COMPRESSIONAL WAVE SPEED AND ABSORP-
TION MEASUREMENTS IN A SATURATED
KAOLINITE-WATER ARTIFICIAL SEDI-
MENT

Charles Allen Martinek

NAVAL POSTGRADUATE SCHOOL

Monterey, California

THESIS

COMPRESSIONAL WAVE SPEED AND ABSORPTION MEASUREMENTS
IN A SATURATED KAOLXNITE-WATER ARTIFICIAL SEDIMENT

by

Charles Allen Martinek

Thesis Advisor: R. S.
Co-Advisor: 0. B.

Andrews
Wilson, Jr.

March 1972

Appfiov&d ^on. pubtlc /teXeoie; du>t/Ubijution uyitunLte.d.

Compressional Wave Speed and Absorption Measurements
in a Saturated Kaolinite-Water Artificial Sediment

by

Charles Allen Martinek

Lieutenant, United States Navy

B.S., United States Naval Academy/ 1966

Submitted in partial fulfillment of the
requirements for the degree of

MASTER OF SCIENCE IN OCEANOGRAPHY

from the

NAVAL POSTGRADUATE SCHOOL
March 1972

/VI3 5 9'*

./

ABSTRACT

The absorption coefficient for ccmpressional waves in a water-
saturated kaolinite clay was measured in the frequency range 100 to
150 kHz using a pulse technique with spherically diverging waves. The
measurement also permitted determination of the sound speed, V . For
one condition of the clay with a 77% porosity, the sound speed was
1422 m/sec. The absorption coefficient, a, was found to be frequency
dependent, satisfying the empirical relationship a = 0.033 f dB/m, f
being the frequency in kHz. No dispersion of wave speed with frequency
was observed. These results were used together with the results of
dynamic shear (rigidity) modulus measurements made with a torsional wave
viscoelastometer to calculate the complex Lame constants of a viscoelastic
model.

TABLE OF CONTENTS

I. IMRQDUCTION 7

II. THEORY 10

A. COMPRESSTONAL WAVES 10

B. THE VISCQELASTIC MODEL 11

C. THE VISOOELASTOMETER 13

III. EQUIPMENT AND PROCEDURES 14

A. THE SEDIMENT TANK 14

B. GOMPRESSIONAL WAVE MEASUREMENTS 14

C. THE VISCQEIASTOMETER 18

D. WET DENSITY AND POROSITY 19

IV. RESULTS AND DISCUSSION 20

V. EXPERIMENTAL PROBLEMS 24

VI . CONCLUSIONS AND RECOMMENDATIONS 26

BIBLIOGRAPHY 36

INITIAL DISTRIBUTION LIST 38

FORM DD 1473 39

LIST OF TABLES

I . Compressional Wave and Sediment Properties 28

II. Comparison of Methods for tetermining Shear Moduli 29

4

LIST OF ILLUSTRATIONS

L. The Viscoelastometer 30

2 . Cross-Sectional View of the Tank 31

3 . Received Signal Waveform Record 32

4 . Block Diagram for Compressional Wave Measurements 33

5. Plot of SPL + 20 log1Q r vs Range (r) 34

6 . Sediment Sampler 35

ACKNC^n^DGEMENTS

The author wishes to express his gratitude to Professor 0. B. Wilson,
Jr. and to Professor R. S. Andrews for their patience, encouragement and
counsel throughout the course of this research. Thanks are also extended
to Lieutenant Commander J. Donegan for his instruction and assistance
with the boxcar integrator and to Mr. R. Moeller and Mr. T. Maris for
their talent in constructing many of the mechanical devices used during
the project. The project received support through contract with the
Office of Naval Research.

I. IMTODUCTION

For sane problems of sound propagation in the ocean, the ocean bottom
can be satisfactorily described using the Bayleigh model. Mackenzie [1]
showed that the Bayleigh model can be applied to cases where sound was
obliquely reflected at grazing angles (measured between the ray and the
plane of the bottom) greater than the critical angle. However, at
smaller grazing angles the model can not account adequately for bottom
losses. In those cases where the attenuation of sound in the sediment
becomes important, a more realistic viscoelastic model should be
employed which considers the effects of rigidity and absorption.

The complex Lame" constants (X, \i, X' and y1) of the viscoelastic
model are theoretically related to four observable quantities, the speeds
of propagation of compressional and shear waves and the attenuation of
these waves. The effectiveness of the viscoelastic model is therefore
governed by the precision and accuracy of the values obtained for the
complex viscoelastic moduli. The moduli can be calculated through measure-
ments of the acoustic properties mentioned above. Measurement of shear
wave propagation by direct methods is the most difficult of the observations
to make, particularly in soft sediments, because of its high attenuation
and the physical problem of generating transverse wave motion. One pro-
cedure to obtain indirectly the shear wave speed is the measurement of
the speed of a surface wave (Stoneley wave or Rayleigh wave) propagating
along the sediment-water interface. When the speed and attenuation of
the Stoneley wave is determined, shear wave speed and attenuation constants
of the sediment can be determined [2] . Other prerequisites for this type

of calculation require the knowledge of canpressional wave speed and
attenuation and the density of the sediment. Hamilton et al. [3]
provide a sample calculation illustrating this procedure.

Numerous researchers have conducted tests to determine the compres-
sional wave speed and attenuation and, to a lesser extent, surface wave
speed and attenuation of sediments either in situ or in the laboratory.
Urick [4, 5] developed expressions for compressional wave speed and
absorption in kaolinite suspensions. Urick and Ament [6] also outlined
a theory for a complex propagation constant whose real part yielded a
wave speed and whose imaginary part yielded an absorption coefficient.

Laughton [7] conducted laboratory experiments on ocean sediments,
measuring compressional and shear wave speeds only. He was able to make
direct shear measurements on compacted sediments, but not on uncompacted
material because of its low rigidity.

Hampton [8] reported on the results of measurements on the acoustic
properties of sediments, including compressional wave speed and attenuation
measurements of dispersed and undispersed kaolinite sediments.

Hamilton and his associates at the Naval Undersea Research and
Development Center have conducted both Stoneley and compressional wave
measurements. Their efforts culminated with in situ measurements of both
waves from the research submersible DEEPSTAR 4000 at stations close
together and in the same sedimentary environment. With the data, Hamilton
was able to calculate both elastic and viscoelastic constants for the
sediments. They were prevented from making both sets of measurements
during the same dive by the quantity of unique equipment required for each
measurement procedure.

This problem may be reduced by use of a torsional wave visco-
elastometer developed at the Naval Postgraduate School by Hutchins [9] ,
Cohen [10] and Bieda [11] . The instrument measures the loading effects
caused by the rigidity of a sediment on a torsionally vibrating rod.
These effects can be analyzed to calculate the real and imaginary parts
of the shear (rigidity) modulus. Determination of the shear modulus by
this method could possibly provide a better method to determine shear
wave properties than by conducting Stoneley wave speed and attenuation
measurements.

This experiment was part of a process for validation of the visco-
elastometer measurement method. Since the viscoelastic parameters
also relate to the sound absorption, it is necessary to carefully
measure the sound speed and absorption in sediment. Comparison of the
results of these measurements with those obtained by the viscoelastometer
can give an indication of the validity of the latter method.

A compressional sound wave was propagated by an electrostatic source
through a water-saturated kaolinite sediment. The signal received by a
hydrophone was recorded and analyzed to obtain values of the compressional
wave speed and absorption. Viscoelastometer measurements were then made
on a core sample of the sediment in which the sound wave experiment was
conducted.

II. THEORY

A. CQMPKESSIONAL WAVES

For spherically diverging waves, the equation for the sound pressure
level (SPL) in decibels can be written [12] :

SPL = SL - 20 log1Q r - ar (1)

where SL is the source level, r is the range and a is the absorption
coefficient. The logarithmic term represents the spherical spreading loss
in decibels. By rearranging terms, the relation

SPL + 20 log10 r = SL - ar (1A)

provides an equation which is convenient for plotting experimental data on
linear graph paper. The slope of the curve of Equation (1A) should be a
straight line with units of decibels/unit length, the absorption coeffi-
cient. The intercept of this curve at a unit distance is the value of
the source level in decibels. Equation (1) assumes a homogeneous and
isotropic medium and the absence of reflecting surfaces. For a finite
sized source, the inverse square law divergence applies only at distances
from the source that are large in comparison with the radius of the piston
source. Due to interference effects, the axial pressure near the surface
of a piston undergoes wide variations with changes in range, until the
distance is greater than d2/2X, where d is the diameter of the piston and
X is the wavelength [13] .

10

B. THE VISCOELASTIC MODEL

Foliating the development used by Hamilton et al. [3] , the viscoelastic
model uses complex Lame constants (y + iy1) and (A + iAl) to account for
absorption. For simple harmonic motion, the time factor e w is used.
Ccmpressional and vertically polarized shear waves traveling in the sedi-
ment can be described in terms of displacement potentials <f> and $. For
a viscoelastic solid, these displacement potentials must satisfy the
following wave equations:

p It2 ♦ = (X + S^2* + (X' + 2m') |t V2<t> (2)

p |p i> = yV2ij, + y' |r- V2ij, (3)

where p is the density of the solid. Bucker [14] has solved these
equations in order to determine the complex Lame constants. The resulting
equations are:

1/V2 - l/t2 = p/(A + 2y) (1 + <£) (4)

2Aptp = pq^/d + qp) (A + 2y) (5)

1/Vf. " l/t2 = p/y(l + q2) (6)

2Asts = pq/yd + q2) (7)

where V and V are, respectively, the ccmpressional and shear wave

speeds and

A1 + 2y'

% == A + 2y

y'
11

(8)

Here, t and t are related to the absorption of the compressional and
P s

shear waves by:

ap = -20(log10 e) (a>/t ) (9)

ag = -20 (log1Q e) (w/ts)

In this experiment/ y and y' were determined from measurements by the
viscoelastcmeter, and the campressional wave speed and absorption were
determined by direct measurement. By using the viscoelastic equations,
X and A ' can be calculated . Values for the expected shear wave speed and
absorption can also be calculated.

Assumptions and approximations upon which the model is based are
listed below:

1. the use of complex lame constants to account for attenuation does
not specify the mechanisms involved;

2. the dilatational or bulk viscosity is set equal to zero, i.e.,
X' + 2y'/3 = 0;

3. the complex lame constants are independent of frequency, implying
that the real parts, A and y, governing the compressional and shear wave
speeds , and the imaginary parts , X ' and y ' , governing energy losses are
also independent of frequency (most observers, with the notable exception
of Hampton [8] , have not observed any dispersion with frequency) ;

4. absorption in decibels/unit length is assumed to increase linearly
with frequency, a = kf (Cole 115] and Wood and Weston [16] have found an
approximate linear dependence in natural sediments) .

12

C. THE VISCOELASTOMEIER

The description, theory, and operation of the viscoelastometer have
been thoroughly reported by Lasswell [17] , Bieda [11] , Walsh [18] and
others. The viscoelastometer, as shown in Fig. 1, consists of a rod-
shaped torsional irechanical oscillator which is excited at one of its
mechanical resonance modes by a torsional piezo-electric crystal located
at its center, setting up a standing wave along the axis of the system.
The torsional motion of the rod surface in contact with another medium
generates a shear wave which propagates radially outward from the rod.
The loading effects of the medium, such as a soft clay, cause a measure-
able change in the mechanical damping and resonance frequency of the
viscoelastometer. Electrical measurements of these changes can be
related to the complex rigidity modulus through a procedure which uses
Newtonian fluids for calibration of the device.

13

III. EQUIPMENT AND PROCEDURES

A. THE SEDIMENT TANK

An artificial ocean sediment was formed by a saturated kaolinite-water
mixture contained in 4 ft by 8 ft by 3 ft steel tank (Fig. 2) . The
tank rests on 9 inches of sand and is surrounded by 1 ft of sand on the
lower half of the tank's sidewalls. The sand was installed to act as a
damping mechanism for reflection of waves from the walls of the tank and
floor vibrations. Kaolinite clay is a hydrated aluminum disilicate with a
grain diameter comparable to the clay size particles found in many ocean
bottom sediments. It was chosen for this experiment for the additional
reason that it is commercially available in a fairly pure state. The depth
of the clay was approximately 70 cm.

The bottom of the tank is lined with ^-inch diameter copper tubing
which can be used for heating the clay with steam. Prior to conducting
measurements/ the clay was covered with water, thoroughly stirred in an
attempt to break up any clumps and to homogenize it, and heated to drive
off any gas bubbles that may have existed in the clay. Hampton [8]
emphasized the importance that even small quantities of gas can have on
acoustic properties.

B. CQMPRESSTONAL WAVE MEASUREMENTS

A horizontally-oriented beam of compressional waves was generated in
the clay approximately 25 to 30 cm below the clay-water interface by a
7.1-cm diameter electrostatic transducer similar to one constructed and
described by Palatini [19] . The transducer was a piston-type source with
a 1-mil thick aluminum coated Mylar film (a DuPont polyester film)

14

attached to a slightly roughened flat plate. The transducer was polarized
by a 300-v battery. Since a thin layer of air was entrapped between the
plate and the Mylar film, the air pockets acted as a spring against which
the film moved when the applied alternating signal voltage gave rise to
an alternating electrostatic force. The motion was expected to be
essentially uniform over the surface and the response was shown by Palatini
to be independent of frequency at high frequencies in the mass-controlled
region where kd>>l (d is the diameter, k is the propagation constant) .

The electrical drive to the transducer consisted of a gated sine
wave, usually eight cycles, which was provided by an oscillator and a tone-
burst generator. The output from the tone-burst generator was passed
through an additional gate and clipping circuit developed by Cohen [10]
to reduce leak-through when the gate is closed. The driving tone-burst
was amplified in a power amplifier and stepped up with a 6:1 transformer,
passed through a polarizing circuit driven by a 300-v battery and then to
the electrostatic transducer. The frequency of the signal was controlled
at the oscillator and monitored on a frequency counter. The voltage
output could be controlled at both the oscillator and the power amplifier
and was kept constant at 53.5 v RMS by monitoring it on a vacuum tube
voltmeter .

The receiver was a ^-inch by ^-inch cylindrical barium titanate hydrophone
mounted on a rack-and-pinion assembly to provide smooth and easy positioning
of the transducer. The received signal was amplified (usually 60 dB) and
passed through 60- and 120-Hz filters to eliminate low frequency hum. High
frequency noise was reduced by also passing the signal through a low pass/
high pass filter set at 180 and 85 kHz. The signal was fed into the boxcar

15

integrator where it was scanned by a slowly moving gate and reproduced on
an X-Y recorder. Both the gate and the received signal were monitored on
the oscilloscope. A typical record of the direct arrival sound pulse is
shown in Fig. 3. A block diagram of the system is shown in Fig. 4. This
signal processing method had the advantage that it provided records which
have enhanced signal to noise ratios and which can be measured more
precisely than can photographs of the cathode ray oscilloscope.

The boxcar integrator synchronously sampled an input signal with a
variable width, variable delay gate, which can be slowly scanned across
the input signal. That signal passed by the gate was averaged by variable
time constant integrators, the output of which was the average of the
number of repetitions of the input signal over the gate width interval.
Because the average value of noise over a number of repetitions was zero,
an improvement in signal to noise ratio occurred. When the gate was
scanned across the return signal from the transducer, the waveform was
reproduced on the X-Y recorder.

The signals were analyzed to obtain both ccmpressional wave speed and
absorption. The gate on the boxcar integrator was calibrated with a
time-mark generator at 10-ysec intervals from 0% to 100% of the boxcar's
scan/delay scales. The fixed delay (16 ysec) between the trigger of the
transducer signal and the 0% value on the scan/delay scales was determined.
The time of the first arrival of the signal was then read off the waveform
trace and the delay time was added to get the total travel time. This was
divided into the horizontal range to determine the compress ional wave
speed.

16

The absorption coefficient was determined by a comparison of the
amplitudes measured in millivolts at various ranges. During the course
of the experiment/ it became clear that, in addition to the direct path
signal, there was some interference caused by possible side wall reflec-
tions/ sediment-water interface reflections and other undetermined
multipath transmissions. For this reason, only the first two and one-
quarter cycles were used for analysis since they appeared to be free of
any such interference. The amplitudes in millivolts of the first three
positive peaks and the first two negative peaks were measured. Then the
values for four half -cycles were determined by adding the amplitudes of
the first positive and first negative peaks, the first negative and
second positive peaks, and so forth. The values obtained for the four
segments were then averaged, and the average was used as a representative
amplitude for the given frequency and range. The level of this voltage
was calculated in decibels relative to an arbitrary value of 1 mv by the
equation:

SPL = 20 log-.Q (voltage, mv)

The reference distance for the spherically divergent term was chosen as
1 cm also for the reason of convenience. Equation (1A) was entered with
the SPL values out to a range of 1 m and plotted as illustrated in
Fig. 5. The slope theoretically should be a straight line, the value of
which is the absorption coefficient in decibels/meter. Since scatter
did exist, the slope was determined by a least squares fit. A linear
regression program was run on a Hewlett-Packard 9100A calculator to
determine the best fit by minimizing the sum of the squares of the
deviations of the data points from the straight line.

17

C. THE VISOOELASTCMETER

The viscoelastometer used to provide shear modulus data was the same
type of instrument used by Bieda [11] and Lasswell [17] . It is 10.5
inches long with a ^-inch diameter cylindrical rod whose torsional
oscillation was controlled by a hollow barium titanate transducer mounted
in the center of the rod. The transducer was 1.5 inches long and ^-inch
in diameter. It was constructed from an axially-polarized cylinder which
was cut into two parts along the longitudinal axis and rejoined after the
inversion of one half and the insertion of two electrode grids. The
transducer was wrapped in fiberglass thread under tension and covered with
an epoxy resin to improve the contact at the joints. The rod was construc-
ted from two sections of a constant modulus alloy, Nl-Span-C. These parts
were heat treated and highly polished.

The viscoelastometer was supported by clamping at the center of the
transducer using a tubular steel framework which housed the electrical
leads to the transducer. In this way the clamp did not interfere with
the functioning of the viscoelastometer since the transducer center was a
node of torsional motion for all the resonant modes. The electrical
connections were kept watertight by the application of a silicone rubber
coating.

The rod was first calibrated in Newtonian fluids of known viscosity.
The resonant frequency and electrical resistance were then measured in
air and in the artificial sediment in order to obtain the changes in
resonant frequency and electrical resistance required to calculate the
rigidity. A sample core of the sediment in which the sound wave experi-
ment was conducted was obtained and placed in a water bath maintained at

18

a temperature of 20 C. Three sets of measurements were taken on the
core approximately 12 hr apart which were used by Lieutenant J. Morgan
to calculate the real and imaginary parts of the rigidity.

D. WET DENSITY AND POROSITY

The wet density is the weight per unit volume of the water-saturated
sediment. A known volume of the sediment was obtained by the use of an
instrument fabricated by the Physics Shop at the Naval Postgraduate School

and shown in Fig. 6. This sediment sampler had a known volume of 24.68

3

cm . The sampler could be lowered to the desired depth in the sediment

with the only disturbance to the sediment being along the walls of the
cylinder. When in place, top and bottom plates were rotated across the
cylinder, trapping the sediment enclosed. The bottom plate contained a
rubber gasket to prevent leakage of water while the sampler was in the
upright position. The sample was emptied into a weighing dish and
weighed. The ratio of the wet weight divided by the volume equaled the
wet density. After being heated in an oven at 105 C for 24 hr / the
sample was weighed again, with the weight loss assumed to be entirely due

to evaporation of the entrapped water. Assuming that 1 g of water occupies

3

1 cm , the difference in weight in grams between the wet and dry sample

was equal to the volume of voids in cubic centimeters in the sample.
Porosity was then determined by the relationship:

_ .. Volume of Voids
*>™s^ = Total Volume '

Hampton [8] used the term volume concentration which is related to porosity

by:

Volume Concentration = 1 - Porosity.

19

IV. RESULTS AND DISCUSSION

Table I shows the results obtained from the compressional wave speed
measurements in the tank. The speed of sound in water was computed
using Wilson's formula [12] . The horizontal range measurements were
accurate to within 0.2 cm; the determination of arrival time was accurate
to within 5 ysec. The calculations of the compressional wave speed were
then accurate to within ±1.5%. The ratio of the sound speed in the
sediment to that in water is somewhat lower than would be expected.
Cohen [10] and Walsh [18] both observed ratios greater than 0.98 for
kaolinite-water sediments with approximately the same porosity. Data
collected by Hamilton [20] for shallow water sediments off San Diego
gave a sound speed ratio of 0.97 or greater.

A possible explanation for this difference was the existence of some
gas bubbles in the sediment. Another indication of this possibility was
the observation of some acoustic reverberation in the received sound
pulse following the direct arrival. Since the reverberation was much
smaller than the direct arrival, the scattering cross-section per unit
volume of the inhamogeneities which caused the reverberation must also
have been small.

The absorption coefficient was determined using Equation (1A) and is
shown in Table I for the frequencies used in the experiment. Fitting
these points with a linear equation in frequency resulted in an absorption
coefficient

•

a = kf dB/m

20

-2
with k = 3.3 x 10 , and where f is the frequency in kHz. This result

agrees well with studies made by Hamilton [21] . He predicted a value for

k of between 0.02 and 0.06 for an artificial sediment with porosity in the

70 to 80% range. Hampton [8] reported a value for the absorption of

approximately 4 dB/ft (approximately 13 dB/m) for kaolinite of nearly

1 37
the same porosity at 100 kHz with a frequency dependence of f . Wood

_2

and Weston [16] determined an absorption coefficient equal to 2 x 10

dB/ft-kHz (approximately 6.6 dB/m at 100 kHz) in mud that showed a linear
frequency dependence.

One of the original objectives of this research was to determine both
the ccmpressional and shear wave speeds and absorption in the sediment.
Attempts to duplicate Walsh's [18] measurements of surface waves were in
vain. Although basically the same equipment and procedures were used, a
surface wave could not be observed in this sediment. Since a direct com-
parison of the results obtained from applying the viscoelastic equations
to those obtained from the viscoelastometer could not now be made, it was
decided to assume a value for the shear wave speed in order to make a
rough comparison of the two methods.

Values for the real and imaginary parts of the shear modulus
(y and y1) as computed from viscoelastometer measurements are listed in
Table II for one of its mechanical resonance modes. The values are the
same order of magnitude as those obtained by Cohen [10] in kaolinite.
Although Walsh [18] had arrived at a value for the shear wave speed (V )
of approximately 23 m/sec, both Cohen's values and the measurements
reported here indicate that a shear wave speed of less than 5 m/sec is
more realistic for the very soft sediment being studied. Values for
y and y' were calculated using the following viscoelastic equations [3]

and experimental data:

21

y = pv2

8.686w

t =

P a

_ 2

Sp " (t /v - v /t )
* jf p p' p'

V t a

3a (X + 2y)
^ =-RT

p = 1.386 g/cm3

V = 5 x 10 2 cm/sec (assumed value)

5

to = 2ir(1.56 x 10^ Hz) where 15.6 kHz
was one of the resonant modes of
the viscoelastometer .

a = 5.15 x 10" 3 dB/cm (extrapolated
from 100 kHz to 15.6 kHz)

V = 1.422 x 105 cm/sec.
P

Table II compares the results of the two methods. The value of y was

5 2
equal to 3.5 x 10 dyne/cm from theory, the same order of magnitude as

that measured by the viscoelastometer. The calculated value of y1 was

5 2

360 x 10 dyne/cm , two orders of magnitude greater than the viscoelasto-
meter measurement. Examination of the parameters in the viscoelastic
equations reveals that the determination of y' is relatively insensitive

22

to changes in the absorption coefficient or the shear wave speed when

V is small. It should be noted that the viscoelastameter results used

s

here are approximate since they are based on a very limited number of
observations. However/ they are comparable to observations reported by
Cohen [10] for a very porous kaolinite mixture.

23

V. EXPERIMENTAL PROBLEMS

The sediment, even after being thoroughly stirred, lost its homo-
geneous state in a matter of hours. Settling and compaction took place
which produced distinct vertical gradients. By lowering one's arm through
the clay, a definite change in the sediment rigidity could be felt, ranging
from a nearly fluid slurry at the surface to a compacted mass at the
bottom. The stratification caused by the changes in density and porosity
with depth was neither spatially nor temporally uniform. Horizontal
gradients, while not as pronounced as the vertical gradients, also were
present. The presence of small clumps of clay caused further discon-
tinuities in the gradients. Pronounced and changing stratification and
gradients then did not allow an ideal medium for the propagation of
sound waves and comprised a major problem area.

After the sediment had been reasonably outgassed and homogenized,
initial attempts to obtain compressional wave measurements were thwarted
by equipment problems. Among those were the shorting out of the trans-
ducer by water leaking into it and low signal-to-noise ratios caused by
high frequency noise probably generated internally by some of the
equipment. By the time these and numerous minor procedural and equip-
ment problems were corrected, the sediment had time to develop stratifi-
cation and gradients. Attempts to determine sound absorption coefficients
showed that the medium no longer exhibited the inverse square law for
spherical spreading and was therefore unsatisfactory for further experiments,

24

The sediment was again heated and thoroughly stirred. With increased
porosity and decreased density, the sound speed decreased as expected [22] ,
but once again the value was low judging by the ratio of the sediment to
water sound speeds. Seme reverberation due to scattering from bubbles
or other inhomogeneities was observed. This could have affected the
observed absorption coefficient, but the effect is believed to have been
small.

Failure to obtain a surface wave measurement indicated other problem
areas. The sediment in this report was the same kaolinite used by
Walsh [18] . However, these measurements were made with a layer of water
overlying it while, in Walsh's experiments, the sediment was covered
with a thin film of water and the surficial layers were much stiffer.
With the combined effects of the water layer and the extensive stirring
of the sediment shortly before the experiment, the sediment surface was
extremely soft. Attempts to place geophones on the sediment surface
resulted in the geophones sinking several centimeters or more below the
water-sediment interface. Both the soft nature of the sediment surface
and the weight of the geophones were contributing factors. Attempts to
keep the geophones on the surface by placing them on a thin plastic
sheet also failed. The sheet was pushed beneath the surface when the
geophones were placed on it. As a result, no surface waves could be
observed.

25

VI. CONCLUSIONS AND RECOMMENDATIONS

An experimental method has been used to determine the speed of propa-
gation and absorption of compressional waves in a saturated kaolinite-

water mixture. For one case of the sediment having a porosity of

3
approximately 77%, a wet density of 1.386 g/cm and a temperature of 20 C,

the sound speed was determined to be 1422 m/sec and the absorption coef-
ficient described by a = 3.3 x 10 f dB/m where f is the frequency in kHz.
Data taken by the viscoelastometer on a core of the same sediment confirmed
earlier results reported by Cohen [10] for basically the same kaolinite-
water mixture. In addition, Bieda [11] and Lasswell [17] took visco-
elastometer measurements in natural marine sediments with good correlation
between their results. Therefore, these results seem to indicate that the
viscoelastometer yields reasonable quantitative estimates of the shear
moduli. Calculation of y from the observed physical properties (V was
assumed since it could not be determined) also confirms that the visco-
elastometer measurements appear to be reasonably accurate. However, a
large discrepancy existed when y' was calculated since the viscoelastic
equations produced a result which was two orders of magnitude greater than
would be expected for this case. The value of y1 is strongly influenced
by the X + 2y term. This in turn is influenced by the difference in V and
V . In sediments with small shear wave speeds, V no longer is a significant

kr S

percentage of V , and the calculated y' becomes too larqe.
P

It is recommended that this discrepancy be resolved by further study.
If the viscoelastometer is producing valid results, and previous data
indicates that it is, then possibly the theory nay be suspect for low values
of shear wave speed. One assumption which may be questioned is that the

26

bulk viscosity is zero. If other factors are present which cause energy
losses in sediments with small shear wave speed, the present theory may
not totally account for them and thus may yield the anomalously high
value for yf. An example of computations by Hamilton [3] of viscoelastic
constants for a sediment with a shear wave speed greater than 100 m/sec
illustrated that reasonable results for y1 can be obtained from sediments
that exhibit definite rigidity.

The data collected in this report for the sound speed and absorption
were inadequate to provide a complete validation of the viscoelastometer
method. It is necessary to obtain accurate values for both the compres-
sional and shear wave speeds and the absorption. With those values, the
complex Lame constants for the viscoelastic model can be determined.
When this experimental procedure can be satisfactorily accomplished, then
results of viscoelastometer measurements on the same sediment can be com-
pared to validate the effectiveness of the viscoelastometer method. If
the viscoelastic theory is found to be invalid for small shear wave speeds,
another sediment having more rigidity may have to be used in the tank, or
else in situ measurements of natural sediments will have to be taken. If
the theory is correct, then there is a serious question of the meaning of
the imaginary part of the modulus determined by the viscoelastometer.

A recent doctoral dissertation by Borcherdt [23] offers a theoretical
investigation of inhomogeneous body and surface plane waves in a generalized
viscoelastic half space. Possibly the theoretical processes can be
examined in this laboratory environment to provide more information on
viscoelastic properties, in particular, the speed and absorption of shear
waves.

27

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28

TABLE II
COMPARISON OF METHODS FOR DETERMINING SHEAR MODULI

Frequency Theory Viscoelastcmeter

y y' y y'

(kHz) (105 dyne/cm2) (105 dyne/cm2)

15.6 3.5 360 1.4 3.9

29

Transducer
Electrical
Connection

r\

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Barium Titanate
Shear Transducer
Length: 1.5 in

J=-r-^

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NI-Span-C Rod
Length: 4.5 in

NI-Span-C Rod
Length: 4.5 in

Figure 1. The Viscoelastometer

30

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100 kHz

a = 3.3 dB/m

1

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125 kHz

a = 4.2 dB/m

150 kHz

a = 5.0 dB/m

Figure 5. Plot of SPL + 20 log,Qr vs Pange (r)

34

1.225"

1.250"

Figure 6. Sediment Sampler

35

BIBLIOGRAPHY

1. Mackenzie, K. V. , Reflection of Sound from Coastal Bottoms,

Journal of the Acoustical Society of America, v. 32,
1960, pp. 221-231.

2. Stride, E., and A. S. Ginzbarg, Stoneley-Wave Velocities for a

Fluid-Solid Interface, Bulletin of the Seismological Society
of America, v. 46, 1956, pp. 281-292.

3. Hamilton, E. L. , H. P. Bucker, D. L. Keir, and J. A. Whitney,

In situ Determination of the Velocities of Compressional and
Shear Waves in Marine Sediments from a Research Submersible,
Naval Undersea Research and Development Center Technical
Report No. 163, 1969, 28 p.

4. Urick, R. J., A Sound Velocity Method for Determining the

Compressibility of Finely Divided Substances, Journal of
Applied Physics, v. 18, 1947, pp. 983-987.

5. Urick, R. J., The Absorption of Sound in Suspensions of Irregular

Particles, Journal of the Acoustical Society of America, v. 20,

1948, pp. 283-289.

6. Urick, R. J., and W. S. Ament, The Propagation of Sound in Compo-

site Media, Journal of the Acoustical Society of America, v. 21,

1949, pp. 115-119.

7. Laughton, A. S., Sound Properties in Compacted Ocean Sediments,

Geophysics, v. 22, 1957, pp. 233-260.

8. Hampton, L. D. , Acoustic Properties of Sediments, Journal of the

Acoustical Society of America, v. 42, 1967, pp. 882-890.

9. Hutchins, J. R. , Investigation of the Viscoelastic Properties of

a Water-Saturated Sediment, M.S. Thesis, Naval Postgraduate
School, 1967, 30 p.

10. Cohen, S. R. , Measurement of the Viscoelastic Properties of Water-

Saturated Clay Sediments, M.S. Thesis, Naval Postgraduate School,
1968, 57 p.

11. Bieda, G. E. , Measurement of the Viscoelastic and Related Mass

Physical Properties of Seme Continental Terrace Sediments,
M.S. Thesis, Naval Postgraduate School, 1970, 75 p.

12 . Urick , R. J . , Principles of Underwater Sound for Engineers,

McGraw-Hill Book Company, 1967, 342 p.

36

13. Kinsler, L. E., and A. R. Frey, Fundamentals of Acoustics ,

John Wiley & Sons, Inc., 1962, 524 p.

14. Backer, H. P., Normal Mode Sound Propagation in Shallow Water,

Journal of the Acoustical Society of America, v. 36,
1964, pp. 251-258.

15 . Gole , B . F . , Marine Sediment Attenuation and Ocean-Bottom-

Reflected Sound, Journal of the Acoustical Society of America,
v. 38, 1965, pp. 291-297.

16. Wood, A. B., and D. E. Weston, The Propagation of Sound in Mud,

Acustica, v. 14, 1964, pp. 156-162.

17. Las swell, J. B. , A Comparison of Two Methods for Measuring

Rigidity of Saturated Marine Sediments, M.S. Thesis,
Naval Postgraduate School, 1970, 65 p.

18. Walsh, W. E., Jr., The Use of Surface Wave Techniques for Veri-

fication of Dynamic Rigidity Measurements in a Kaolinite-Water
Artificial Sediment, M.S. Thesis, Naval Postgraduate School,
1971, 43 p.

19. Palatini, G. L. , Electroacoustic Properties of Mylar Dielectric

Underwater Sound Transducers, M.S. Thesis, Naval Postgraduate
School, 1966, 88 p.

20. Hamilton, E. L. , G. Shumway, H. W. Menard, and C. J. Shipek,

Acoustic and Other Physical Properties of Shallow-Water
Sediments off San Diego, Journal of the Acoustical Society
of America, v. 28, 1956, pp. 1-15.

21. Hamilton, E. L. , Sound Attenuation in Marine Sediments, Naval

Undersea Research and Development Center Technical Report
No. 281, 1972.

22. Hamilton, E. L. , Sound Velocity, Elasticity and Related Properties

of Marine Sediments, Part I: Sediment Properties, Environmental
Control and Empirical Relationships, Naval Undersea Research and
Development Center Technical Report No. 143, 1969, 58 p.

23. Borcherdt, R. D. , Inhomogeneous Body and Surface Plane Waves

in a Generalized Viscoelastic Half -Space, Ph.D. Thesis,
University of California, Berkeley, 1971, 308 p.

37

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Documentation Center 2
Cameron Station

Alexandria, Virginia 22314

2. Library, Code 0212 2
Naval Postgraduate School

Monterey, California 93940

3. Professor 0. B. Wilson, Jr., Code 61W1 5
Department of Physics

Naval Postgraduate School
Monterey, California 93940

4. Professor R. S. Andrews, Code 58Ad 5
Department of Oceanography

Naval Postgraduate School
Monterey, California 93940

5. Charles A. Martinek 1
222 Sanders Avenue

Somerset, New Jersey 08873

6. Department of Oceanography, Code 58 3
Naval Postgraduate School

Monterey, California 93940

7. Office of Naval Research 1
Code 480D

Arlington, Virginia 22217

8. Oceanographer of the Navy 1
The Madison Building

732 N. Washington
Alexandria, Virginia 22314

9. Dr. William R. Bryant 1
Texas A&M University

Department of Oceanography
College Station, Texas 77843

10. Dr. Davis A. Fahlquist 1
Texas A&M University

Department of Geophysics
College Station, Texas 77843

11. Dr. E. L. Hamilton 1
Naval Undersea Research and Development Center

San Diego, California 92152

38

Unclassified

Security Classification

DOCUMENT CONTROL DATA -R&D

(Security classification of title, body of abstract and indexing annotation must be entered when the overall report is classilied)

ORIGINATING ACTIVITY (Corporate author)

Naval Postgraduate School
Monterey, California

2«. REPORT SECURITY CLASSIFICATION

Unclassified

26. GROUP

3 REPORT TITLE

Ccmpressional Wave Speed and Absorption Measurements in a Saturated Kaolinite-
Water Artificial Sediment

4. DESCRIPTIVE NOTES (Type of report and, inclusive dates)

Masters Thesis; March 1972

j. au THOR(S) (First name, middle initial, last name)

Charles Allen Martinek

6 REPOR T O A TE

March 1972

7M. TOTAL NO. OP PAGES

40

7b. NO. OF REFS

23

ta. CONTRACT OR GRANT NO.

6. PROJEC T NO.

9a. ORIGINATOR'S REPORT NUMBER(S)

9b. OTHER REPORT NO(S) (Any other numbers that may be assigned
this report)

10. DISTRIBUTION STATEMENT

Approved for public release; distribution unlimited.

I. SUPPLEMENTARY NOTES

12. SPONSORING MILITARY ACTIVITY

Naval Postgraduate School
Monterey, California 93940

13. ABSTR AC T

The absorption coefficient for ccmpressional waves in a water-saturated,
kaolinite clay was measured in the frequency range 100 to 150 kHz using a
pulse technique with spherically diverging waves. The measurement also per-
mitted determination of the sound speed, VD. For one condition of the clay
with a 77% porosity, the sound speed was 1422 m/sec. The absorption coef-
ficient, a, was found to be frequency dependent, satisfying the empirical
relationship a = 0.033 f dB/m, f being the frequency in kHz. No dispersion
of wave speed with frequency was observed. These results were used together
with the results of dynamic shear (rigidity) modulus measurements made with
a torsional wave viscoelastometer to calculate the complex Lame constants of
a viscoelastic model.

DD

F0RM 1473

1 NOV «S I *T / *J

S/N 01 01 -807-681 1

(PAGE 1)

Unclassified

39

Security Classification

A-31408

Unclassified

Security Classification

KEY WORDS

ROLE W T

Viscoelastic

Acoustics

Absorption

Sediment

Rigidity

,T»M473 <BACK>

101 -807-682 I

Unclassified

40

Security Classification

A- 31 409

Thesis
M35915

13381

Marti nek

Compress. onal wave

speed and absorption

measurements in a sat

urated kaolin. te-

water artificial

sedi-

ment.
AUG 9 &5

5317

/

Thesis

M35915
c.l

**r*i l 133859

Marti nek

Congressional wave
speed and absorption

measurements in a sat-
urated kaolinite-
water artificial sedi-
ment.

thesM35915

Congressional wave speed and absorption

3 2768 002 12828 2

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