefficient and Reynolds number (Wade1l, 1934; Rouse, 1950; Albertson,
1953; Schulz, et al., 1954; Prandtl and Tiet jens, 1957; Zeigler and Gill,
1959; Briggs et al., 1962).

Wadell (1933) was the first to define shape rigidly and he did so in
terms of a sphere, since it has a higher settling velocity for a given
volume than any solid of any other shape. Wadell (1934) pointed out that
irregularly shaped solids do not have diameters in the geometric sense and
that any computations using diameters must deal with spheres or relate
some measurable property of the particle to a sphere. One such basic
relationship is the nominal diameter, which is the diameter of a sphere
having the same volume as the particle.

Several geometric shape expressions have been proposed involving a
ratio of the triaxial dimensions of a particle: a = long axis; b = inter-
mediate axis; and c = short axis (Briggs, et al., 1962). Krumbein (1942)
suggested the following expression, which his investigations showed was
related to sphericity as defined by Wadell1:

| 2
Qa e/a) Ge) (5)
Corey (1949) suggested a simplified shape parameter which he called the

shape factor (S.F.):

Sailg = tos
(ab)@ (6)

where all axes were mutually perpendicular. Corey selected the expression
c/ab2 for his shape factor because he and others found that the particles
usually oriented themselves in the fluid so that they presented the
greatest resistance to the passing fluid, thus having the maximum projected
area, as discussed by Wadell (1934) and Krumbein (1942), oriented normal
to the path of motion. For this reason, Schulz,et al. (1954) considered
Corey's shape factor a logical dimensionless shape parameter expressing
the relative flatness of the particle. Corey found difficulty drawing
lines of constant shape factor in a Cp - Re diagram using the triaxial
measurements in the equations for Cp and Re and concluded that the nominal
diameter should be used for the characteristic length and area in the Cp
and Re parameters.

In reference to the use of triaxial measurements to represent the
geometry of a particle, Schulz, et al. (1954) state that they may not
be fully adequate but that they are simple and convenient and any more
adequate system would be greatly complicated; and that it is highly im-
probable that a simple method can be devised to completely describe shape
because of the great variability in shape found in natural sediments.
Zeigler and Gill (1959) also state that the Corey shape factor may not be
the best description of shape but point out, however, that it gives a
reasonable correlation with drag coefficients and does indeed show that
grains with different shapes plot in a predictable manner on a Cp - Re
diagram. Zeigler and Gill (1959) used the data on natural sands of
Schulz, et al. (1954) to compute graphs and tables of settling velocities
of particles with different shape factors.

Briggs, et al. (1962) felt that although shape can be estimated from
grain geometry, in studies of entrainment, transport, and deposition, it
should be measured by means of its effect on the hydraulic properties of
a similar particle having some ideal shape as suggested by Wadell (1932).
Using a smooth sphere of equal nominal diameter, mass density and volume
as reference, they developed a Dynamic Shape Factor (McCulloch, et al.

1960) by dividing the settling velocity of the nominal sphere (Vy) into
the settling velocity of the particle (Vp):

2

DSF = (Vp/Vp) (7)

For particles affected by both inertial and viscous forces (1< Re < 500),
the shape factor would be of the form:

DSF = a(Vp/Vn) + b(Vp/Vn)2 (8)
where

E\ sp joy) Sal Eyovel (Coy/e))) & Re

Briggs, et al. (1962) found a good, but not perfect correlation
between their hydraulic shape factor (DSF) and the common geometric shape
factors, and gives regression formulae for estimation of DSF from triaxial
shape factors. McCulloch, et al. (1960) applied a correction to the Corey
shape factor depending on the values of the axial ratios, b/a and c/b,
which apparently was used by Briggs,et al.(1962) in computing the regression
formula for this factor.

DESCRIPTION OF PRESENT INVESTIGATION
Area of Investigation

The study area at Virginia Beach is located on the Atlantic seaboard
22 miles north of the Virginia-North Carolina State line, about 7.2 miles
south of Cape Henry, and 19 miles east of Norfolk, Virginia (Figure 1).

Methods of Study

Sampling. Sand samples were collected at 25-foot intervals along
three transects (Figure 1), normai to the seashore, from the berm zone to
a depth of approximately 20 feet. Additional samples were collected at
shorter intervals in the breaker zone at the 15th Street and 3rd Street
transects (Table 5, Addenda). Sampling was accomplished by hand or with
pipe dredges. Technicians attempted to sample only the upper 2 centimeters
of the beach surface at all times. Offshore portions of the 15th and 3rd
Street transects were sampled from existing fishing piers. The offshore
portion of the transect at the Camp Pendleton boundary line was sampled
from a U. S. Army DUKW at pipe stations 25 feet apart. Additional samples
were collected at two places from the swash-—backwash zone (Figures 1, 2),
from the vicinity of Rudee Inlet (Figure 3) in the zone where the inlet
outflow was expected to affect the sediment distribution, and from the
top of the swash zone (Figure 2) at 200-foot intervals parallel to the
shoreline. Samples along the transects were collected near the time of
low water. Samples from the top of the swash zone, Rudee Inlet, and the
swash-backwash zones were collected 2 to 3 hours earlier than those
collected from the transects.

Samples from the berm, breaker, and shoaling wave zones of the three
transects were mixed and subsamples from this mixture used for determina-
tion of the average shape factor (Table 3) and mineral composition (Table
2) for the whole area.

Determination of Shape Factor. A Corey shape factor was evaluated
(Table 3) for the fractions of the mixture of sands (mentioned above)
retained by No. 18 and No. 230 sieves (A.S.T.M. Sieve Scale). Triaxial
measurements were made microscopically with the aid of an ocular microm-
eter and the calibrated fine-focusing adjustment knob. Since the shape
factors calculated for both the coarsest and finest fractions were so close
in value it was considered unnecessary to make shape factor determinations
on any of the intermediate sized fractions.

The Dynamic Shape Factor (DSF) was computed (Table 4) only for
samples from the 3rd Street pier transect, using Equation 8.

Determination of Mean Settling Velocities and Nominal Diameters.
Forces acting on a sand grain that is settling in still water are the
gravitational forces (acting downward), and the fluid resistance and
buoyancy forces (acting upward).

Mathematically:

Gravitational force OF = 4/30? P. g (9)
S Re

Fluid resistance force (F_) = 6Tr y Ws qa24r (10)

Buoyancy force (FR) S 4/3mr> Pe & (11)

where

density of grain in ea/em

no)
i]

s
Pe = density of fluid in em/cm>
r = radius of sphere in cm
pf! = dynamic viscosity of fluid in ayV/aeesen
Me = settling velocity of solid in cm/sec
vy 2
P \3
Gy) a ches Cowmrleions 2 — / (9 a
2 f
d 2
n
d = nominal diameter (mm), or the diameter of a sphere
n ; :
having the same volume as the particle
che Ny Pr
R_ = Reynolds number = ead ae
€ ted

At terminal fall velocity, the forces balance so that there is no
net force,

Fog: Feb ik (12)

and from the definition (2) of Reynolds number,

YD i 2IP-

(13)

When solving for V, standard tables are available for the determination
of and p¢ (at various temperatures) and Re may be determined from the
tables of Schulz, et al. (1954) that take into account the drag coefficients
associated with various particle shapes and densities,

If some expression is desired of the size of a particle settling at
terminal velocity, such as nominal diameter dy, one can solve for particle
radius:

2
3 ge cota ir | Dine | (14)
ie ee Cp. - Pp) g 24

All of the values for settling velocity and particle size reported in
this study are based upon settling analyses run with a copy of the Woods
Hole Rapid Sand Analyzer, WHRSA (Whitney, 1960; Zeigler, et al. 1960), and
upon values found in tables published by Zeigler and Gill (1959). The
Woods Hole settling tube (Figure 4) measuresfall rates of all immersed
sand grains over a l-meter distance by sensing the changes of pressure
produced by the sand suspension as a function of time. Electronics of the
system used were identical to those published by Whitney (1960, Plate 4),
with the exception that the bellows, pressure case, and the differential
transformer were replaced with a Sanborn bidirectional, differential gas-
pressure transducer (Figure 4). A resume of the reliability and precision
of the analyzer is presented by Zeigler, et al. (1960). Reproducibility
of results is excellent.

Prior to analysis, samples were dried and split with a micro splitter.
Because a few shell fragments larger than 4 mm. in diameter occurred in
some of the samples, they were picked out of each of the sample splits.
Final splits of 8- to 10-gm. weight were introduced into the analyzer.

It was assumed that there was no interparticle interference and no
particle-wall interference during the sediment analyses. It was also
assumed that surface roughness of the grains had a negligible effect on
the measured fall velocities.

An output curve from a typical settling analysis performed on the
analyzer is shown in Figure 5. By using a Gerber variable scale, it is a
simple matter to scale off the height of a given curve into 100 equal
divisions. If, then, one desires to estimate the median settling velocity
of the sample he refers to the 50th percentile of the curve of pressure
versus time. In the case of Figure 5, one obtains 24.2 seconds for the
l-meter fall, or a fall velocity of 4.2 cm/sec (at 24.2 seconds, 50 per-
cent of the sample has settled one meter, as indicated by the pressure-
time curve).

Zeigler and Gill (1959) developed a very useful set of tables for
the conversion of particle settling velocity to particle diameter. Their
tables express the solution of Equation 14 in terms of nominal diameter
dn, and are formulated for pure water at various temperatures over the
range 20-279 C. The tables assume a particle density of that of quartz

(2.65) and have been computed for dn in the range 0.1 through 2.0 mm.
Their tables also employ the Corey shape factor (Equation 6). By using
the median value of 24.2 seconds for the l-meter fall result shown in
Figure 5, one determines from Zeigler and Gill's tables that the median
nominal diameter of the sample, for shape factor 0.7, at 26° C., is
0.289 mm.

The following nonparametric statistical measures were used for
estimating mean settling velocity My, and mean nominal diameter Mz,
from the analyzer curves

= PAO PSO se SO (15)
3

My or Mz

where P20, P50, and Pgo are the 20th, 50th, and 80th percentiles, re-
spectively, and P is expressed in seconds for determining My,or nominal
diameters,for determining Mz. Sorting of the distribution curve for
nominal diameters was estimated with the following equation for the sort-—
ing coefficient:

So 2 2805 E20 (16)
P50

Equation 16 was first used on similar data by Miller and Zeigler (1958).
The closer Sp is to zero, the better is the sorting of the sample, for
the spread of the size distribution decreases as Sy approaches zero.

Determination of Settling Velocity in Nature. Because it was
desirable to obtain values for the settling velocities occurring in the
natural environment, it was necessary to prepare curves (Figure 6) of
settling velocity versus water temperature for representative samples of
Virginia Beach sands from the study area.

Ten samples representative of the swash, breaking wave, and shoaling
wave zones were run in fresh water and in sea water of 15.9, 26.8, and
38.9 of/oo salinity. Temperatures ranged from 39° to 120° F. Mean
settling velocity values were determined from percentiles of the WHRSA
curves using the statistic:

_ PLO 280.37 BIO BIO. 2SO
My = Spa Horny ETE Ga)

McCammon (1962) indicated that this statistic is 93 percent effi-
cient, where the statistical efficiency of a graphic measure is the ratio
of the variance of the distribution of the corresponding efficient
estimate and the variance of the limiting distribution of the graphic
measure,

Salinity affected settling velocity only slightly, the decrease in
settling velocity between fresh and 39 o/oo salinity water being only
about 5 percent. Difficulties in keeping the temperature constant in the
settling tube and difficulties in obtaining representative 10-gram splits
of the coarser grained samples for the WHRSA make the curves of Figure 6
accurate only to a first approximation. The curves are accurate enough,
however, for expressions requiring the use of settling velocity values
for aggregates of sand from the study area at Virginia Beach.

Settling velocities (Vp) for the natural environment (Temp. = 6.9° C;
Salinity = 26.74 o/oo) on 25 March 1963 were used in the computations of
dynamic properties of the particles.

The settling velocities of the corresponding nominal spheres (Vy)
were extracted from the nomogram in Rouse (1937).

Determination of Reynolds Numbers and Drag Coefficients. Reynolds
numbers based on the mean size were computed for each sample using the
equation:

> Cl V
fm p
— 18
Re Ti (18)
where
Pr = 1.0209 (from U. S. Navy H.O. Pub. No. 615)

Gl = M, in cm.

<<
tl

p = Mean settling velocity (in cm/sec) under prevailing
conditions

U

0.0151 poise (from Miyake and Koizumi, 1948)

Drag coefficients corresponding to these Re values were extracted from
Table 1, modified from Schulz, et al. (1954).

Reynolds numbers for the mean nominal spheres (Rp) corresponding to

each of the samples from the 3rd Street pier transect were computed (Table
4) using the following equation from Briggs, et al. (1962):

Rn = n n (19)

Drag coefficients corresponding to these R, values were computed using
another equation from Briggs, et al. (1962):

igre (C)) (20)

where Cp is the drag coefficient of the actual grain, as obtained from
Table 1, and DSF is from Equation 7.

A Reynolds number (R_) was back calculated for the data from the
3rd Street pier transect using DSF values and again following Briggs,
et al. (1962):

2
Bo qi SUSIE) (RY) (21)

This computation was made as a check on the determination of the DSF
value since Rp should in effect be equal to the previously computed Re.

After computation of the Rg values it became obvious that the
Reynolds numbers of the particles involved were quite low. The product
of Re x Cp was computed for many of the samples to obtain a comparison
with the established constant value of Re x Cp = 24 (Equation 4) for
particles within the realm of Stokes' law.

Mineralogy. The percentage by number of heavy minerals and rock
and shell fragments was determined for each of the sieve fractions from
the mixture of Virginia Beach sands (Table 2).

RESULTS AND DISCUSSION
Shape Factor

Table 3 presents the triaxial measurements and Corey Shape Factors
for individual grains from fractions retained on Sieves Nos. 18 and 230.
This table has been included for the use of those who may wish to try
other shape factors based upon these measurements. The respective
average S.F. for these fractions was 0.67 (S = 0.15) and 0.63 (S = 0.13).
As can be seen from the standard deviations,S, variation around these
means is not too great and therefore,.our estimated average shape
factor for each fraction represents the sample adequately. Because
there is practically no difference in shape factor between the two
fractions, they may be combined to obtain an average shape factor for
sands of all sizes in the strip of beach under study. This is justified
by the fact that no difference in shape factor is to be expected in
grains of sizes intermediate between those measured when the latter,
close in size to the largest and smallest grains present in the beach,
failed to show any. The combined average S.F. is 0.65. For conven-
ience in using the tables in Zeigler and Gill (1959) this shape factor
was taken as 0.7. According to the U. S. Inter-Agency Committee on
Water Resources (1958) a shape factor of 0.7 is about average for
natural sediments.

Table 4 presents the Dynamic Shape Factor for samples from the 3rd
Street transect. These were computed using Equation 8. The average DSF
for the transect is 0.57 (S = 0.03). It was not possible to correlate
this DSF value to our calculated S.F. of 0.7 using the regression formula
for mixed Zingg groups given by Briggs, et al. (1962). Their equation,

Ds = dS Seo = O08 (22)
resulted in a DSF = 0.87 when S.F. = 0.7 was introduced into the equation
and a S.F. = 0.47 when DSF = 0.57 was used. The discrepancy is more than

likely due to the apparent use by Briggs, et al. (1962) of correction
factors for S.F., as stated previously. It was impossible to ascertain
these correction factors or their use from the data available. However,
comparison of Reynolds number (Rp) back calculated using Equation 21
(Table 4), with the Re computed for the same data using Equation 2 (Table
5) shows that they are very close. Thus, computations using either the
Corey Shape Factor or the Dynamic Shape Factor yield almost identical
Reynolds numbers values.

Size Analysis

Table 5 summarizes the data on size parameters for each of the samples
collected. Figures 7, 8, and 9 graphically depict trends in values for the
parameters. It is to be noted that the mean and median nominal diameters
are very close in value in all transects. In all, the shoaling zone
presents a more or less constant mean size throughout its extent. There is
an abrupt increase in mean size in the breaker zone with a subsequent in-
crease thereon inshore into the swash-—berm zone. Nevertheless, some
interesting differences in the distribution of mean size along the three
transects are noticed. The greatest increase at the breaker zone is found
at the 15th Street pier transect, while the smallest increase is found at
the 3rd Street transect. The Pendleton Line transect presents an inter-
mediate increase. However, the 15th Street transect shows the smallest
mean size at the swash-—berm zone with sizes much smaller than those at the
breakers, while the 3rd Street transect evidences the greatest increase in
mean size between the breaker and swash-berm zones with the swash-berm
sizes much larger than those both at the breakers and at the swash-berm
zofie at the 15th Street transect. The Pendleton Line transect shows a
pattern similar to that of the 3rd Street pier transect, but the largest
mean size at the swash-berm zone is approximately the same as in the
breakers.

The curves for sorting show the poorest sorting in the breaker zone
at the 15th Street transect and Pendleton Line transect, but not at the
3rd Street transect. In the latter, sorting is relatively uniform through-
out the length of the transect, with the poorest sorting found at the
halfway point in the shoaling zone. The best sorting is found in all
transects generally just inshore of the breaker zone, with good sorting
present near the top of the swash-berm zone.

The average size parameters for the different beach zones in each of
the three transects are shown in Table 6. The swash and berm zones above
the swash zone at time of sampling are combined, because the lower limit
of the berm zone was not established for this investigation. These data
show in a very gross fashion that the mean size and median diameters tend
to increase from the shoaling zone toward the swash-berm zone in the
three transects, although the differences found are not very large. Mz
and Mq do not change significantly between the breaker and swash zones at
the loth! Street itransect. = Somting an ali=transects is poorelsit) ain the
breaker zone and best in the swash-berm zone, although the differences
between zones are not very large except possibly at the Pendleton Line
transect.

The average Mz and Mq for samples collected from the top of the swash
zone are smaller than those for the combined swash-—berm zone. This in-—
dicates that these parameters are smaller in the swash zone than in the
berm zone since the data of Table 5 generally show higher values for the
samples farthest inshore from the breaker zone.

Analysis of the data on size parameters for samples taken in the
vicinity of Rudee Inlet is presented elsewhere (Harrison, Krumbein, and
Wilson, 1964).

Reynolds Number and Drag Coefficient

Transects. The data for Reynolds number and drag coefficient for
the infinite fluid of the settling tube are summarized in Tables 4 and 5,
and Figures 7, 8, and 9. (Data for additional breaker zone samples appear
in addenda to Table 5.) It is to be noticed that the curves for Re follow
almost perfectly the pattern of the Mz curves. This is as expected since
the only variables in the equation used to calculate Re were the mean
diameter of the sample and the corresponding settling velocity, the
kinematic viscosity of the water being constant. Thus, Re is generally
smallest in the shoaling and swash zones and highest in the breaker zone
and toward the berm zone. Cp is a function of Re in the range of Re found
in our study. In this range Cp varies inversely with Re. Therefore, an
almost perfect negative correlation exists between Cp and Re, with lowest
drag coefficients in the breaker and berm zones and highest in the shoal-
ing and swash zones.

The Re values for the samples from the three transects are quite
small, most of them being smaller than 10. Very high Reynolds numbers
were found only in the breaker zone samples collected as part of the swash-
zone profiles. Related to these generally low Re values are relatively
high drag coefficients, as expected from the inverse relationship involved.
It is to be noted that the kinematic viscosity of the sea water on the
sampling day (1.91 x 10-5 ft2/sec) was relatively high and this contributed
significantly to the low Reynolds numbers found.

The last column in Table 5 presents the product of Reynolds number
and drag coefficient for most of the samples. In all cases they are more
than the value of 24, given by Rouse (1937) for particles within the range
of Stokes' relationship but seldom more than 48, or twice 24. Thus,
owing to the relatively high viscosity of the sea water on 25 March 1963,
the sand grains exhibited dynamic properties not too dissimilar from those
to be expected for finer grains. It is interesting to note that this
product (Re x Cp) is almost the same for particles with shape factor of
0.7 and 1.0 up to Reynolds numbers of about 30 (Table 1).

The data for average Reynolds number of the different beach zones in
the three transects appear in Table 6. These indicate that there is little
or no difference in Reynolds number in the shoaling zone along the whole
length of the area sampled. Several "t'"' tests showed that the differences
were not significant (P<0.01). Although differences between the breaker
zones at the 3rd Street transect and the 15th Street and Pendleton transects
appear to exist, "t'" tests failed to show any difference between the three
transects (P< 0.05) because of the large variances involved. Differences
between the swash zone at the 15th Street transect and at the other two
transects could be considered different in spite of the very few samples
taken. Nevertheless, it should be kept in mind that a great variability
among samples is characteristic of the swash zone (Krumbein and Slack,
(1956) and, therefore, attribution of significance to this difference
could be unfounded. Definite differences, corroborated by "t" tests
(P <0.05), are present between the swash-berm zone at the 15th Street
transect and the other two transects, while the difference between the 3rd
Street and Pendleton transects is not significant (P <0.01).

Rudee Inlet Area. Figure 10 presents Reynolds number isolines for
the stations in the vicinity of Rudee Inlet. The left-hand vertical axis
demarcates the 3rd Street fishing pier. The dotted lines and arrow at the
400-foot mark on the lower horizontal axis indicate the approximate
position of the inlet channel and direction of water flow at the time of
sampling. Isolines Re = 9 and Re = 13 were not extended beyond their limits
toward the 3rd Street pier because data collected from the pier a short time
later indicated values much lower than 9 and 13. Thus, it may be assumed
that the inshore and offshore components of these isolines become con-
tinuous on the south side of the pier. It is to be noted that Re values
inside isoline Re = 13 can be quite high; e.g., 54.78 at station S-13.

Isoline Re = 9 can be considered to approximately demarcate the
boundaries of the effect of the inlet outflow on the characteristics of
the beach sediments. Reynolds numbers of 5 and 6, as shown by samples from
stations outside of isoline Re = 9, are expectable since most of the
stations were beyond the zone of significant breakers. This conclusion is
supported by the data collected at the 3rd Street pier stations (Figure 8).
Thus, the data show clearly the effect of the Rudee Inlet outflow in alter-
ing the normal pattern of distribution of sediment properties along the
beach strip studied, as reflected by the distribution of Reynolds numbers.

Swash—backwash Zone. Trends of values determined for the samples
taken in the swash-backwash zone (Figure 2) may be summarized as follows:
mean size--slow increase in seaward direction over upper half of zone,
rapid increase over lower haif; sorting--best near landward side and in
upper half of zone, rapidly becomes poorer in seaward direction in lower
half of zone; Reynolds numbers under existing natural conditions (but for
infinite fluid)--slow increase in seaward direction over upper half of zone,
rapid increase over lower half. Limited data (Table 5) indicate that, for
a given uprush, the mean size and Reynolds number are greater at slack
water than after the backwash, on the upper five-sixths of the swash-
backwash surface. As would be expected from this finding, sorting (Table
5) is worst at slack water of the uprush.

Mineralogy

Table 2 presents data on the relative abundance of components other
than quartz grains found in the different sieve fractions of the mixed
Virginia Beach sands. Heavy minerals were significantly abundant only in
the residue fraction passing through the No. 230 sieve, while rock and
shell fragments were of greatest significance in the fraction larger than
2mm. It should be noted here that these two fractions were found to be
a very small component of the mixture of sands both in numbers and in
weight. Nevertheless, the presence of rock and shell fragments in the
breaker zone is of great significance in the determination of size param-
eters and dynamic properties. Although the amount of sediment finer than
0.062 mm tends to increase offshore from the breaker zone, it can be
assumed that its significance remains small in analysis of size and
dynamic properties and may be considered negligible within the length of
our transects. Zeigler, et al. (1960), state that a monomineralic (i.e.,
quartz) assemblage may be assumed when the quantity of heavy minerals is
small.

Application of Data

The importance of the values presented in this descriptive study to
the practical problems of beach nourishment: and beach protection, and to
many academic problems relative to the erosion, transportation, and
deposition of sand, will come only when said values find their way into
mathematical expressions. The values herein reported are for only a
specific set of conditions. In order to demonstrate the possible use of
the values, some equations are presented and mean or extreme sea-state and
particle-characteristic values are substituted into them for illustrative
purposes. The first example (Table 7) shows the dependency of the slope
of the beach in the shoaling wave zone on particle and sea-state properties.

The slope values of Table 7 are determined from the average mean
nominal-diameter values of Table 6 for the shoaling wave dynamic zone and
are based on; (1) the measured values of water temperature and salinity

at Virginia Beach, taken by the U. S. Coast and Geodetic Survey (C. Taylor,
1963, oral communication), and (2) the mean value for wave period and the
first mode for the distribution of wave heights for 5 years' running
records of waves made at the U. S. Navy's Cape Henry wave gage. The
average values of 5.3 seconds (for wave period) and 2.0 feet (for wave
height) were determined by the significant height method of analysis.

Mean water depth at the wave gage approximated 18 feet. The mean values
(Table 7) for temperature, salinity, and kinematic viscosity at Virginia
Beach are) 50.800 bms 625.77) 0/oomand 1. 31x 10-5 £t2/sec. Expectable upper and
lower limits to these ranges are given in Table 7.

On the basis of several theoretical and laboratory studies, Eagleson,
et al. (1963) developed an equation for the determination of the size of
grains (De) in oscillating equilibrium on a sloping sand beach (neglecting
reflection coefficient) of the form:

i 7/6
2 £ i 2/3
ay S¢ I\ © T
Dwaarel ole a) a | or | (23)
e iL g TL, So =" SF sing ee AE
where
D, = sand grain diameter, in feet
H, = wave height in deep water, in feet

V = kinematic viscosity of fluid (ft/sec)
Lo = wave length in deep water, in feet
2

g = gravitational constant, 32.2 ft. per sec

s = specific gravity of fluid or sediment, as specified

2
er] = G) ambliarsteet(oyal, sea, (He uy ee ee
2 sinh© kh + koh

Where: k = wave number = 27/L

h

water depth

oy beach slope

Substitution of the values mentioned previously (into Equation 23)
gives a measure of the effects of varying particle sizes (expressed as
nominal diameters) and kinematic viscosities on beach slopes (Table 7) in
the shoaling-wave zone. The three particle sizes chosen for Table 7 would
correspond roughly to mean sizes of sand found: (1) offshore, within a few
miles of Virginia Beach (0.12 mm ), (2) in the dunes at Cape Henry and along
Virginia Beach (Wentworth, 1930, Figures 112, 114, 115, and 116), and (3)
offshore 10 to 40 miles in restricted zones (M. N. Nichols, 1963, oral

communication). The values of beach slopes for the various conditions
(Table 7) are illustrative of expectable trends in slope modification only
and are not recommended for the designing of future beach nourishment
projects at Virginia Beach, without qualifications. For a further insight
into the problem of slope modification the reader is referred to the entire
paper of Eagleson, et al. (1963), especially the section on the equilibrium
beach profile (1963, p. 43).

A brief investigation of dynamics in the swash-backwash zone was also
made utilizing the expression of Ippen and Verma (1953) and the data of
Figure 2 and Table 5.

Their equation, adapted here and solved for slope angle, is of the
form:
T 7 -0.3
_ 1
Ve = 0.12w| sé 2 (Sq 1, ON) (24)
e

where

Ve = the mean backwash edge velocity just large enough
to initiate movement of a given sized particle

w = grain terminal fall velocity under natural conditions
(ft/sec)

dn = grain nominal diameter (feet)
Ss = specific gravity of grains (2.65)
S = slope of energy gradient

k, = effective hydraulic roughness length (2.5 k, where k
is average grain diameter of bottom)

To approximate Ve, the maximum backwash velocity and depth were
determined at the midpoint of the slope and the following relation solved
1819 Wes

2 = log (1 + tg/aq)
V max Ve | =a | (25)

where tq = depth of flow and a = the boundary--reference axis distance.
Surface samples of the sand were taken at the grid points or along the

single lines shown in Figure 2, immediately after recession of the backwash.
Backwash velocity was determined by introducing dye at slack uprush and
timing its movement over a measured distance downslope. (Ten-minute

averages of the heights of the plunging breakers at 13th Street and at Elm
Street showed 0.9 and 1.2 feet, respectively, for samples taken on Figure 2.)

Results (not presented) of our attempts to test equation 24 for its
applicability for prediction of swash-backwash slopes met with only limited
success when the computed slopes were compared to those actually observed.
Factors such as lift forces exerted on the grains due to groundwater move-
ment through the foreshore face and the imprecision of the measurement
techniques, may have contributed heavily to the inability to find a good
correlation between observed and computed slopes.

Beach Model Comparisons

Miller and Zeigler (1958) developed a model relating dynamics and
sediment patterns in the regions of shoaling waves, breaking waves, and
the swash-backwash zone. Their model, based on theoretical considerations
and published experimental results, was intended to hold for these dynamic
zones "in a state of equilibrium."" Miller and Zeigler's trend maps (1958,
Figure 22) for median sediment size and for sorting throughout the three
dynamic zones showed the trends summarized in Table 8. Also summarized in
this table are the observed trends of this study (based on Figures 7, 8,
and 9).

Table 8 indicates rather poor correlation between model and observed
trends, the best correlation coming between predicted and observed median
(mean) size in the breaker zone. Special effects, such as outflow of
Rudee Inlet current at 3rd Street (Figure 1) and the presence of numerous
pilings at the landward ends of the 3rd and 15th Street pier transects may
have adversely influenced this comparison in three places. Still, the
comparison is rather poor.

A further comparison of the observed trends for the swash-backwash
zone, with the model trends of Miller and Zeigler's (1958) "foreshore"
zone, shows that after backwash, observed sorting becomes poorer in the
seaward direction. The model predicts improved sorting. Observations
(Table 5, Figure 2) indicate an increase in mean size toward the sea in
the swash-backwash zone, and this was predicted by the model.

SUMMARY REMARKS

It was the main purpose of this paper to attempt a description of the
dynamic and related properties of the immersed beach sediment grains under
the conditions prevailing at the time of sampling. An extension of the
description over the range of expectable kinematic viscosities of sea water
at Virginia Beach (Table 7) can be accomplished from the tabulated values
of this report.

The calculations of Reynolds number involved the density and dynamic
viscosity of Virginia Beach ocean water of 26.74 o/oo salinity at a
temperature of 6.9° C. and the settling velocity of the particles of a

given size in such a fluid in a quiescent state. Since the density and
viscosity of the water were constant, it follows that the differences in
Reynolds number between particles were determined by their settling
velocities (which in turn depended on the nominal diameter and specific
gravity of the particles). Thus, the determinations of the Reynolds
number are based directly on the settling velocity of the particles.

The numerical magnitude of the Reynolds number conveys the relative
significance of the inertial (Vp x dn) and viscous (V) forces in action.
Reynolds numbers less than 0.001 say, would make one confident in ignoring
inertial forces. Reynolds numbers higher than 1,000, on the other hand,
would suggest that viscous forces might be ignored (although in reality
these can never be entirely ignored). The results of this investigation,
however, did not yield Reynolds numbers of such low or high magnitudes.
The majority of our values ranged between 2 and 15 (Table 5).

Because the sediment sizes involved ranged around 0.250 - 0.300 mm ,
a predominance of inertial forces was expected. The viscosity of the
water at the low temperature encountered at the time of sampling, however,
was high enough to significantly reduce the magnitude of Re. Not only are
the Reynolds numbers found relatively low but they fall within the range
where laminar flow changes into turbulent flow, i.e., inertial forces take
significant prominence over viscous forces. At Reynolds numbers above the
range of Stokes' Law (Re = 2, as extended by Oseen and Goldstein) the flow
lines around the particle separate from the particle surface and enclose a
discontinuity; a wake or low-pressure zone is formed. When this separation
is well formed, inertial forces predominate significantly. But this trans-
formation to significant predominance of inertial forces is gradual. The
zone of separation has a poorly defined appearance at Re = 3 but gradually
takes on a more clearly defined appearance as the Reynolds number is in-
creased until at Re = 20 the separation zone has a well-defined vortex
downstream from the particle (Schulz, et al., 1954). It should be noted
that within the range of Re = 3, to Re = 20, inertial forces are definitely
greater than viscous forces, but the viscous forces still exert a signi-
ficant influence in retarding the motion of the particles through the fluid.

The effect of the high kinematic viscosity of the sea water in lower-
ing the magnitude of Re (and consequently increasing that of Cp)resulted in
most of the sand grains exhibiting dynamic properties more akin to those of
much finer grains which are subject to greater drag resistance. At the
same time their dynamic behavior was not much different from that of
perfect spheres since at these low Reynolds numbers the drag resistance on
particles with S.F. = 0.7 and S.F. = 1.0 (as indicated by Cp values in
Table 1) is almost identical.

The distribution of Reynolds numbers along the different beach zones
in the three transects follows closely the distribution pattern of mean
size values, as expected from the relationship between these two parameters.

The indicated trend is for the magnitude of the inertial forces to increase
slowly toward the breaker zone where they reach their maxima. Shoreward of
the zone of high breaker energy they decrease again. The extension of high
Reynolds numbers in the swash-berm zone is an indication of the effect of
previous waves breaking closer inshore at times of higher tidal reaches.

An important result of this investigation comes in the realization of
the significant effect on the dynamic properties of the immersed sands
exerted by the high kinematic viscosity of the ocean water at Virginia
Beach at the time the study was conducted. This factor's importance was
also confirmed in an independent investigation (Harrison and Krumbein,
1964) of the relative importance of various environmental parameters on
mean size in the shoaling-wave zone at Virginia Beach.

20

ACKNOWLEDGMENTS

The authors are indebted to Mrs. Patricia C. Morales for her patient
typing of drafts of this paper.

The help of Dr. John M. Zeigler and Mr. Carlyle Hayes in building a
modified copy of the Woods Hole Rapid Sand Analyzer is much appreciated.

2i

REFERENCES

Albertson, M. L., 1953, Effect of Shape on the Fall Velocity of Gravel
Particles; Proc. Fifth Hydraulics Conf., Univ. Iowa, Iowa City,
pp. 243-261.

Briggs, L. I., D. S. McCulloch, and F. Moser, 1962, The Hydraulic Shape
of Sand Particles; Jour. Sedimentary Petrology, v. 32, pp. 645-656.

Brown, C. B., 1950, Sediment Transportation, Engineering Hydraulics,
edited by Hunter Rouse; New York, John Wiley and Sons, pp. 769-857.

Corey, A. T., 1949, Influence of Shape on the Fall Velocity of Sand Grains;
unpublished M. S. thesis, Colorado A. & M. College, 102 p.

Eagleson, P. S., B. Glenne, and J. A. Dracup, 1963, Equilibrium Character-
istics of Sand Beaches; Jour. Hydraulics Div., A.S.C.E., no. 3387,
D5 VI-Si6

Goldstein, S., 1929, The Steady Flow of Viscous Fluid Past a Fixed Spherical
Obstacle at Small Reynolds Numbers; Proc. Roy. Soc. London (A), vol.
23

Harrison, W. and W. C. Krumbein, 1964, Interactions of the Beach-Ocean-
Atmosphere System at Virginia Beach, Virginia; Technical Memorandum
No. 7, Coastal Engineering Research Center.

Harrison, W., W. C. Krumbein, and W. Wilson, 1964, Sedimentation at an
Inlet Entrance (Rudee Inlet-Virginia Beach, Virginia); Technical
Memorandum No. 8, Coastal Engineering Research Center.

Ippen, A. T. and R. P. Verma, 1953, The Motion of Turbulent Particles
Along a Bed of a Turbulent Stream; Proc. Minn. Internat. Hydraul.
Conv., Minneapolis, Minn.

Ippen, A. T., and P. S. Eagleson, 1955, A Study of Sediment Sorting by
Waves Shoaling on a Plane Beach; Beach Erosion Board Technical

Memorandum No. 63, 83 p.

King, C. A. M., 1959, Beaches and Coasts; London, Edward Arnold, Ltd.,
(Publishers), 403 p.

Krumbein, W. C., 1942, Settling Velocity and Flume-Behavior.of Non-
Spherical Particles; Trans. Am. Geophys. Union 23, pp. 621-633.

Krumbein, W. C. and H. A. Slack, 1956, Relative Efficiency of Beach
Sampling Methods; Beach Erosion Board Technical Memorandum No. 90.

22

McCammon, R. B., 1962, Efficiency of Percentile Measures for Describing
the Mean Size and Sorting of Sedimentary Particles; Jour. Geology,
v. 70, pp. 453-465.

McCulloch, D., F. Moser, and L. Briggs, 1960, Hydraulic Shape of Mineral
Grains; Geol. Soc. America Bull., v. 71, p. 1925.

Miller, R. L. and J. M. Zeigler, 1958, A Model Relating Dynamics and
Sediment Pattern in Equilibrium in the Region of Shoaling Waves,
Breaker Zone, and Foreshore; Jour. Geology, v. 66, pp. 417-441.

Miyake, Yasuo and Masami Koizumi, 1948, The Measurement of the Viscosity
Coefficient of Sea Water; Jour. of Marine Research, v. 7, pp. 63-66.

Newton, Isaac, 1687, Philosophia Naturalis Principia Mathematica, London.

Oseen, C. W., 1927, Neuere Methoden und Ergebnisse in der Hydrodynamik;
Akademische Verlagsgesellschaft Leipzig.

Prandtl, Ludwig and O. G. Tietjens, 1957, Applied Hydro- and Aero-Mechanics;
New York, Dover Publ., Inc. pp. 86-143.

Reynolds, Osborne, 1883, An Experimental Investigation of the Circumstances
which Determine Whether the Motion of Water Shall be Direct or
Sinuous, and of the Laws of Resistance in Parallel Channels; Phil.
Trans. Roy. Soc. vol. 174, Papers, v. 2, pp. 51-105.

Rouse, Hunter, 1937, Nomogram for the Settling Velocity of Spheres; Nat.
Research Council Ann. Rept., 1936-37, App. 1, Rept. Com. Sedimentation,
1937, pp. 57-64.

Rouse, Hunter, 1938, Fluid Mechanics for Hydraulic Engineers; New York
Dover Publ. Inc., 422 p.

Rouse, Hunter, 1950, Fundamental Principles of Flow; Engineering Hydraulics,
edited by Hunter Rouse; New York, John Wiley and Sons, pp. 1-135.

Rubey, W. W., 1933, The Size Distribution of Heavy Minerals within a Water-
laid Sandstone; Jour. Sedimentary Petrology, v. 3, pp. 3-29.

Schiller, L., 1932, Fallversuche mit Kugeln und Scheiben, "Handbuch der
Experimentalphysik", vol. IV-2, Akademische Verlagsgesellschaft m.b.H.,
Leipzig.

Schulz, E. F., R. H. Wilde, and M. L. Albertson, 1954, Influence of Shape
on the Fall Velocity of Sedimentation Particles; Colorado A. & M.
Research Foundation Report to the Missouri Research Division, Corps
of Engineers, U. S. Army, Omaha, Nebraska, M. D. Sediment Series,
No. 5, 161 p. (Mimeographed).

23

Shapiro, A. H., 1961, Shape and Flow; New York, Doubleday and Company,
Anchor Books, 186 p.

Sitokes. G. G., 185i) (On. the! Eftelctiotythe internal enictionsoreshuddsmonn
the Motion of Pendulums; Trans. Cambridge Philos. Soc., v. 9, pp.
8-106.

U. S. Inter-Agency Committee Water Resources, 1958, Some Fundamentals of
Particle Size Analysis; Inter-Agency Comm. Water Resources, Sub-
committee Sedimentation, Rept. No. 12, Washington, U. S. Govt.
Praintines Otekcel 155) spk

U. S. Navy Hydrographic Office, 1962, Tables for Sea Water Density; H. O.
Pwipil, NOs OLS, Bod.

Wadell, H. A., 1932, Volume, Shape and Roundness of Rock Particles; Jour.
Geology, vol. 40, pp. 433-451.

Wadell, H. A., 1933, Sphericity and Roundness of Rock Particles; Jour.
Geology, vol. 41, pp. 310-331.

Wadell, H. A., 1934, The Coefficient of Resistance as a Function of
Reynolds Number for Solids of Various Shapes; Jour. Franklin Inst.,
v. 217, pp.459-490.

Wentworth, C. K., 1930, Sand and Gravel Resources of the Coastal Plain of
Viredinia-) Budell s25) Van) IGcolay Sunmvelye pPia lor.

Whitney, G. G., Jr., 1960, The Woods Hole Rapid Analyzer for Sands;
Reference No. 60-36, Woods Hole Oceanographic Institution, Woods
Hole, Mass.

Zegrzda, A., 1934, Settling of Gravel and Sand in Clear Water; Leningrad
Scient. Res. Inst. of Hydrotechnics Transactions, 12: 30-54.

Zeigler, J. M. and Barbara Gill, 1959, Tables and Graphs for the Settling
Velocity of Quartz in Water, above the Range of Stokes’ Law; Reference
No. 59-36, Woods Hole Oceanographic Institution, Woods dole, Mass.,
IS jo, SS weiloilos, elael giceyolaiss.

Hesuelese, Jo Wa, Go Go Winstiinasy, Sie, Elintel Co Ro Islkesves, LYOO, Wools Isloile

Rapid Sediment Analyzer; Jour. Sedimentary Petrology, vol. 30,
pp. 490-495.

24

TABLES

Drag coefficients as a function of Rg for naturally worn
fragments,

Percent by number of mineral components in mixture of Virginia
Beach sands.

Grain triaxial measurements and Corey Shape Factor of mixed
Virginia Beach sands.

3rd Street Pier Stations. Computed dynamic properties of the
nominal spheres and Dynamic Shape Factor of the particles.

Virginia Beach samples, March 25, 1963, 15th Street Pier.

Average statistical parameters for the different beach zones
in the transects sampled.

Effect of water temperature and salinity and mean particle
size or bottom slope in the shoaling-wave zone for a local
mean (significant) wave height of 2.0 feet and period of
5.3 seconds and for a mean water depth of 18 feet.

Comparison between postulated trends of sediment parameters
and observed trends.

25

Table 1 .--Drag Coefficient as a Function of R, for naturally worn
fragments (Table 15, Schulz, et al. ,1954)

Cy Rox Cp
Ra SolFo> Oos) ORS O57 ORS ale (0) SE =O S.F.=1.0
aS 2510 ZaAL sO 19.4 ILS),© 29.10 23} 5)
2 20K 2 16.8 15.4 14.9
3 14.9 12.4 das 2 MONS 33.60 32.4
4 I 50) SoS) iso) 8.6
5 ORS Sia Vas Tod
6 Sol 7.45 655 6.38 39100 S78
7 85 dk Sa7 5.85 5.6
8 Vos Sodl 558 505
3) So) SOS 4.9 4.65 44.10 41.8
10 6.5 Bs 25) 4.55 4.3
als) SOS 4.1 3.45 S528 Lo 75 48.45
20 4.3 3.4 2.88 DoS) 2.68 37/50) 53.60
30 Soo) Ao Ye Zo Le 2.14 2.08 68.40 62.4
40 Boal Does 1.94 dhe Sil ES
50 2.85 Debs 1.74 eo 59) e516 87.00 78.0
60 2o YO ae S)5) LZ SO 1.45 1.40
70 2.60 1.83 1.49 Noss No 104.30 90.3
80 De SO ilo 7S 1.41 MAZS deo Zab
90 2.47 al W, be SS) ods 1.14
100 2.45 altGull 1. 30 ali. 1.08 130.00 108.0
150 236 1.45 1.14 0.94 0.895
200 2.34 Le SS ne OW 0.84 Oo79 214.00 158.0
300 Bee Mes) dis 2 ORS 0.67
400 2.40 30 1.00 ORAL 0.60
500 2.45 akg Suk 1.00 0.695 ORS 55 500.00 BUT oD
600 250) 133 RO 0.685 0.528
700 Do SYS) dos? OS 0.683 0.502
800 oss) 1.40 1.04 0.680 0.488 832.00 390.4
1000 2.65 1.48 1.08 0.675 0.460 1080.00 460.0
1500 25 10) AL oak 1.14 0.670 0.428
2000 2o TO 1.68 abo aby 0.670 0.410 2340.00 820.0
3000 2.63 ako. 710) 20) 0.680 0.400
4000 255) 5) abo YO) Io Zal 0.682 0.400
5000 2.46 bo) abo 20) 0.695 0.401 6000.00 2005.0
6000 2.38 1.66 Ig aly) 0.700 0.402
7000 25 Gal 1.63 dbo Jus} O05 0.404
8000 2.26 alee dL dy 0.705 0.406 9360.00 3248.0
10000 Do Ald Igy 1.14 O)5 720) 0.410 11400.00 4100.0
15000 Zo dual 1.40 1.08 Ops/alile 0.414

26

Table 2 .--Percent by number of mineral components in
mixture of Virginia Beach sands.

Sieve No. Mesh size % Heavy % Rock % Shell

(mm) minerals fragments fragments
10 2.00 0 18 20
18 1.00 ) 12 14
35 0.50 10 0 0
120 0.125 ale. 0 0
230 0.062 alk 0 0
Residue < 0.062 & 50 0 0

eilh

Table 3.--Grain triaxial measurements (in micrometer units)
and Corey Shape Factor of mixed Virginia Beach sands.

8, 2s = c/(ab)é

Sieve No. 18

a D Cc Sak Cte Manner. Soi.
61 56 20.88 0.35 53 50 27.60 0.53
45 30.21 28 ORS 106 58 OS)a Sj 0). 50
38 30 27.60 0.81 47 36 20538 0.49
56 53 40.65 0.74 43 36 26.85 0.68
Sy 62 Deo Val O30 50 49 31.70 0.70
56 40 25, 1S 0.54 55 45 31.33 0.63
5S) 45 alals abs) ig Zak 76 Sy 57.44 0.87
65 56 LSS O29 63 48 34.31 0.62
64 37 23.49 0.48 49 40 32.07 O72
86 59 17.00 0.23 54 46 26.85 0.53
Syl 34 16.78 0.40 72 46 42.89 0.74
51 32 23.87 O55) 45 40 Selo ay) 0.78
U2 36 35.06 0.67 43 38 25008 0.63
40 36 27.23 0.71 SH 43 33.04 0.66
54 53 32.45 0.60 60 43 33.04 0.65
39 38 32.82 OSS gil 64 32.30 0.42
56 41 32.82 0.68 58 42 SiS) 0.63
66 55 41.03 0.68 55 47 43.49 0.85
55 47.37 44 0.86 52 48 44.98 0.89
42 41 27.60 0.66 52 49 44.61 0.88
59 47 S35 De) O75 81 55 44.61 0.66
53 39 29.46 0.64 102 54 39.76 0.53
86 53 37.30 Oo55 45 43 23> 57 0.64
56 45 34.31 0.68 50 38 23.34 0.53
49 36 35.68 0.82 57 43 S7oa2 O75
110 S7/ 46.99 ONSS 69 62 46.84 0.71
72 50 PAS) clk 0.41 AS 50 37.07 0.58
50 54 S35 Sil 0.76 56 34 SLOSS) 0.72
78 63 48.86 0.69 68 41 2S) 6 (Sal. 0.56
Sill 31.70 31 OR 56 43 34.91 Oo Hal
65 56 44.76 0.74 74 43 41.99 0.74
62 47 33.19 0.61 76 65 58.41 0.83
56 Si 20.09 Oo Sd 101 56 48.34 0.64
76 40 40.65 0.73 44 40 23557) 0.68

28

Sieve No. 18 Page 2

a D Cc sme
58 48 36.77 0.69
61 54 36.40 0.63
63 40 34.91 0.69
70 46 43.11 0.76
73 66 31.18 0.44
70 48 30.80 0.53
48 49 99.31 0.65
67 By 42.74 0.63
54 38 37.89 0.83
63 39 39.01 0.78
67 MNO) BS 0.81
81 65 50.95 0.68
80 68 49.83 0.67
48 45 30.43 0.65
85 63 61.02 0.83
56 57 43.11 a.76
67 ASO . ag 0.80
57 41 23.72 0.49
73 AB. Als O76
60 60 53.18 0.88
58 An AG 0.72
67 62 38.64 0.96
56 35 97.07 0.79
106 68 57.29 0.80
79 69,60 61 0.82
35 Gh 1G BD 0.92
74 52 47.22 0.83
59 61 49.45 0.82
100 66 48.71 0.59
68 a9) BB Ou7al
87 54 42.37 Oneal
84 59 50.95 0.72
2
Sy = 67.59 S* = 0.0227
2 2 0.67 S = 0.15
Bae = AD.98 SX = 0.015
($x)2/n = 45.684
ny = 200

29

Table 3 cont'd

=

[—(¢2) SS) (uo) Ke) SS)

=

Eo

hb

pon

jot
WODMDWUONNONOHDOWODMDAKFWODOONONUNODANWDAWOUDWDWOAN ONAN

42

icp)
a]

SISA OOF LO O19) OL OLO lOO 1OjO1O FO 1161 OL O19 1O (OOF OlLOlO1O1O sO .@ O11 OLOl@ ro lLorleLe)

ANDNADANFUNDWOUDUWDAHNANNAMAAPYNUNUBPUDWAYNNINNAHDHAANBRADMN
OCFFODOONNFONUOONUNONBODHPYNEFRBADHDDAONWUOOUNUWOOBDAOH UN

Sieve No.

30

230

Page 3

i

bh

bh

hb

OWOONNOWOFWONDWODOHKHNODNWOONNWOWDOWOOWMDADAKPAWYNDAOUWOWHO
SS
NO

Bo oPe

=

=

w
ban]

SOLOLOLOLOLOLSLO(SLOLO(OlO LO LO (OL LOO COLO LOO LO OlOLS CLO LO 1S 19 SOLO Le Le 19 1E 12)

Sieve No. 230 Page 4

a D c S.F
13 10 10.05 0.88
16 12 10.05 O72
15 10 10.05 0.82
12 12 7.95 0.66
15 15 9.00 0.60
22 aval 7.95 0.50
14 19 7.95 0.61
15 10 5.86 0.48
18 13 9.00 0.58
19 12 7.95 0.52
19 12 7.95 0.52
14 14 7.95 0.56
19 14 7.95 0.48
12 aah 7.32 0.63
Da, 13 10.05 0.60
18 13 10.05 0.65
18 TAL 7.95 0.56
18 10 9.00 0.67
‘0 = 68,82 Ss? = 0.016
x = 0.63 8 = 0,127
$x? = 41.73 Sx = 0.0127

3

Table 4 .--3rd Street Pier Stations. Computed dynamic properties
of the nominal spheres and Dynamic Shape Factor
of the particles.

Station Vn Rn Cp, Vea ne DSF Rpt
A 4.9 10.53 3.07 0.55 0.57 7.95
B 4.3 8.48 8. il 0.55 0.57 6.40
c 4.9 10.40 3.05 0.53 0.55 Defi
D 4.5 9.12 3.16 0.55 0.57 6.89
E Aaa 7.61 8.76 0.50 0.53 5.54
E 8.6 6.22 4.59 0.53 0.56 4.65
G 8.8 5.29 5.66 0.52 0.57 3.99
H 3.8 6.90 4.29 0.55 0.58 5.26
I 4.3 8.54 8.50 0.56 0.58 6.50
J 2.5 eral 4.59 0.55 0.58 4.80
K 4.1 7a 3.90 0.52 0.55 5.64
L 2.6 eni7 4.58 0.52 0.55 4.58
M 5.1 4.78 5.72 0.53 0.57 26:
N 3.18 6.22 4.59 0.53 0.56 anes
0 B57 6.64 4.50 0.56 0.59 5.10
P 2.8 4.05 8.66 0.55 0.59 Qala
Q S27 ere 4.50 0.56 0.59 5.08
R al 1.55 ene 0.50 0.53 5.50
S 4.1 7.64 3.85 0.52 0.55 5.67
7 5.6 13.21 2.69 0.55 0.50 9.34
u 4.3 8.39 Aig 0.55 0.57 6.33
V oI. 4.63 6.30 0.49 0.53 8.57
W 4.4 8.80 4.01 ONSs 0.57 6.64
x 2.8 5. i 5.77 0.55 0.58 4.12
Y 6.4 7 1S 2.32 0.59 0.60 13.28
Z 6.2 iS. 2.41 0.58 0.59 12.37

AX 6.3 16.54 2.48 0.58 0.59 12.70
BX 6.5 18.21 2.45 0.64 0.65 14.67
or 606 19.12 2.27 ONer 0.67 15162
DX 5.9 14.81 2.51 0.58 0.59 11.38
EX 6.0 15.26 2.47 0.58 0.59 11.72
EX 6.5 17.90 2.23 0.59 0.60 13.87

w Rp is Rg for actual particle back calculated using equation RN (DSF) (Rn)?

32

Station

dp
I
NKSSSCHAPVTOZSHPAGHROWMVOWD

QSL SLURS eee

i
j=

SLOLOLO LO LOO LOLS OL LOO AO OLOLO TO

CIOLOJOLOKO LOLOL OL OLO1OLO1 OOO, OO@

SLOLOLO OVO TOLOLOlOl@loroe Ole 101 %©

COOOOOOOOOOOOOOOoOo ©

Table 5

Virginia Beach Samples

March 25, 196

15th Street Pi

M, So

199 0.471 al
209 0.502 2
238 0.619 2
262 0.689 2
286 O.77aL 3
266 OR722 2
265 0.662 2
246 0.659 2
257 0.734 2
245 0.662 2
244 0.611 2
266 0.682 2
268 0.650 2
255 0.625 2
291 0.683 3
263 0.494 2
252 0.615 2
240 0.597, 2

Too Fine
257 0.616 Be
DUS 0.600 Dn
267 0.714 Di
267 0.625 Ds
297 0.604 3
332 O.770 8
569 1.060 Ws
239 Oo SaL/ Qs
302 0.520 Bo
350 0.505 Al,
Souk 0.626 Bo
381 0.855 4.
302 ORSuls Bo
314 ORS29 8.
376 0.558 A.
348 0.516 4.
328 0.412 or
287 0.432 3

(continued on next

33

3

Ce

Nh

HH
DOWOFNYNANDODWAOAHnDUUMNS

lee

OBHDFUUNAFAHFHSPHPUUNHDHPONN

OQ
oO

bE
Ww
DN
[oo@)

OON DONNY WOON ONIN ONW
oO a oO
(es)

fim
DHOUNMNHDONMNADAMOAMOOAO WO
~N
we)

RexCp

33.

36.

37.

34.

38.

38.

41.

43.
50.
82.

39.
46.

46.

48.

26

98

50

69

dtl

54

85

12
57
44,

60
84

82

39

Table 5 Cont'd Page

Station Ma M, So Vp Re Cp

38rd Street Pier

A ORSOV, ORIG On 752 SROs Lod Sot
B 0.298 0.290 0.607 Clo Zul 6.28 6.34
© 0.295 O- Sie 0.776 8557 Ve S32 5555
D 0.284 0.298 @, 757 3.34 To S52 50 55)
Es 0,252 0.273 0.769 2). $8} 5.40 Hisalt
EF 0.242 0.254 0.640 262 4.49 Siz.
G 0.228 0.236 0.627 2.38 3679 B86
H 0.247 0.267 0.748 2.83 Seal) Toe
a 0.269 @ 292 0.866 3.245 6.40 6.27
J 05245 0.258 O,779 2.68 4.67 T1092
K 0.243 OL273 OR O2ar Di, Sal See oak
L 0.242 0.252 0.677 Di 5S) 4.40 8.34
M 0.208 6227 ORV 2a 2.265 BoAy 10.05
N 0.230 0.254 0.852 Dal? 4.49 8.2
O 0.247 0.264 OReiSuk Qed 4.94 7.64
2 0.207 he 2als} OR Seal 2,075 2, 38} I 8
Q 0.250 0.263 0.744 2 1o5 A, Sal 7.64
R 0.262 Oo 27at 0,629 B Si. Soe Vo2
S 0.268 0.274 0.623 296 5.48 A®)
ab 0.346 ORS47/ 0.705 4.14 9570 5589)
U OR 209 0.287 0.548 So dl7/ 6.14 VSS
V 0.220 0.220 Ooe27/ Qoaly) 8528} Lik, $0
W 0). Qstal 0.294 0.658 3.28 5 Sal 7605
x 0,28, 0.241 0,542. DAS 8598 9.95
% 0.388 0.394 0, 784 4.915 13.08 Bo 87
Z Ose77 0.382 0.448 A, V2 AD eau} 4.09
AX 0.386 0.386 ORS93 4.78 12.47 4.22
BX 0.412 0.412 Os 507 5 22 ASS 3,78
CX 0.431 0.426 0.538 5.44 15.66 So 89)
DX 0.368 0.369 Oo 585 Ay 52 LG 27 A Dy
EX 0.369 0.374 0.444 an595 das Gal 4.20
EX Oo. 87 0.405 0.596 5508'S I84 73 Bo 78
Pendleton Line
AA 0.420 0.424 0.554 5405 wis ieows 3.40
A 0.401 0.410 0.576 5), dg 1485 8. 59
B 0.452 0.439 0.449 5.685 16.86 8525
@ 0.440 0.4383 0, Seal 5.56 I65 27 Boel
D Oo S87 0.348 0.528 A ASS 9576 4.66
IE; O.858} 0.364 0.586 4.43 10.89 4.34
F 0.259 0.268 ORS55 2aS5 yen aS To8D
G 0.270 0.276 0.648 2355 53 Sal 7.00
H 0.414 0.462 dL 4s Bag) 6.005 67S 808
AL 0,255 Os2 7.1L ORAL Bh Sil, 6 e2 Ves)
J 0,254 ©, 268) 0.625 2, 765 A. Sil, T5859
K 0.294 O,Si2 0.789 8475 Vo Gab 5585
M 0.294 OmZonE 0.540 Bo Ass) 6.36 6,29

(continued on next page)

34

(continued on next page)

35

Table 5 Cont'd 3
Station Mg M, So Vp Re Ch RexCp
L 0.242 0.250 0.582 227, 4.56 V5 95
N 0.258 0.265 0.648 23795 5.00 765 8745
O 0.245 0.256 0.661 2.65 4.58 7.94
ap 0.245 O5257 0.710 2.665 4.62 V0 9a
R 0.242 0.256 0.719 2.65 4.58 7594 36.36
x 0.245 ©,255 0.689 2.68 4.61 7.94
Uu 0.242 O,258) 0.747 2.615 4.46 8.16
W 0.226 0.236 0.716 25875) Bo Vs 9.36 35.38
V 0.263 0.278 0.859 So 085 55 (59) 6.06
Q 0,256) 0.276 0.837 23 9)55) ya 510) 6.20
2 OR2333 0.246 0.742 2 Sal5) Al, -AL7/ 8.62
P+300 ORESual ORME, 0,927 585 2.46 Io 72 880.75
Top of Swash Zone
15-1 0.365 0.353 0.610 AT Al) 5 Aus} AE 55 46.31
dl5=2 0.303 0.306 0.590 3.48 Toll So 7/5
15-3 0.296 0.303 0.564 Bo48 75 O2 5.85
15-4 OR299 0.304 OF S59 3.44 7.06 582 41.08
15-5 0.298} 0.305 0.617 3.47 UodlS So HS
15-6 Oo esal 0.338 0.637 85 99 Jo dll 4.86
15-7 0.828) 0.324 0.603 Sea 8.25 5a 22
15-8 0.375 0.389 0.810 4.83 12569) 8,89) 49.36
15-9 ©, 86 0.384 0.872 Ao 15 12533} 4.11
15-10 0.8387 0.347 0.727 4.14 9.70 4.67
15-11 0.283 0.289 ORS93) 8520 6.24 6.41
15-12 ORuks 0.316 5 527 3.64 Vall 5.40 41.95
15-13 @oeulal 0.314 0.684 3.61 7.66 5.45
15-14 0.367 0.361 0.544 4.38 10.68 4.33
15-15 0.363 0.367 0.842 4.48 Dak, dal 4.26
15-16 0.378 0.370 0.626 4.54 IBS 4.22 AT) 39)
15-17 Oxsis9 0.348 0.828 4.16 9678 4.65
15-18 0.289 @5297/ @, 72 S588 6.68 6.06
15-19 0.265 Oo.273) 0.618 2 5 CY 542 6.65
15-20 0.303 0.324 Os772 8677 3525 522 43.06
15-21 0.821 0.323 0.635 3605 8.18 50 Als}
15-22 0.288 0.287 0.538 So dk7/ 6.14 5. 88}
15-23 0.301 0.302 0.674
15-24 Ons 95 0.360 0.544
P-19 0.334 0.334 0.670 8, 98 8.87 4.94 43.81
P-18 0,258} O.257 0.569 2.67 4.63 8.06
P-17 0.296 08295 (0) 3{Salal 3.30 64 5)/ Goals}
P-16 0.272 @,275 02573 2338} 5.583 6.90
P-15 0.244 0.246 0,479 2 52 4.18 8.62 36.03

Table 5 Cont'd Page 4

Station Mg Me So Vp Re Ch RexCp
Pp-14 0.244 0.249 0.483 2.56 4.30 8.48
P-18 @,252 O>257 @,.575 2G) 4.63 8.06
P-12 - - Missing - -
jealal 0,257 0.257 ORS 05 2.67 4.63 8.06
P-10 OR253 0.258 ORS29 2.68 4.67 HeS2 36.
P-9 0.269 0.274 0.501 2, NS 5.48 OO
P-8 OR256 0.264 0.554 2.78 AS95 7.60
P-7 0.261 Os27aL 0.582 26 Sal 55 Oe 1520
P-6 0.242 OR255 0.640 2.64 4.55 8.10 36.
P-5 0.267 0.280 0.685 8.07 5.80 6.70
p-4 Os277 0.292 0, 7/58 3.24 6589) 6.27
P-3 0.263 0.269 0,577 Qo Ba Aa. 7.30
P-2 0.238 O.25il 0.630 258 Ay 8.34 36.
P-1 0.289 0.303 0.778 343 VT 502 5535

Swash Zone Profiles

Elm Street

Grid -
A-1 0.309 0.326 0.666 8579 8.34 3, dB Cye
A-2 ORsuls ORs 0,765 85 BS) S$), ala 4.86
A-3 0.452 0, 558 1.676 7 Ga Deel 2 AO
A-4 AL, al@al, 1.394 2 ASS TAL, 5 136.65 120 680
B-1 0.316 0.326 0.686 8.79 8.34 3,12
B-2 0.314 0.334 O05 789 8. 98 8.87 4.94
B-3 ORSYS5 OR 2Ar 1.800 8.2% 89.97 Ip G4 TI 0
B-4 0.347 0.493 2. ilal 6. 5aL ZIoS 2.76
C-1 Omsats ORSS3 0.945 A. 2y A), Abe} Ay, jal Aa.
C-2 ORSOW 0.342 0.856 4.06 9.38 4.74
C-3 0.506 0.671 by S62 7. 6%" 34.47 2 AS 74.
C-4 ORSON OesOn 0.558 8.89) 6.89 Be.
2nd Profile
D-3 0.412 0.503 1.424 6.65 22.60 2 WO 61.
D=-9 0.348 0.368 0.876 4.50 Mag ay 4.25 AT]
D=4 0.643 0.680 Lo SS7 To6° 34.94 Peeks 74.
D-10 ORS50 O.475 liGy/al! Geng ILS) 6 87 2.95 SSE
D- 5 0.983 ENON 1.480 am OWs V5.0 26 a5 OSE
D-11 0.301 O—825 0.883 Bo V8 8.30 55 dL} MD.
D-6 0.508 0.690 Do lZD Tao 36.38 2.06 VE
D-12 0.490 Oo 755 2.622 8.4% 42.87 1.88 80.

Swash Zone Profiles

IZ cheSeneei

Grid -
A-1 0.368 O5870 0.524 4.54 ILL 85 4.22 AT).
A-2 0.482 0.498 Omsie7, 6557 DP » Alal, 2 18 60.
A-3 ORGS) 0.661 On777 Te Sk Bo Sal. PD «, AUS)

(continued on next page)

36

Table 5 Cont'd Page 5

Station Mg M, So Vp Re Cp RexCp

A-4 L225 Is 222 15265 12508 Cis) avs Le Sil 129

B-1 O5839) 0.344 0.622 4.09 8), 50 4.70

B-2 0.364 @OR3I92 @, 922 4.88 12,32 3.89 50

B-3 0.948 0.956 0.683 MOL Ss 67.86 Io Sal 102

B-4 0.806 ILoalL Ve 2, SAL ia, Be 883597 15688

C-1 0.850) O.857 0.631 A. BS 10.44 867 38

Cc-2 0.346 0.346 0.624 Al, Ag} 9565 4.69

C-3 0.720 0.708 @O.997 ToS Sui oue 2,00 US

c-4 2.528 2.441 0.520 DoS 85iL, Sal Tel 355

2nd Profile

B-1 0.488 0.488 0.956 6.48 21.20 Ds Bal. 5S)

B-7 0.490 0.490 ORS, 6.47 Dag A 2.80

B-3 0.806 0.806 0.392 8.9% 48.49 oT 85

B-9 O. 87 Oo BaL7 0.343 @), ale 50.26 aS

B-4 0.983 0.983 0.684 10) 5 9° 712,43 1.40 AYO.

B-10 ORZ730 0.730 0.863 8.2" 40.47 Lo 98

B-5 0.830 0.830 Lo O77 eh 52. is} ike 72 89

B-11 O. 749 0.749 0.982 8.4% AD, 58 dk, Sal

B-6 Lo LO) Lo also 0.970 12,6 102.98 Io 23) ABD

B-12 1.087 1.087 0.827 iL Be 86.71 eS? ALAS},
Off Rudee Inlet

12N 0.417 0.414 0.698 5.26 TA. Val 3.44 50.

S-11 0.303 @ 292 OFGSS 3.24 6.89 6.20

S-10 0.296 0.290 0.586 8522 6.30 6.30

S-9 0.288 0.283 0.586 8}5d2 5596 6.50 SSE

S-8 0.284 O20) 0.637 2.88 5625 Vo20

12-M O.8S7 0.388 0.682 4.82 12.64 BoSS)

S-7 0.290 0.286 0.552 SER 6.10 6.43 89),

S-12 0.410 Oog95 0.589 Al, 38) SEG 3579

9-N 0.444 0.449 0.514 5.80 17.60 302

S-13 0.473 0.853 0.526 9,5 G4. 78 Lo 67 al

12-S 0.298 O5,29i1 0.649 B28 6.34 6.30

9-M 0.405 0.409 0.547 Sodl/ 14.29 3.60

S-36 ORSIS9 0,359 0.618 4.36 10.58 4.44 46.

S-14 0.518 0.522 0.565 6.93 24.45 2, 58

S=-25 O.877 0.382 0.510 A W2 ID. Als} AL «La,

S-5 0.358 0.282 1.184 8}, 110 54 $0) 6.60 38.

S-6 0.288 0.284 0.566 85 I8} 6.00 6.50

8-S 0.350 0.382 0.418 4.72 ID, LS Ay, TAL

S-15 0.435 0.427 ORS555 5.46 IS, 75 8}, al 580

S-16 0.454 0.436 0.674 5.60 55 50) 3.30

S-17 0.384 0.340 O. 705 4203 3), BS 4.83

S-18 0,629 0.300 0.923 8,88) 6.85 5,92 40.

(continued on next page)

37

Table 5 cont'd Page 6

Station Ma Mz, So Vp Re Cp RexCp
S-19 OR 297, 0.284 Oo 757 Soaks} 6.00 6.50
S-20 O.251 0.238 0.676 2.41 Sosy 9.10
S-27 0.276 0.253 OAS: Dal: 4.46 8.20 36.57
S-26 0.254 0.248 0.653 2.54: 4.25 8.49 Sos
ADDENDA

15th Street Pier Breaker Zone
hy = = = = = S o
Z-2 0.309 0.284 0.809 Bods 6.00 6.50
AX - - - - - - -
AX-1 0.341 ORS SS 0.648 4.02 S)o als} 4.82 44,24
AX-2 Op, Salil 0.296 0.760 Se 6.63 Gulls
AX-3 @, Bel 0.274 0.667 Bs HO 5.48 7.00
BX - - - - - -
BX-1 0.495 0.470 O597/6 GodlZ 19.44 2B Sal 595 5/
BX-2 Omsuky OR SHES 0.641 85 SS VoV2 5.45
BX-3 0.254 OR 250 0.556 257 4.34 8.45
CX - - - - - -

38rd Street Pier Breaker Zone
S S = = oo = =
S-2 0.316 0.316. 0.658 3.64 Votd 5.42 426 la
ap o = = = oo =
T-1 0.324 Oo sub7 0.697 3.66 7.84 5589)
T-2 0.266 O6257/ 0.494 Dols7/ 4.63 8.06
T-3 0.288 O5279) 0.548 3.05 5.74 Gru B35 S7/
U = = a 4 ran 2
u-1 0.264 O29 0.463 ZO) AD 7.47
u-2 0.258 OR252 0.500 259) 4.40 8.34
u-3 0.267 0.266 0.462 DBD 5507 Wo Sal. Ch3350)7/
V = 5 —; = nm =
V-2 0.290 0.288 0.506 SoalS) 6.20 6.64
W x = ae = = =

“These values were extrapolated from Figure 2 of Inter-Agency
Committee on Water Resources (1958) and possibly are lower
than what would have been obtained if the range of Figure 6's
curves had been extended to include larger particle sizes.

38

Ss} US Se

shot
oheh

GL“ SiI-16 +7
T6°L -8ZL°§

GOP SUHLG UL
ILS So 1
OL°6 -E6°€
GLE “136 -G

OELGES WL)
466 6 3915 8)
SS °6¢é-T6°€
BES) —GG2E

ehuey

v6 °€T
oS
69°8
60

£0°€T
vo'S
Gms
9o°S

96°8
€v'°8
8L°6
€9°v

“AY

6L8° 0-620

98S °O0-6v7'0
heh

SS L2SGes) "oO

£66 0-075 °0

vel’ O-€6E “0
~8S9°O-TVS 0
SOL°O-LdE "0
Té6 “O-TES “0

SS8°0-¢éTv 0
3065 °0-SOS ‘0
OO ULL “O)
TEE OR Een O

S6E°0-8ES "0

6€v'O-8vEe 0

Shoe.
Shon

viv’ 0-vSc'0
VG OR ESE» ©

9Sv 0-698 °0
2b66°O-Tvé'O
97° 0-792 0
L0€°0-40¢°0

T8€°0-28¢°0
3056 °O-c0€ °O
LVS °O0-vES"O
oLé°O-S6TO

pe_odeTToo etTdwes suo ATUO us»

pegoetTToo setduwes omy ATuoO

66¢°0

€0v 0
89¢°0
86¢°0
Svc°O

€6€°O
£9¢°0
c8¢c°0
€S¢°0

eee O
9dE°O
9EE°O
€vc'O

68€°0-907¢°0

6€v O-LEEO

Pont
ee

o9v°0-€96°0
oLE O-Z6T 0

Tév 0-89€°0
%L86°O-TEC'O
LvE°0-65e°0
9TE*O-ETS'O

ble O-T6¢'0
~87€ *O-O0€~O
69S °0-6€¢°0
T6¢é°O-66T 0

petdwes sqoesuer, 9yq UT seUo0Z
yoreq AUsdeTJTP 9yQ FOF SdJojoweared TeotastTqeqs ehersay--°

“eh

vOe"O

000
6S¢°0
8TE°O
6S¢°0

T6€°O
95¢°0
08¢°0
49¢°0

LEO
vce" 0
ee "0
SSé°0

9 eTqeL

auoz ysems jo doz

wdieg-Us ems
USeMS
auo0z cJeyeorg
auoz HhurtpTeoys
BUTT UOVeTPUSeg

wieg-Us eMS

USeMs

auoz Jeyeedg

auoz HurtpTeoys
Jetd JeedAS pag

waieg-Ysems

USeMS

auozZ Jeyeerg

auoz hHutTeoys
detd 4808c9S Yast

39

Table 7.--Effect of water temperature and salinity and mean particle
size on bottom slope in the shoaling-wave zone for a local
mean (significant) wave height of 2.0 feet and period
of 5.3 seconds and for a mean water depth

of 18 feet
WATER Slope
Kinematic Particle indicated from
Temp. Sal. viscosity nominal diameter Eq.(23) (degrees
(°F) (0/00) (@=> ft?/sec) (mm) and minutes)
85.0 3550) OFS Opae2. 4358
56.8 DoT nS 0.12 5° BO!
S250 16.0 ios) @5a2 Go alg
85.0 S5)5 0) O59 0.288 2B OS
56.8 2500 168 0.288 2D? BR
32.0 16.0 aly) 0.288 DO” 53
85.0 35.10 O59 0.700 @° 55"
56.8 AS 7 alas} 0.700 Io? OF
S25 (0) 16.0 69) 0.700 IL 20)"

40

Table 8.--Comparison between postulated (Miller and Zeigler, 1958) trends
of sediment parameters and observed trends (Figures 7, 8, 9).

Miller and Zeigler This Study

Shoaling-wave zone:

Sorting progressively
improves moving shore-
ward to breaker zone

Median size increases
shoreward to breaker
zone.

Breaking-wave zone:

Foreshore zone:

Sorting best

Median size largest

Sorting irregular but
relatively high near
base, more regular but
poorer near top

Median size pro-
gressively decreases
moving landward

4

Sorting exhibits reversing
trends (Figs. 7, 8) or im-
proves shoreward (Fig. 9).

Mean size increases slightly
toward breaker zone (Fig. 9),
stays roughtly constant (Fig.
8), or shows reversing trends
Gaga.

Sorting worst (Figs. 7, 9)
or relatively good (Fig. 8).

Mean size largest (Figs. 7,
9) or relatively large (Fig.
8)

Sorting relatively high and
uniform throughout extent
(Figs. 8, 9) or irregular
and high near base (Fig. 7)
becoming high and uniform
near top.

Mean size irregular (Fig. 7)
or increasing landward (Figs.
8, Me

10.

FIGURES

Location of study area and station designations for sampling
along transects and along top of swash zone.

Sampling grids and foreshore slopes at sites of swash-backwash
sampling.

Sampling stations at Rudee Inlet.

Schematic diagram of Woods Hole Rapid Sand Analyzer.

Sediment analyzer output curve of pressure (P) versus time (T).

Settling velocity as a function of water temperature for samples
from the shoalirg-wave, breaking-wave, and swash zones.
Curves are for fresh water and would be displaced about 0.01
cm/sec to left for water of maximum expectable salinity
(36 o/foo).

Trends of values for mean size, Mz (nominal diameter); sorting,
So; and mean Reynolds number, Re, for infinite fluid under
natural conditions at 15th Street transect, 25 March 1963.

Trends of values for mean size, MZ (nominal diameter); sorting,
So; mean Reynolds number, Re; and mean drag coefficient,
Cp, for infinite fluid under natural conditions at 3rd
Street transect, 25 March 1963.

Mean size, Mz (nominal diameter); sorting, Sj; and mean Reynolds
number, Re, for infinite fluid under natural conditions at
north property line of Camp Pendleton, 25 March 1963.

Mean Reynolds number isolines for Rudee Inlet area, 25 March 1963.

42

DISTANCE IN FEET

: \Sth Street Pier
Lx—~ —— A
15-1" ores

((}—smmmmt 13TH STREET SWASH—BACKSWASH SAMPLING

15-5Se

SHOALING

OCEAN

ATLANTIC

INDEX MAP

BREAKER ZONE AT TIME OF SAMPLING

SWASH-—BERM ZONE
SWASH ZONE AT TIME OF SAMPLING

3rd Street Pier
A

ir}
Zz
a
a)
a
{e)
a6
o
©
Zz
{e)
=)
a
=
WW
Ww
w
z
ud
Oo
Zz
<¢
=
w
a

ATLANTIC OCEAN

Se ELM: STREET SWASH—BACKSWASH SAMPLING

P-10¢

North Property Line,
>P+300 Camp Pendleton

FIGURE 1. LOCATION OF STUDY AREA AND STATION DESIGNATIONS FOR SAMPLING
ALONG TRANSECTS AND ALONG TOP OF SWASH ZONE.

43

UPRUSH

Sino EM

A B Cc
a AFTER
AT SLACK OF RECESSION OF
UPRUSH BACKSWASH
Bl af SoS ae
| tan=0.0639 NOT SAMPLED tan=0.0596
B3 B9
e— BACKSWASH B4 Blo BACKSWASH
Ht.=0.5 ft. Ht.=0.5 ft.
Vel.=3.6 ft/sec Vel.=2.7 ft/sec
B5 Bll
—---- B6 Be
PLAN VIEW PLAN VIEW

BEMeSineEr

A B Cc
——-——- D3 D3I=—
Beach slope =0.0871
D4 DIO
BACKSWASH D5 Ol BACKSWASH
Ht.=0.5 ft. Ht.=0.4 ft.
Vel.=4.0 ft/sec Vel.= 5.0 ft/sec
D6 DI2---—--
PLAN VIEW
Beach slope = 0.0871
RSS (0) 5 10 20
Bae __=_____SSS=I

PLAN VIEW FEET

FIGURE 2. SAMPLING GRIDS AND FORESHORE SLOPES AT SITES
OF SWASH-BACKWASH SAMPLING.

44

009

oos

“LSINI 33qnNe LV SNOILVLS SONI TdWvs “€ Sundls

1334 NI SONVLSIO
OO” OO€ 002
\

SNOILVLS

0Ol

JIdWVS

SNOZ
y3NV3Ns

ool

002

oo€

SONVLSIA

Jhelels) IN

45

STORAGE AND DE-AERATION TANK

———__>
HOT WATER

REFILLING WATER

GATE ASSEMBLY
GATE SW. (SET)

GATE RELEASE SW.

COLUMN

AMPLIFIER
RECORDER

PRESSURE
LINES

BI-DIRECTIONAL DIFFERENTIAL
GAS-PRESSURE TRANSDUCER

|

| DRAIN | OVERFLOW

FIGURE 4. SCHEMATIC DIAGRAM OF WOODS HOLE RAPID SAND ANALYZER.

46

RECORDER PAPER

T
(SEC)

CK (CG CCOOQRCKMKK

RELATIVE P (%)
FIGURE 5. SEDIMENT ANALYZER OUTPUT CURVE OF PRESSURE (P) VERSUS TIME (T).

47

WATER TEMPERATURE (T) IN DEGREES C

ogZ

"(00/0 9€) ALINITVS S1GVLOSdX4d WAWIXVW SO YALVM HOS L447 OL
D4S/WD 10:0 LNOGVY GADV1dSIG 34d GINOM GNV YSLVM HSAs AOA FAV
SSANND ‘SANOZ HSVMS GNV ‘SAVM-ONINVAYNE “JAVM-ONITVOHS SHL WOUS
SA1dWVS NOS JUNLVYAAdWAL YSLVM JO NOILONNA V SV ALIDOISA ONIILLAS “9 SaNdls

OD3S/IO NI (CW) ALIOOISA SNITLLAS NVAW

fo)
1

Ol

S|

ee Cae Te oe eee ee ee LT

oO
it
es

u

Ge

/
“YSLVM HS3Y4 4O4S
Juv SSAYND “SANOZ
HSYMS ONV ‘SAVM
—ONIMV3SYNE ‘SAVM—ONI
-1IVOHS WOYS SAIdWVS
Y¥O4 SYNLVYSdW3l
YSLVM JO NOILONNS V
Sv ALIDO13SA ONIVLLAS /

—

SSS

SSS SS SSS

oslo

O3S/L43 NI (PW) ALIOOTSA ONITLLSS NVSW

(e)
t+

fe}
ive)

(>)
o

[o)
ie

4 $33Y950 NI (1) SYNLVYSAdDWSL YSLVM

48

OS
00
da ‘Ayloojan Buijjyjas uDayy

re)

vo

90

80

Ol

'€96L HOUVW SZ ‘LOASNVYL LSSYLS HLSL LV SNOILIGNOS
AVENLYN YSGNN GINIS ALINISNI YOS “UY ‘YAAWNN SGIONASY NVAW CNV
6 'ONILYOS ‘(MSLIWVIG TVNIWON) 7W ‘4ZIS NVAW YOs SANIVA SO SAN3XL “2 ANNI

SNOZ WY3a—HSVMS | ANOZ | SNOZ SAVM ONIIVOHS
YysyvsyE
== SS ol ES

LS

(4a;aWDIP |DUIWOU) 2 ‘eZIs UDs\
2) ‘Yaquunu spjousay Uday) >) JO GNSYL

°s ‘ONILYOS JO GN3YL

SSS SS SS SS SS So a oo re I US el
XA —— My 2———— Vv

£0

770

JL

1
mM

ol
wo t+

(98S/ wd)

49

BS
(exe)

re)

vo

90

80

o}i]

"C961 HOYNVW SZ ‘LOAS
“"NVaLl LaaYdLS Gee LV SNOILIGNOD WaNLVN YsGNN GIN1a ALINIANI
YO4 ‘99 ‘LN3IDISS5OD OVC NVAW GNV “4 ‘YSEWNN SGTIONASY NVAW

“S ‘ONILYOS ‘(YSLSWVIG TVNIWON) *W “SZIS NVSW NOS SANTIVA 4O SGNSYL 8 JYNdIS

ANOZ tee | ANOZ
Wu38—HSVMS Y3anVvsaYE SAVM SNITIVOHS

ee oe a

(4a;awWDIP |DUIWOU) Zyy ‘azIs UDaYy
da ‘Kyio0}an Buljyyas uDayy

} dO QN3YL

®y ‘YSEWNN SGTONASY 40 GNSYL

99 ‘LN3I91S4S9O09 OV 4O GN3YL

Os ‘ONILYOS JO GNS3YL

rat

ol

[-

-80

(wi )

50

‘€96L HOYNVW SZ ‘NOLSTGN4d dWVD 4O ANIT ALYISdONd HLYON
LV SNOILIGNOD TWYNLVYN YSGNN GINTS S3LINISNI NOS “°Y ‘YSSWAN
SATIONASY NVAW GNV “°S ‘ONILYOS ‘(YSLAWVIG TVNIWON) 7W ‘4ZIS NVAW 6 JYNdIS

ANOZ ANOZ ANOZ
OG WY38—HSVMS Yysanvsaya AAVM ONITIVOHS
vO ZW ay
JN
oO -O i PNeues
: Sl S28
ae 9S ‘Buljsog .
Me) ess NN
Se NS 5
\ 7
80 SG Se
\e- EN
AO) ff
ol 2 se ol gee ea = 4
£0 NX ca
(42}awWDIP |DUIWOU)
el ZW ‘azis ubayy) / ~~?
vO ;
vl :
SO Ol
3
2
ay
“saquinu spjoukay :
Sl

S|

009

‘C96L HONVW SZ ‘VANV LAINI AIGNY YOS SANITOSI YSEWNN SGIONASY NVAW “OL AYNdIS

1333 NI JONVISIG
00S oob oo¢ 002 00!

|

SNOZ
ysyvsuE

foxe]

002

oo€

JONVLSIC

IEEIS\E}) IN]

52

‘rood st uostiedwod 3nq ‘Tapow JaTsatz pue TaT{[TW-S96T
4&q pazyotpeid asoy, yyTM paredwod are sauoz ITweUAp ay} yNOYsnoIYy
SuTzIOS pue azts uevaw FO spuat} paAtasqgQ ‘pataptsuod st oauoz
aAem-duTTecys ut sadotTs ydeaq uo puke saTIt1Ied pues jo satyradoid
Dtweudp uo A}TSOISTA IT}eWAUTY JO aduez,IOdwt sy, ‘*poeredwod pue
PazyeTNOTed atam “Te ja SddtIg FO 1oO,Dey adeys Itweudq pue 10},9"eF
adeys s,AaztogQ ‘*yUaTITFFa09 Berip ueow pue ‘Taqunu sptouday ueaw
‘AYTIOTSIA ButT}}aS ueaw :atamM Satdwes ay} Jo satziadoid aqtissap
0} pesn sjuaWaInseaw “JaTUL sapny FO AYTUTITA ay} UT puke Ydeaq
ay} ssorse sjoasuer} ¢ BuoTe ATSnosauez [nuts uaye}, satdwes pues jo
Taqunu agieq~T e& Fo AjYTIOTAA BuTT}}es ueawW UT SUOT}JeTIeA IT}eWazSAS
azATeue pue sinseow 0} paustsap Apnjs e IOJ pajuasaid ore sztnsay

daISISSWIONN 6 “ON WhONVYOWHW TVOINHOEL

"y ‘owetTy-SeTezow IIT
*mM ‘uOSTIzIeH II

OTFEL I

“SNTTE OT pue
SeTqe} g dutpntour ‘dd go ‘pooT taquacaq ‘oweTy
-SeTerow “Yy pue uostizey "mM Aq ‘WINIOUIA ‘HOVHE
VINIOUIA LV GNVS GHSYXWWI JO SHILYHdOUd OIWVNAC
‘@A‘YD¥ag eTUTSITA

v

stsA[euy }Juawtpes “¢
"@

sassad0Ig er0ys ‘T

‘O'd ‘*HSVM ‘dO ‘“UFINSO “SHU “OYONT TvLSvOO AWuy’S‘n

‘rood st uostiedwod 34nq ‘[Tapow JaTstez pue IJaeT[TtW-So96T
Aq paz2tpaid asoyu} yyIM patedwod are souoz oTweUAp ay} }NoYsnoIYyy
Sut}ios pue azts ueaw FO spuar} paAtasqQ ‘parteptsuod st au0z
aAeM-SuTTeoys ut sadoyTs ydeeq uo pue saTIt}yIed pues jo satz1edos1d
otweudp uo AYTSOOSTA IT}eWSUTYH FO aduez,TOdwTt sy, ‘paredwoos pue
pezetnoTes aram “Te ya sddtig fo 10,9eqy adeys Itweudq pue 1oz,.eTF
adeys s,Aat0j ‘jUaTITFJJa09 3eip uesw pue ‘raqunu sprouday ueow
“AYTIOTAA Buty}}as uvaw :atem satdues ayy Fo satjytadoid aqtiosap
0} pasn sjuswainseaw “jZaTUT aapny FO A}TUTITA dy} UT PUe YyIeaq
ay} ssoroe s}oasuez}y ¢ JuoTe ATSnosuejz{nwrTs uaye} SatTdwes pues Fo
Tequnu adie~T e@ FO AYTIOTAA ButT}}aS UesW UT SUOT}eTIeA I9T}eWa4SAS
azATeue pue ainseaw 0} paustsap Apnys e 3OozZ payuasard are szypnsoy

da IdISSVIONN 6 “ON WNGNVYOWHW TYOINHOEL

“yu ‘oweTy-seTezow III
“mM ‘uostizey iit
OTITL I

5 “SNTTF OT pue
SaTqe} g dutpnqtout ‘dd gc ‘po6t raequadeq ‘owety
-SeTeiow “Yy pue uostizeyH “mM Aq ‘VINISUIA ‘HOVHE
VINIOUIA LV GNVS CHSYHWWI JO SHILYHdOUd OIWYNAC
‘eA ‘YDBag BTUTSITA *

v

stsAyTeuy }UuaWTpas “¢
@

sassad01g aro0ys ‘Tt

‘O°d ‘"HSVM ‘HO ‘UHINHO “SHU “OMONA IvLSvyOO AWYY'S’A

*zood st uostiedwod 3nq ‘ TapoW TeTSatzZ pue JaTTTW-So6T
Aq pa}2tpaid asoy} YIM patedwod are sauoz dtweudp ayy ynoysnoryy
Sut},IOS pue ezts ueawW JO Spuat} peATasqQ ‘paraptsuod st 9auoz
aAeVM-SuTTeoys ut SadoTs ydeaq uo pue saTItj,I1ed pues Fo satyroedorzd
otweudp uo AjTSODSTA IT}eWaUTY JO aduez,Todwt syL ‘*paredwood pue
payeTnoTed otom "Te ya S3sdtIg FO 10,9eq odeys Otweudq pue 10,IeF
adeys s,Aazt0pD ‘*jUaTITFFa0o9 B3eip ueaw pue ‘raqunu sprfouday ueau
‘ATIOTSA BuTT}}aeS uvaw :arem satdues ay} FO satziadoid aqtadsap
0} pasn sjUusWaINseaW ‘zaTUT svsapny FO AyTUTOTA ay} UT pue YyIeaq
ay} ssorde sy oasuez} ¢ SuoTe ATSnoaue},[nNutTs uaye} satdwes pues jo
Taqunu asieq~T e& Fo AYTIOTAaA But{T}}as uvaW UT SUOT}eTIeA IT}eWaSAS
azATeue pue sinseoaw 0} paustsap Apnys e& IOJ pajuasazd are szytnsoy

GHIAISSVIONN 6 “ON WNGNVYOWHW TVOINHOL

“y ‘oweTy-seTeirow III
*m ‘uosftizey II
OTIEL I

“SNTT?E OT pue
saTqe} g sutpntout ‘dd zg¢g ‘po6t Taquaceq ‘oweTy
-saTeJow "y pue uostizey ‘Mm Aq ‘SWINIOUIA ‘HOVE
VINIOUIA LV GNVS CHSYHWNI SO SHILYHdOUd OIWYNAG
"eA ‘yYoeag etuTsITA °

v

stshTeuy }JUuewTpas “¢
@

sassad0Ig ar0Yys “T

‘O'd ‘°HSVM ‘HO ‘YHENHO “SHY “SUYONT IvLSvOO AWuy’s*nA

*zood st uostzedwod 4nq ‘TapoW IaTsatzZ puke TJaTTTW-So6T
Aq pe yotperid asoy} yytM peredwod are sauoz dtweudp ay} ynoYysnoryy
Suy}IOS pue azts uvawW FO Sspusat}, PpaAtasqgQ ‘peTaptsuod st auoz
aAem-SutTeoys ut sadoTs yo¥aq uo pue saTot}y1ed pues Fo saty1adoid
atweudp uo A}TSOISTA IT}eWaUTY FO aduezTOdwT ay *paredwod pue
payeTnotTes atam "Te 4a s3stIg FO 10,9eqy adeys Itweudq puke I0O},IeF
adeys s,Aar0p ‘“jUuaeTITFFa09 Berip uesw pue ‘Iaqunu spTouday ueow
‘AYTIOTOA BuTT}}es uvow :ataM SaTdwes sy} JO satyradord aqtsdsap
0} pasn s}UuawaInseaWw “LaTUT svepny Jo AytuTOTA ay UT pue Yydeaq
ay} ssoise sjdasuer} ¢ SuotTe ATSsnoauej, [nuts uaye}, satTdwes pues jo
Taqunu adieyT e Fo AYTIOTAA ButT}}as ueawW uF suoT}eTIeA IT}eWazSAS
azATeue pue aInseaw 0} pausdtsap Apnys e JOF payuaseid are sz[nsay

da1dISSVIONN 6 “ON WOGNVYOWHW TVOINHOSL
“y ‘oweTy-saTeiow IIT

*m ‘uostizey Il “SNTTT OT pue

eTIEL I SeTqei g dutpntout ‘dd zo ‘po6T taequaseq ‘ouety

Dy -SaTeIOW “yY pue uostzieH “mM Aq ‘WINIOUIA ‘HOVE

stsAyTeuy juautpas *¢ VINIOUIA LY GNVS GHSUSWNI JO SHILYAdOUd OIWVNAG
“eA ‘yoeag BTUTSITA “2

sassao0Ig a10ys "T ‘O'd ‘*HSVM ‘HO ‘YHLNHO “SHY “SYONT TVLSVOO AWYY’S*n

‘rood st uostzedwod jnq ‘Tapow TaTsatzZ puke I2aTTIW-S96T
Aq pezy2tpaeid asoy} YIM patedwod are sauoz ItTweUAp ay} yNoYsnorYy
3utjIos pue azts ueaw JO spuat} paazTasqgQ ‘pataptsuod st sauoz
aAeM-SuTTBoys ut sedoTs yo¥aq uo pue satTIt}Ied pues jo satz1adoid
Dtweudp uo AZTSOISTA IT}eWsUTYy FO aduez,stodwut sy, *patedwod pue
peyeTNoTed stam "Te Yo S3stIg FO 10},5deq adeys Itweudq puke 10};IeF
adeys s,Aat0p “jJUaTITJJa02 Beip ueaw pue ‘Taqunu sprfouday ueosw
“AJTIOTSA BuTT}}asS uesw :aztaM Satdwes ay} Jo sat}iaedord aqtidsap
0} pasn sjuaWaInseaw “}EeTUL sepny Fo AjTUTITA 93y} UT puke YdeeEq
ay} Sssoride s}dasuet} ¢€ BuoTe ATSnosuez[nwtTs usye} satTdwes pues fo
Taqunu a31e~T e FO AJTIOTSA ButTyT}}aeS uesW UT SUOT}eTIeA IT}BWa SAS
azAyTeue puke sinseaw 0} paustsap Apnys e IozZ pajuaesaid are sytnsay

dHISISSVIONN 6 “ON WhONVYOWHW TVOINHOFL
“y ‘oweTy-seTeziow TII

"m ‘uostiiey II “SNTTE OT pue

eTIIL I setqe} g Zutpntout ‘dd zo ‘pooT aquedaq ‘owety

Dy -SeTeiow “Yy pue uostizey “Mm Aq ‘VWINISUIA ‘HOVE

stsAyTeuy }uawtpas “¢ VINIDOUIA LV GNVS GHSUAWWI JO SHILYHdOUd DIWVNAG
BA‘ YIBeg BTUTSITA °Z

sasseo0ig ai0ys “T ‘O’d ‘*HSVM ‘dO ‘YdINHO “SHY “OSYONA TVLSVOO AWYV'S‘’N

“rood st uostiedwod 3nq ‘Tepow JeT3tez puke IeTLTTW-S96T
Aq pa}yotpeid asoy} yyIM patedwod sre souoz ItTweUAp dy} }NOYsNoTYy
3utjIoOs pue azts uesW JO spuet} paAtTasqgQ ‘“pateptsuod st osu0z
aAeM-SutTTeoys ut sadoTs ydeaq uo pue satTotzIed pues Fo satz1tadoid
Otweudp uo A}TSOOSTA IT}PeWsUTY JO aduez,IoOdwt sy, ‘*paredwod pue
payetTnoTe> a1am “Te ja S33tIg Fo 10j,Deqy adeys 2tweudq pue 10},9eF
adeys s,Aazt0D ‘"jJUaTITJZa0O Beip uvaw pue ‘iaqunu spTouday ueosw
‘AYTIOTAA Butt i}as uevawW :ataemM SatTdues 94} FO Satjyiadord aqtidsap
0} pasn sjUaWaInseaw “jyaTUL aapny FO A}TUTITA dy} UT pUe Yydeaq
ay} ssoise sj .esuel} ¢ BuoTe ATSnosuej,TnwtTs uaye} satdwes pues jo
Joqunu odie, & FO ALTIOTAA BZutT}}9aS ueaw ut SuUOT}eTIeA IT}eWAa}SAS
azATeue pue ainseaw 0} paustsap Apnis e Joy pajuasaid are s}yTnsay

dHISISSVIONN 6 “ON WNCNVYOWEW TVOINHOL
“y ‘oweTy-seTerow TIT
*m ‘uostizey II

eTITL I

: “SNTTF OT pue
soTqe} g dutpntout ‘dd zo ‘po6T Iaquedseaq ‘ouwetTy
-SeTeIow “y pue uostizey “mM 4q ‘VINIOUIA ‘“HOVEE
VINIOUIA LV GNVS GHSYHWWI JO SHILYHdOUd OIWWNAG
‘BA ‘YDeag eTUTSITA

b

stsAyTeuy jUaUTpas “¢
@

Sassad0Ig e10YS ‘T

“O'd ‘*HSVM ‘HO ‘UAINHO “SHU “OYONA TVLSvOO AWuV'S*n

*zood st uostiedwod 4nq ‘ TapOW TaTZatzZ pue I2eTTTW-S96T
Aq pazoFpetd asoy} u}TM pazedwod are sauoz dtweudp ay} YNoYysnoryy
Sut}IOS pue oezts ueaw FO Sspuat} paAITasqQ ‘“pataptsuod st auo0z
aAeM-3uTTeoys ut sedo,Ts yoeeq uo pue saTdt}yI1ed pues jo satyIisedoid
Dtweudp uo AjTSOOSTA IT}eWSaUTY FO aduez,IOduT ay, ‘*paredwod pue
pozyetTnoTed atom “Te ya SB3TIg Fo 10,9¥y adeys Itweudq pue 103,deF
adeys s,Aat0p “*4UuaTITFFI09 Seip ueaw pue ‘raqunu sptoudsay uesw
‘AYTIOTAA BuTT}}aS uesw :atam SatTdwes sy} FO satytedoid aqtidsap
0} pasn sjuoWwaeInseaW “jSeTUT sapny FO A,TUTITA ay UT pue Yydeaq
ay} ssorde szoasuerl} ¢ SuoTe ATSnoauejtTnuts uaye} satdwes pues jo
Toqunu as1eqT e Jo AjYTIOTAA BuTT}}esS UBaW UT SUOT}ETIeA IT}eWAaYSAS
azAyTeue pue aInseaw 0} paustsap Apnjs e IOJ payuesaid are sz} Tnsay

da IdI SSVIONN 6 “ON WAGNVYOWHW TVOINHOTL
“y ‘owetTy-seTeiow TIT

"mM ‘uostizeyH IT “SNTIT OT pue

eTITL ie satqe} g sutpntout “dd zo ‘po6T Jaquaceq ‘ouerty

Y -SaTeIOW ‘y pue uostzzeH *M 4q ‘VINIDUIA ‘HOVHE

stshTeuy juautpas “¢ VINISUIA LV GNVS GHSYSWNWI JO SHILYHdOUd OIWYNAC
“BA ‘yoeeg BTUTSITA “2

sasse00Ig azoys *T ‘O°d ‘*HSWM ‘HO ‘YHLNSO “SHY “OYONA TvLSvOO AWuY’S"A

‘rood st uostzedwod 3nq ‘{TapoWw TaTSatzZ puke TJaT—TtW-So96T
Aq pa}otpard asoy} yytM paredwod are sauoz otweUuAp day} 4yNoYysnorYy
Sut}IOS pue azts ueaw FO Sspuat} PaATasSqQ ‘patTaptsuod st auo0z
aAem-SutTeoys ut sadoTs yoeaq uo pue saTdtyI"ed pues Jo sat}1adoid
atweudp uo A}TSOISTA IT}eWAUTY JO |sdue,IOdWT sYyL *paredwod pure
poyeTnoTeos otom “Te yo S38tIg Fo 103987 adeys Itweudq pue 10}, DeF
adeys s,Aat0D ‘JUuaTITFJa0D 3erip uesw pue ‘Taqunu spTouday uvaw
‘AYTIOTSA BuTT}}aes uevaw :atam Satdwes ay} FO satjziadoid aqtissap
0} pasn szUuoWaInseaw “JeTUT asepny Jo ATUTITA 9|Yy} UT PUue Ydeaq
ay} Sssoroe sj2asuet} ¢€ BuoTe ATSnoaue,,TNwts uaye} SaTdwes pues Fo
Jaqunu asieqt e Fo AjYTIOTAA BuTT}}aeS ueaW UF SUOT}ETIeA ITZeWaYSAS
azATeue pue ainseaw 0, paustsap Apnjs e IOF pajuasard are sjtnsay

daIAISSVIONA 6 ‘ON WAGNVYONHW TVOINHOSL
“y ‘oweTy-saTeiow III

*m ‘uostizey II “SNTTT OT pue

TITEL I satqe} g dutpntout “dd zo ‘pot Taquaseq ‘oweTy

y -SaTeIOW "y pue uostsieH “mM Aq ‘VINIOUIA ‘HOVEE

stshTeuy Juawtpas “¢ VINIOUIA Ly GNVS GHSYAWNI JO SHILYAdOUd OIWWNAG
"eq ‘yoeag eTuTsItA °Z

sassao00ig at0ys “T “O°d ‘*HSWM ‘SO ‘YaLNHO “SHY “OYONT TvLSvOO AWYV’S*n

+