Measurement of viscoelastic properties of some recent marine sediments by a torsionally oscillating cylinder method.

MEASUREMENT OF VISCOELASTIC PROPERTIES
OF SOME RECENT MARINE SEDIMENTS BY A
TORSIONALLY OSCILLATING CYLINDER METHOD

Steven Barker Kramer

^a* po! Ca\rtovn»a W

^ontereV,Ca

Monterey, California

TH ESIS

MEASUREMENT OF VISCOELASTIC PROPERTIES
OF SOME RECENT MARINE SEDIMENTS BY A
TORSIONALLY OSCILLATING CYLINDER METHOD

by

Steven Barker Kramer

Thesis Advisor:

R. S. Andrews

September 1973

Tl 56434

kppfwvtd {on public. 'idlexLte.; dt6£rubu.tion anLaniXtd.

Measurement of Viscoelastic Properties
of Some Recent Marine Sediments by a
Torsional ly Oscillating Cylinder Method

by

Steven Barker ^Kramer

Lieutenant, United States Navy

B.S., United States Naval Academy, 1967

Submitted in partial fulfillment of the
requirements for the degree of

MASTER OF SCIENCE IN OCEANOGRAPHY

from the

NAVAL POSTGRADUATE SCHOOL
September 1973

Library

ABSTRACT

A torsi onally oscillating cylindrical probe method, operating in the
frequency range of 0.8 to 3.3 kHz was employed for measuring the visco-
elastic properties of 13 marine samples collected by Shipek grab from
shallow water regions of Monterey .Bay, California. Other mass physical
properties such as wet density, porosity, sound speed, sand-silt-clay-
gravel percentages, mean grain size and sorting were also measured.
Limited precision of impedance measurements permitted only the determina-
tion of the mechanical resistance due to the probe contact with the sedi-
ment. The observed values for various sediments ranged up to a value 65
times the lowest value. Correlations between mechanical resistance and
mass physical properties are studied by graphical means with results
indicating that water content of sediments is a determining factor in the
mechanical resistance of a sediment. A dependence of mechanical resistance
upon frequency is observed.

TABLE OF CONTENTS

I. INTRODUCTION — 8

A. GENERAL - - — 8

B. REVIEW OF LITERATURE ----- - 9

II. THEORY - 12

III. THE VISCOELASTOMETER — 15

A. DESCRIPTION 15

B. DESIGN IMPROVEMENTS 16

C. CALCULATION OF COMPLEX DYNAMIC RIGIDITY

FROM EXPERIMENTAL DATA 17

IV. EXPERIMENTAL PROCEDURE 20

A. SAMPLE COLLECTION 20

B. MEASUREMENTS - 20

1. Congressional Wave Speed ' 21

2. Complex Dynamic Rigidity 21

3. Vane Shear Test 22

4. Wet Density and Porosity 22

5. Grain Size Analysis 22

V. RESULTS 24

A. LIMITATIONS ON TORSIONAL PROBE VISCOELASTOMETER
MEASUREMENTS --- - — 24

B. DISCUSSION - 25

VI. . CONCLUSIONS AND RECOMMENDATIONS 30

REFERENCES CITED --- 79

INITIAL DISTRIBUTION LIST --- 81

FORM DD 1473 83

LIST OF TABLES

I. Station Location, Water Depth and Bottom Water Temperature 38

II. Measured Torsional Impedance of Sediments 39

III. Measured Torsional Impedance of Sediments Under

Dry Conditions ' 41

IV. Measured Torsional Impedance of Sediments Under

Mixed Conditions 42

V. Mass Physical Properties of Sediments 43

VI. Acoustic Properties of Sediments 44

VII. Textural Analysis of Sediments 45

LIST OF FIGURES

1. Sketch of the Viscoelastometer 32

2. Sketch of the Piezoelectric Ceramic 33

3. Sketch of the Velocity Sensor. 34

4. Sketch of the Vaned Head 35

5. Diagram of Electronics for Experimental Measurements 36

6. Shepard Tertiary Sediment Type Diagram 37

7. R[_ as a Function of Wet Density, First Mode 46

8. Rj_ as a Function of Wet Density, Second Mode 47

9. R(_ as a Function of Wet Density, Third Mode 48

10. Rj_ as a Function of Porosity, First Mode 49

11. R|_ as a Function of Porosity, Second Mode 50

12. R[_ as a Function of Porosity, Third Mode 51

13. R|_ as a Function of Sound Speed, First Mode 52

14. R[_ as a Function of Sound Speed, Second Mode 53

15. R[_ as a Function of Sound Speed, Third Mode 54

16. R[_ as a Function of the Product of Wet Density

and Sound Speed Squared, First Mode 55

17. R|_ as a Function of the Product of Wet Density

and Sound Speed Squared, Second Mode 56

18. R[_ as a Function of the Product of Wet Density

and Sound Speed Squared, Third Mode 57

19. R[_ as a Function of Percent Sand, First Mode 58

20. Rl as a Function of Percent Sand, Second Mode 59

21. R|_ as a Function of Percent Sand, Third Mode 60

22. R[_ as a Function of Percent Silt, First Mode 61

23. R|_ as a Function of Percent Silt, Second Mode 62

24. R|_ as a Function of Percent Silt, Third Mode 63

25. R^ as a Function of Percent Clay, First Mode 64

26. Rl as a Function of Percent Clay, Second Mode 65

27. R|_ as a Function of Percent Clay, Third Mode 66

28. R|_ as a Function of Percent Gravel, First Mode 67

29. R[_ as a Function of Percent Gravel, Second Mode 68

30. Rl as a Function of Percent Gravel, Third Mode 69

31. R[_ as a Function of Vane Shear Strength, First Mode 70

32. R[_ as a Function of Vane Shear Strength, Second Mode 71

33. R[_ as a Function of Vane Shear Strength, Third Mode 72

34. R|_ as a Function of Mean Grain Size, First Mode 73

35. R^ as a Function of Mean Grain Size, Second Mode 74

36. R^ as a Function of Mean Grain Size, Third Mode 75

37. R|_ as a Function of Sorting, First Mode. 76

38. Rl as a Function of Sorting, Second Mode 77

39. Rl as a Function of Sorting, Third Mode 78

ACKNOWLEDGEMENTS

The author wishes to express his gratitude to Professors O.B. Wilson,
Jr., and R.S. Andrews for their assistance in this research. The author
also wishes to thank Physicist Donald E. Spiel for his valuable assistance.

Use of the R/V ACANIA, operated by the Naval Postgraduate School , was
essential in this research as was project support received through contract
with the Office of Naval Research, Ocean Sciences and Technology Division.
The sediment velocimeter used in the research was provided by the Navy
Pacific Support Group of the Naval Oceanographic Office, San Diego,
California.

I. INTRODUCTION

A. GENERAL

A better understanding of the transmission and loss of acoustic
energy in marine sediments is needed in order to improve the usefulness
of sound reflection from the ocean bottom. Geologists conducting
seismic research or seismic prospecting are interested in better under-
standing how acoustic energy is transmitted and attenuated in the ocean
floor. The acoustician may be interested in improving the accuracy of
sonic profiling, precision acoustic mapping, and the sonic probe. The
Naval officer may desire a better understanding of the effect of the
bottom upon long range propagation and more reliable predictions of
ocean areas where bottom bounce mode sonar has maximum effectiveness.
Refinements in all of these uses of reflected acoustic energy may ulti-
mately depend upon how accurately energy losses at the ocean floor can
be predicted.

A major difficulty in making energy loss predictions is due to the
variability of marine sediments and in applying a model that describes
this variability. Variability may be the result of both vertical in-
homogenities due to layering or horizontal inhomogenities caused by
changes in sedimentation, situations which are common in ocean sediments,
Another problem is that of developing a reflection process model which
incorporates more realistic values of the physical properties of the sea
floor.

When a congressional wave strikes the bottom, some of its energy is
reflected and some penetrates causing energy losses due to attenuation

8

and to transformation into shear waves and the propagation of the shear
waves in the sediment (Hamilton et al.,1970). The energy losses from
these effects were omitted from some of the earlier models which were
used for bottom loss predictions. The near elastic model, or viscoelastic
model, is one of the more sophisticated models in current use which
accounts for these energy losses.- -In this model, Lame constants in the
Hookean equations of elasticity are replaced with complex Lame constants
whose real part represents elastic activity and whose. imaginary part rep-
resents damping of compressional acoustic wave energy or energy losses
due to friction (Hamilton, 1969). Researchers have hoped that the vis-
coelastic model would provide accurate reflection coefficients, but
comparisons between experimental results and theoretical calculations
have had mixed success (Bucker et al., 1965; Akal,1972). There exist
problems in determining values of the viscoelastic parameters for use in
acoustic reflection modeling.

B. REVIEW OF LITERATURE

Investigators have attempted to measure complex Lame, constants by four
different methods. The Stoneley wave technique has been used by Hamilton
et al . (1970) and Bucker, Whitney, and Keir (1964) and the torsional wave
vibration technique has been described by Gallagher (1968). Another method,
the direct measurement of shear wave speed in sedimentary rocks, was noted
by White (1965). The torsionally oscillating cylinder method was developed
by Mason (1947) and McSkimin (1952) for use in polymer research.

At the Naval Postgraduate School (NPS), investigators have studied
various designs of a viscoelastometer utilizing the torsionally oscillating
cylinder method in an attempt to directly measure one of the complex Larn'e
constants, the complex dynamic rigidity. Hutchins (1967) used a torsional

wave viscoelastometer in the frequency range near 38.8 kHz to measure the
complex shear modulus (complex dynamic rigidity) in a kaolini te-water
mixture which simulated an ocean sediment. Cohen (1968) extended the
frequency range of Hutchins' viscoelastometer, and studied a kaolini te-
bentonite-water artificial sediment and showed that this mixture exhibited
shear moduli independent of frequency. The complex dynamic rigidity of
some shallow water marine sediments was measured by Bieda (1970) and
correlated with mass-physical properties of these sediments. Lasswell (1970)
attempted to verify the rigidity values of Beida by another method and found
them to be in close agreement. Walsh (1971) also attempted to verify the
viscoelastic measurements of complex dynamic rigidity of previous investi-
gators. Using kaolini te and water as a model for the ocean bottom, shear
wave speeds were found to be similar to those calculated from previously
measured values of rigidity. A newly designed viscoelastometer was used
by Engel (1973) when measuring rigidity of shallow water clayey silt marine
sediments. Results of these studies showed trends between complex dynamic
rigidity and mass-physical properties of the sediments which were in agree-
ment with other investigators. The instrument used by Engel was originally
intended for in situ use but it was found to be too sensitive to temperature.
In an effort to overcome temperature dependence and to provide an in situ
capability, Morgan (1972) designed and constructed a basic version of a
vaned torsionally oscillating cylinder type of viscoelastometer. Improve-
ment of this design was carried out in early 1973 by Physicist Donald E.
Spiel of NPS. This instrument was used in the measurements reported here.

The purpose of this research is to measure the complex dynamic rigidity
of marine sediments with a newly designed torsional wave viscoelastometer
and to correlate measurements with mass physical properties. The following

10

sections describe the operation and design of the viscoelastometer, the
theory of measurement, and experimental procedure. Following these
sections, a discussion of results and recommendations for future research
are presented.

11

II. THEORY

The torsional oscillation of a cylinder embedded in a sediment will
generate shear waves which propagate into the sediment. This type of
instrument system, called a viscoelastometer, measures the mechanical
impedance due to the radiation reaction from the shear waves using torque
and angular velocity sensors located in the cylindrical probe. The
mechanical impedance can be related to the real and imaginary components
of the complex dynamic rigidity modulus for the medium. The Voigt model
of a viscoelastic solid is convenient for the specification of these com-
ponents. A development of this model is presented by Ferry (1970).

McSkimin (1952) developed a relationship between the components of
the dynamic rigidity modulus and the mechanical radiation impedance
presented by contact with the walls of a cylinder executing simple har-
monic motion.

If the specific impedance for the generated shear waves is given by:

Z0 = Ro+JV (])

where R0 and X0 are the specific resistance and reactance, respectively,
then the real and imaginary components of the dynamic rigidity modulus,
G = G-J+JG2 (Voigt model) are given by:

G = Ro "Xo and G2 = 2R°X° (2)

Psed PSed "

The term Psecj is the wet density of the medium. A relationship between
the measured torsional impedance due to contact with the sediment, ZL,
and the specific impedance of shear waves, ZQ, is found by first defining
torsional impedance as:

Z = T (3)

L IT •

12

where T and Q are the applied torque and angular velocity of the cylinder
respectively. The cylinder of length L and radius a is assumed to be
oscillating in pure torsional simple harmonic motion without slip at the
cylinder^sediment boundary. The wavelength of the shear waves generated
is assumed to be \/ery small compared to the dimensions of the cylinder and
it is assumed the wave is rapidly attenuated. . In this case, the torsional
impedance and the specific impedance for the shear waves is given by:

ZL = BZ0 . (4)

It is shown below that:

B = 27ra3L0 . (5)

The area of the cylinder in contact with the sediment is 2TraL. The

shear mechanical impedance presented to the cylinder by the shear waves

is:

Z = 2TraLZ0 = T/F?rce, = I (6)

m ° Velocity v »

where v is the velocity associated with the shearing motion at the wall
of the cylinder and F is the shearing force exerted on the sediment.
Therefore:

F = 27raLZQv . (7)

The torque thus defined is;

T = Fa . (8)

Substituting equation (7) for F gives:

T = 27ra2LZ0v . (9)

Using the relationship n = v/a, equation (3) becomes:

2 Tra^LZnv _ 0_,3,

Z = ^a LZoV = 2Tra3LZn = BZn . (10)

L o 0 u

13

For the instrument used in this research, B is equal to 85 cm , giving
the specific mechanical impedance of the sediment as:

Zo = h= Ro+J'X° • (11)

where:

R. XL

R0 = 8^-and X0 = 35 . (12) (13)

Substitution of these quantities into equation (2) provides the real and
imaginary parts of complex dynamic rigidity.

14

III. THE VISCOELASTOMETER

The viscoelastometer used in the data collection for this report was
originally designed by Morgan (1972), but it has been modified as described
below.

A. DESCRIPTION

While the probe is operating at mechanical resonance, the shaft and
the vaned head are driven together in torsion by the piezoelectric barium
titanate transducer located below the support flange (Fig. 1). With the
vaned head (Fig. 4) submerged in a sediment, shear waves are generated and
propagated radially outward from the head as the viscoelastometer executes
torsional simple harmonic motion. The radiation of shear waves has a
loading effect on the mechanical system as described above and the piezo-
electric barium titanate ceramic torque sensor produces a voltage propor-
tional to the torque loading (Fig. 2). This voltage is increased by a
preamplifier and its magnitude is read from a voltmeter. The angular
velocity sensor inside the steel tube and probe head produces a voltage
proportional to the angular velocity of the head as the coil oscillates
around the essentially stationary permanent magnet (Fig. 3). This vol-
tage is amplified by a preamplifier and read from a voltmeter. The phase
difference between the torque voltage and the velocity voltage is read
from the phase meter. The frequency of the oscillation is measured from
the frequency counter (Fig. 5) connected to the drive oscillator. Nor-
mally, the system is operated at a frequency which gives torsional reso-
nance and a concomitant increase in amplitude of motion. Drive levels
are adjusted to give an adequate signal to noise ratio in the sensor
outputs.

15

B. DESIGN IMPROVEMENTS

Improvements have been made in a number of details of the viscoelasto-
meter described by Morgan (1972) although the basic principles of operation
were retained (Fig. 1). The technique for cementing the barium titanate
ceramics to the stainless steel tubing was improved. The ends of the
ceramics were carefully notched and the steel tubing ends facing these
notched ends were drilled with several holes to a diameter and depth of
1/16 inch (2.46 mm). This was done to increase the shear strength of the
ceramic-steel bond. The position of electrical leads from the ceramic was
changed from the middle of the ceramic to the end to facilitate electrical
connection. Integrated circuit preamplifiers were constructed and located
inside the probe tube. The preamplifiers for the velocity sensor and the
torque sensor were designed for a gain of 400 and 0.05, respectively. The
velocity sensor coil was rewound with No. 44 gauge wire to produce a 280 ohm
coil and the permanent magnet was suspended by No. 30 spring bronze wire.
These changes increased the sensitivity of the velocity sensor. The coil
and permanent magnet assembly were placed inside a mild steel cylinder.
Figure 2 shows a sketch of this cylinder with the assembly inside.

The vaned head used in this research was constructed of aluminum and
is illustrated with dimensions in Figure 3. Substituting aluminum for
stainless steel reduced the mass of the head from 40.9 to 13. 6g which
allowed the moment of inertia of the head to be much smaller and thus
increased the sensitivity of the instrument. The support handles inter-
fered with calibration and were replaced with a spring steel support wire.
The details of the electrical cables were modified. The length of the
three RG 58C/U coaxial cables connecting these leads with the various
meters was increased from the length of approximately 3 m to 152.5 m.

16

This additional length was needed for in situ work. The integrated circuit
preamplifiers and more sensitive angular velocity sensor improved signal
to noise ratio considerably so that the voltage amplifier and filter, used
previously, were not needed. A frequency meter was added to the transducer
circuit. The circuitry used in this experiment is illustrated by a block
diagram in Fig. 5. The models of the equipment are as follows: three
Hewlett Packard Model 400L voltmeters, a Dranetz 305-PA-3002 phase meter,
a Tektronix Model 555 oscilloscope, a General Radio Model 1309A oscillator,
a Krohn-Hite Model DCA-50B power amplifier, and a General Radio 1192B
frequency counter.

C. CALCULATION OF COMPLEX DYNAMIC RIGIDITY FROM EXPERIMENTAL DATA

The torsional mechanical impedance for the oscillating cylindrical
probe is the ratio of torque, T, to angular velocity, Q, expressed in
equation (3). It is measured using torque and angular velocity sensors
which provide voltages Vj and v , respectively, proportional to these
mechanical quantities. If K is the proportionality between the electri-
cal and mechanical values, then:

Z = |K|

'T

v
v

eJ*e , (14)

where K is determined by calibration of the torque and velocity sensors
as described by Andrews and Wilson (1973). Masses of known moments of
inertia are attached to the probe when it is vibrating in air, where it
is assumed that the torsional impedance is purely reactive and consists
of the inertia of the probe itself and the added mass. Using a series of
masses of known moment of inertia, a value for K can be determined. The
term e is determined from the observed phase angle, e0, between torque

17

and velocity voltages when the instrument is embedded in the sediment.
The phase angle correction, due to phase shifts in the preamplifiers, is
made by the equation:

e = e0 - e* , (15)

where e* is determined by:

e* = e' - 90° , (16)

where e is the phase angle between the torque and velocity voltages when
the instrument is unloaded or in air.

The calculation of specific mechanical impedance follows the develop-
ment presented by Andrews and Wilson (1973). Torsional impedance Z defined
in equation (14) has two parts:

Z= ZH + ZL , (17)

where Zm is the impedance due to the inertia of the cylindrical probe alone
and Zl is the impedance due to the load applied to the probe by the sediment
(equation 3). The value for Zm in equation (17) is calculated by:

ZH = J a)IH . (18)

where I , the moment of inertia of the probe alone}is determined from

asurements of impedance Z made in air where Z^ = 0. The torsional mechani-

me

cal impedance, Z , due to contact of the probe with the sediment has both
real and imaginary parts:

ZL = RL+jXL . (19)

The term R|_ is the mechanical or radiation resistance of the load on the
probe and is found by the equation:

RL = Zcose . (20)

18

The mechanical reactance X^ of the load is found from the relation:

XL = Zsine - ZH , (21)

where Z is determined by equation (14). Calculating the specific mechani-
cal resistance and reactance by equations (12) and (13), respectively, and
substituting these quantities into equation (2) gives the complex dynamic
rigidity of the sediment.

19

IV. EXPERIMENTAL PROCEDURE

A. SAMPLE COLLECTION

Thirteen samples of marine sediment were collected from Monterey Bay,
California, at depths up to 85 fathoms (155.4 m) (Table I). From the time
of collection until laboratory measurements were completed, a great deal
of care was exercised to keep the samples as undisturbed as possible or
conditions as near to those in situ as possible. A Shipek grab sampler,
selected to collect samples, provided sample dimensions large enough in
area and depth to allow several insertions of measuring instruments into
different locations in a given sample. The large dimensions of the sample
bucket also helped to reduce the wall effects on the measurements taken
with the viscoelastometer and the vane shear machine.

When the sample was brought aboard the research vessel (NPS R/V
ACANIA) , the bucket was carefully removed and placed in a wood rack which
provided stability for the sample. The samples were kept submerged in sea
water, sealed in plastic bags and stored in the ship's refrigerator. The
samples remained covered with sea water in their original containers and
refrigerated throughout the experiment in order to approximate in situ
conditions.

B. MEASUREMENTS

The measurements for each sample were conducted in a standard sequence
so that a previous measurement would cause a minimal disturbance in the
sample for the next measurement. The sequence of measurement was as
follows: compressional wave speed, torsional probe measurements, vane
shear test, and wet density and porosity. Finally, grain size analysis
was performed on the samples.

20

1 . Compressional Wave Speed

The first test on the samples was compressional wave speed measure-
ment. The Underwater Systems, Inc., Velocimeter Model USI 101 was used to
measure the time delay between a transducer and receiver submerged at a
fixed distance into opposite sides of the sediment in the sampler bucket.
The bracket fixing the distance between the transducer and receiver did
not penetrate more than a few millimeters into the surface of the sediment:
therefore, the sample between the receiver and transducer was essentially
undisturbed. The arrival time of the signal was read from the oscilloscope
of the velocimeter and the temperature of the sediment was recorded using
a United Systems Corp. Digital Thermometer. Later, the time delay in sea
water was measured at the same temperature at which time delay measurements
were made in the samples, and thus a temperature correction was unnecessary

2. Complex Dynamic Rigidity

The next step was to conduct measurements with the torsional probe.
Before insertion of the probe in the sediment, certain measurements were
made while the instrument was in the unloaded condition (i.e., suspended
in air). The following data were always recorded at a drive voltage of
3 v: frequency of mechanical resonance at three modes, torque sensor and
velocity sensor voltages at each resonant mode, and the corresponding
phase angle between the two voltages. The sample, still in its original
container and saturated with water was placed under the viscoelastometer
and the vaned head was lowered carefully into the sediment. The depth of
penetration was recorded and the drive voltage was increased to 15 v. A
waiting period was established until the temperature of the probe reached
the temperature of the sample. This temperature was then recorded and
the same data were recorded as in the unloaded condition and at resonant

21

frequencies of about 0.8 kHz, 2.2 kHz, and 3.1 kHz. Depth of penetration
was varied in some samples and in others there were several insertions of
the vaned head at different locations.

3. Vane Shear Test

The third step was the use of the Wykeham-Ferrance Engineering Ltd.
Vane Shear Machine which had the Diversified Marine Corporation Laboratory
Vane Shear Transducer and Adapter Kit Model LVST-015 attached. This adapter
kit is fully described by Cepek (1972). The constant speed drive motor
which is also a modification allows an X-Y plotter to trace a curve of torque
versus angle of rotation as the vane rotates in the sediment at a rate of
20°/min.

The samples, still in their original containers, were placed under the
vane so that it would penetrate an undisturbed region of the sediment.

4. Wet Density and Porosity

The last measurements taken which could be affected by disturbing
the sediment were wet density and porosity. These were calculated for
each sample by filling two stainless steel cylinders of known volume with
sediment and then weighing them on an electric chemical balance. The
samples were then oven dried for 24 hours at 105 C and, after cooling in
a dessicator to prevent absorption of moisture, were reweighed. Two
densities and porosities were then calculated and averaged for each sample.

5. Grain Size Analysis

Analysis of the grain size distribution was also carried out for
each sample. A portion of each sample was washed thoroughly by first
mixing with water in an electric blender and then washing into a jar
where settling took place. After settling, water was carefully decanted
and tap water was added again for a second washing. After setting again,

22

water was decanted from the sediment and the sediment was washed through
a 40 (0.062 mm) sieve. The fraction of the sample with grain sizes coarser
than 40 (sand and gravel) was oven dried and size analysis was performed
by sieving. The distribution of grain sizes finer than 40 (silt and clay)
was determined by pipette analysis.

23

V. RESULTS

A. LIMITATIONS ON TORSIONAL PROBE VISCOELASTOMETER MEASUREMENTS

The calibration of torque and angular velocity sensors and the accuracy
of all measurements permit a precision of about 5% or 6% in the calculated
components of torsional impedance presented to them. The real part of this
impedance, the mechanical resistance, R|_, which is due only to contact with
the sediment is thus precise to within about 5%. The imaginary part of
this impedance, which can be measured to within about 6%, is dominated by
the inertia of the probe. In many cases, the contribution to the reactance
from the sediment is comparable to the uncertainty in the total reactance.
Therefore when equation (21) is used to calculate X. , a large uncertainty
in X[_ may occur. As a result, values of X|_ are not precise enough to
justify calculation of both the real and imaginary parts of complex dy-
namic rigidity. Therefore, values of rigidity are not presented as had
originally been intended. Since R|_ is sensitive to both the elastic (G-,)
and the anelastic (G2) properties of the sediment, it is a measure of the
viscoelastic properties of the sediment. As a result of this sensitivity
it is useful to test correlations between values of R|_ with other measured
properties of each sediment. This may be done using graphical methods.

If X[_ could be considered as small and insignificant, then G-] is approxi
mately proportional to R^ and a comparison between the relation of R. and
other properties from this experiment and similar relationships for the
real part of dynamic rigidity obtained by other investigators may be useful.

Measurements of R^ were conducted at three different frequencies so
that the relative size of the probe (in terms of wave length) are different
in each case. This will change the coupling to the medium and therefore

24

will give rise to a sensitivity of radiation or mechanical resistance to
frequency. The computation of this effect could not be completed. This
leaves uncertain whether frequency dependence in R. is due to a change in
basic viscoelastic properties with frequency or merely to a change in the
coupling between the probe and the medium.

An important limitation to the conclusions, that may be drawn from the
graphs presented is the small sample size used in this experiment. Thir-
teen separate samples were analyzed and twenty-three viscoelastometer
measurements were performed. A larger sample size would give more credi-
bility to apparent trends.

B. DISCUSSION

Most of the values of mechanical resistance and reactance measured
with the viscoelastometer are presented in Table II. Also included in this
table are the frequency at which each measurement was made, the depth of
penetration of the vaned head into the sediment, and the wet density of
each sediment. In many of the sediments several measurements were taken
with the viscoelastometer (these data are indicated by small case letters
accompanying the large case letter and number, the latter identifying the
original sediment sample). Values of R, range from 0.88 x 10^ to 32 x 104
g-cm^/sec, frequency of measurement ranges from 0.87 to 3.3 kHz, and depth
of penetration ranges from 4.49 to 7.49 cm. The data in this table repre-
sent measurements conducted under conditions of minimum sample disturbance,
saturated sediments, and with all samples at nearly the same temperature.

In several cases, there are large differences in the values of \
measured in different regions of the sample. This variability is apparently
caused by horizontal and vertical inhomogenities which exist in the sedi-
ments. Some of these inhomogenities were readily apparent, for example,

the existence of biological forms and or pieces of gravel near the measuring

25

site. The amount of disturbance to which the samples were subjected is
uncertain. It is impossible to determine, in each case, whether the value
of R|_ at a particular site in the sample was the result of the effects of
collection, handling, and/or temperature variation upon the structure of
the sediment.

Table III lists the same kinds- of data presented in Table II but
measured under different laboratory conditions. These measurements were
conducted near the edge of three of the samples where the sediment was
somewhat elevated and therefore partially drained. As expected, the
measured mechanical resistance in these regions was in general larger at all
frequencies than most values recorded for the submerged portions of the
sediments. These values of R|_ range from 13 x 10 to 28 x 10- g-cm^/sec.

Measurements with the viscoelastometer were repeated in each W-series
sediment sample (Table I) after it was thoroughly stirred and the remolded
sample placed into a cylindrical container. These data are presented in
Table IV. The range of values for radiation resistance in these nearly
homogeneous sediments is 0.49 x 10^ to 4.1 x 10^ g-cm^/sec. These values
are in general lower than those observed in the "undisturbed" and saturated
sediments in Table II and are also smaller than values measured for the
dryer sediments listed in Table III. The values of R. are lower since
any cementation or compaction existing in the samples was destroyed by
remolding. The differences in R^ between the individual "homogeneous"
samples is not nearly as large as differences in R^ between the various
"undisturbed" samples. This may indicate that the viscoelastometer is
indeed responding to properties of the sediment such as structure,
rigidity, and water content.

26

Values of R. listed in Table II are used as the dependent variable
in all of the graphs presented. The independent variables are as follows:
wet density, porosity, compress ional wave speed, the product of the square
of compressional wave speed and the wet density, percent sand, percent
silt, percent clay, percent gravel, vane shear strength, mean grain size,
and grain size distribution standard deviation (sorting). Values of R.
are compared with each of these independent variables at each of the
three frequencies of mechanical resonance, about 0.87-, 2.2 and 3.3 kHz
for the first, second and third modes, respectively.

The comparison of mechanical resistance with density (Fig. 7, 8 and
9) exhibits a general increase in resistance of the sediment with in-
creasing density, particularly in the second mode. The results obtained
by Hamilton (1969), Beida (1970), and Engel (1972) indicated an increase
in dynamic rigidity with increasing density. Rigidity is lower in sedi-
ments with high porosity (lower density) since there are fewer inter-
particle contacts due to the presence of water between the particles
(Hamilton, 1969). An increase in R[_ with decreasing porosity is observed
in all three modes (Fig. 10, 11 and 12).

The measured compressional wave speeds in the different types of
sediments used in this experiment are distributed over a moderate range.
Mechanical resistance appears to show a fairly strong trend with sound
speed, increasing as the sound speed decreases (Fig. 13, 14 and 15). An
increase in sound speed with an increase in rigidity (or mechanical resis-
tance of the sediment) might be expected since with increased rigidity
there are probably more particles in contact which should also affect
the compressive modulus. Beida (1970) did not show such a relationship
between the dynamic rigidity and sound speed.

27

Data, including the ratio of the speed of sound in a sediment to the

compressional wave speed in water, the in situ compressional wave speed,

2 7

and pC are presented in Table VI. A comparison between the Rl and p C'

shows no apparent trends (Fig. 16, 17 and 18). However, Engel (1973)
found trends between the real part of dynamic rigidity and pC^ which
showed a slight increase in rigidity with an increase inpC^. This was
in agreement with Hamilton (1969) and Beida (1970).

The types of sediments considered in this research are different from
those studied by Engel (1973) which were primarily clay and silty clay
types. Most of the sediments analyzed in this experiment are the silt and
sandy silt types with one sample of the silty sand type and two other
sand types (Fig. 6). One sand type sample contained a large percentage
of gravel (Table VII). The depositional environment of the sediments
collected for this experiment is also different than those of other
investigators. Sediments presently under consideration were collected
from shallow water (Table I) and most other researchers obtained sediments
from much deeper locations where the rates of deposition and compaction
are slower. The differences of sediment type and depositional environment
may account for some of the apparent disparities in trends between results
reported here and those of other investigators.

A comparison of R|_ with the percent of sand indicates an increase in
R. with an increase in percent sand for all three frequencies of resonance
(Fig. 19, 20 and 21). The resistance might be expected to increase due
to the friction from more particles of sand in sediments of higher per-
centages of sand. An inverse relationship is observed in a comparison
of R. to the percent silt where \ increases as the percent silt decreased,
This again may be a clue to the presence of water between adjacent par-
ticles reducing resistance to movement (Fig. 22, 23 and 24). Only the

28

first and second modes show a slight trend with R. which increases as
percent clay decreases (Fig. 25, 26 and 27). The comparison of R|_ with
percent gravel shows an increase in mechanical resistance with an in-
crease in percent gravel (Fig. 28, 29 and 30) perhaps due to less water
between particles.

Vane shear strength reported by Engle (1973) and Beida (1970) indicated
a slight increase in vane shear strength with rigidity. A similar result
is observed in the comparison between R[_ and vane shear strength in Fig.
31, 32 and 33, although it is not a strong dependence.

Mean grain size and sorting (deviation) presented in Table VII are
compared with R^. Values of R|_ increase as the mean grain size and sorting
increase (Fig. 34 through 39). This result is in agreement with the be-
havior of Rl when compared with percent sand, silt, clay, and gravel.
Greater amounts of larger grain sizes in these comparisons show an in-
crease in R, . It is also noted that, as would be expected, porosity tends
to decrease with increasing standard deviation (i.e., poorer sorting).

In general, the values of Rl exhibit a frequency dependence. At the
first mode (lowest frequency), values of R|_ are relatively lower, parti-
cularly in the range of the smaller values, than in the second (inter-
mediate frequency) and third modes (highest frequency). Second mode R,
values are larger than first mode values of R^_ and third mode values are
the largest. This pattern, with a few exceptions, is observable in each
graph presented. Neither Beida (1970) nor Engle (1973) found this depen-
dence when analyzing complex dynamic rigidity with independent variables
similar to those reported here. For the reasons discussed in Part A of
Chapter V, it is not possible to draw conclusions from this pattern of
frequency dependence.

29

VI. CONCLUSIONS AND RECOMMENDATIONS

It is concluded that the present configuration of the torsional wave
viscoelastometer fails to measure mechanical reactance of the sediment
with the precision necessary to calculate useful values of real and imag-
inary dynamic rigidity. However, relationships between measured values
of mechanical resistance and other mass physical properties compare favor-
ably in most instances with results achieved by previous investigators
at the Naval Postgraduate School as well as at other institutions.

Summarizing the results, it can be said that sediments which were
maintained in a saturated and undisturbed condition provide values of
mechanical resistance which vary between each sample and at different re-
gions in a sample. Remolded sediments exhibit the lowest values of mech-
anical resistance and the smallest differences in value between different
samples in the experiment. Portions of sediments which were not saturated
show the highest mechanical resistance. Graphical relationships between
measured mechanical resistance and mass physical properties indicate that
the amount of water between particles has a key role in determining the
resistance of a sediment, the resistance increasing with less water present.
The generally observed relationship that values of resistance increase with
an increase in frequency cannot be interpreted at this time.

In the future, the re-evaluation of the assumptions made in the develop-
ment of the relationship of torsional impedance to the viscoelastic model
needs to be carried out. In particular, the assumption that there is no
slippage at the sediment-rod interface may be invalid and needs careful
consideration. Water may easily prevent the contact between the sediment
and the vaned head. In the future a more sensitive torsional wave visco-
elastometer should be developed which incorporates an improved design

30

for the torque and angular velocity sensors with a probe head that
guarantees actual contact with the medium.

31

// / t./ / i /

Electrical Leads

Connecting Plate

Stainless Steel Tube'
Length 26 in.

Piezoelectric Torque Sensor

Drive Head
V/ith Four Fins

B

D

Spring Steel Support Wire

^ Massive Stainless Steel
Supporting Piate

Piezoeleciric Drive
Transducer
Length 3 in.
Dia. 0.75 In.

IC Pre -Amps

Velocity Sensor Internal
(Not Shown)

Figure 1. Sketch of the Viscoelastonveter

32

Electrical Leads

+

Conductor

+

Barium Tinanate

Ceramic
O.D. 0.75 in.
I.D. 0.50 in.

Note:

Notched Ends
not shown

Figure 2. Sketch of the Piezoelectric Ceramic

33

Coil Terminals

Suspension Wire
No. 30 Spring Bronze

cn

Mild Steel Case
Dia. 0.5 in.
Length 1 .25 in

Permanent Magnet

Not shown:
No. 44 wire coil
(280 ohm) around
magnet .

Figure 3. Sketch of the Velocity Sensor

34

Head Dimensions:
I'. D. 1.78 cm.
O.D. 1.90 cm.
Length 4.49 cm.
Vane Width 0.062

cm

Stainless Steel Tube

O-Ring

Drive Head With Four
Vanes

Figure 4. Sketch of the Varied Head

35

CtC

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36

VoCLAY

% SAND

50%

% S I LT

v This point includes percent of
gravel .

Figure 6. Shepard Tertiary Sediment Type Diagram

37

Sample

Latitude
N

Longitude
W

Wat*
1

54 <

ir Depth
rm (m)

;98. 8)

Bot1

Tempe

;om Water
;rature, °C

W-l(a,b)

36-45.2

121-56.9

8.0

W-2(a,b)

36-45.2

121-56.9

54 (

[98.8)

8.2

W-3(a,b)

36-44.8

121-53.2

53 I

[96.9)

8.2

W-4(a,b,c)

36-44.8

121-53.2

53 <

[96.9)

8.2

W-5(a,b)

36-41.6

121-51.2

42

[76.8)

8.2

W-6(a,b)

36-41.6

121-51.2

42

76.8)

8.2

W-7(a,b)

36-38.0

121-54.0

38 1

[69.5)

8.6

S-l (a,b,c)

36-41.3

121.54.2

45

[82.2)

8.6

S-2(a,b,c)

36-38.3

121-56.1

52 1

[95.1)

8.2

S-3

36-38.3

121-56.1

52 1

[95.1)

8.2

S-4

36-45.1

121-55.8

57 I

[104.2)

8.0

S-5(a,b)

36-45.3

121-54.1

65 (

.118.9)

8.0

S-6(a,b)

36-48.3

121-55-0

85 1

[155.4)

8.5

Table I. Station Location, Water Depth
and Bottom Water Temperature

38

Sample

Density
(g/cm3)

1.65

Penetration
Depth
(cm)

Frequency
(Hz)

871

2116

3304

Measured
Mechanical Resistance

(104 g-cm2/sec)

W-la

4.49

3.3

7.9

17.0

W-2a

1.57

4.49

872
2114
3295

1.5

5.3

11.0

W-3a

1.70

4.49

874
2115
3308

1.9

5.5

10.0

W-4a

1.52

4.49

872
2117
3304

1.7
4.2
8.3

W-4b

1.52

4.49

873
2118

3303

1.2

4.4
8.6

W-4c

1.52

6.99

873
2116
3302

8.8
10.2
20.0

W-5a

1.50

4.49

874
2115
3306

2.9
5.1
9.1

W-5b

1.50

6.0

872
2112

3301

2.0
7.2

- 14.0

W-6a

1.51

4.49

875
2114
3306

0.88

3.8

6.8

W-6b

1.51

4.49

872
2114
3303

1.4
5.0
9.2

W-7a

1.57

4.49

872
2114
3299

1.8
4.5
8.4

W-7b

1.57

4.49

876
2114

4.3
9.0

Table II. Measured Torsional Impedance of Sediments

39

Sample

Density
(g/cm3)

1.48

Penetration
Depth
(cm)

Frequency
(Hz)

875
2111
3306

Measured

Mechanical Resistance

(104 g-cm2/sec)

S-la

4.79

9.0
12.0
23.0

S-lb

1.48

6.79

880
2112
3309

14.0
17.0
27.0

S-lc

1.48

7.49

874
2115
3269

9.4
11.0
20.0

S-2a

1.45

4.49

876
2119
3303

4.3

6.4

13.0

S-2b

1.45

6.99

881
2121
3313

15.0
17.0
26.0

S-3

1.43

4.49

872
2118
3300

3.8

6.0

14.0

S-4

1.82

4.49

890
2119
3300

16.0
15.0
29.0

S-5a

1.86

4.49

920
2134
3344

32.0
21.0
27.0

S-5b

1.86

5.0

939
2133
3350

37.0
26.0
29.0

S-6a

1.95

4.49

874
2118
3293

11.0
12.0
25.0

S-6b

1.95

4.89

872
2113
3292

4.9

8.1

20.0

Table II. Measured Torsional Impedance of Sediments (Cont.)

40

Penetration

Measured

Den si ty

Depth

Frequency

Me <

:hanical Resistance

Sample

(g/cm3)
1.65

(cm)

(Hz)
882

(104 g-cm2/sec)

W-lb

4.49

13.0

2117

16.0

3313

26.0

W-2b

1.57

4.49

879
2120
3318 "

13.0
14.0
22.0

W-3b

1.48

6.0

887
2121
3321

16.0
20.0
28.0

*Measurements were taken in an elevated and drained region of
the sample.

Table III. Measured Torsional Impedance of Sediments
Under Dry* Conditions.

41

Penetration Measured

Density Depth Frequency Mechanical Resistance

Sample (g/cm3) (cm) (Hz) (104 g-cm2/sec)

W-l 1.63 4.49

W-2 1.57 4.49

W-3 1.48 4.49

W-4 1.52 4.49

W-5 1.50 4.49

W-6 1.51 4.49

W-7 1.57 4.49

891
2138
3375

0.49

2.8

1.2

892
2138
3375

1.6
3.3
1.6

891
2139
3376

2.1

892
2137
3375

1.1
2.6
1.2

892
2137
3375

1.4
3.3
1.6

892
2139
3375 ,

2.3
3.2
1.4

892
2139
3376

2.9
4.1
2.3

*Measurements taken after sediments were mixed thoroughly

Table IV. Measured Torsional Impedance of Sediments
Under Mixed* Conditions

42

Wet

Vane Shear

Density

Porosity

Strength

Sample

(g/cm3)
1.63

{%)

( ps i )

W-la

66.9

0.046

W-lb
W-2a

1.63
1.57

66.9
70.6

0.071

W-2b

1.57

70.6

0.573

W-3a

1.48

73.0

0.081

W-3b

1.48

73.0 '

0.396

W-4a

1.52

72.0

0.085

W-4b

1.52

72.0

0.363

W-4c

1.52

72.0

W-5a

1.50

70.7

W-5b

1.50

70.7

0.152

W-6a

1.51

76.5

0.085

W-6b

1.51

76.5

0.085

W-7a

1.57

73.0

0.195

W-7b

1.57

73.0

0.195

S-la

1.48

69.9

0.120

S-lb

1.48

69.9

S-lc

1.48

69.9

■■

S-2a

1.45

73.1

0.099

S-2b

1.45

73.1

S-3

1.43

72.5

0.079

S-4

1.82

52.9

0.185

S-5a

1.86

49.4

0.297

S-5b

1.86

49.4

S-6a

1.95

57.3

0.292

S-6b

1.95

57.3

0.292

Table V. Mass Physical Properties of Sediments

43

tompressionai 2

*CSed/ wave Speed Pcsed

Sample Cwater (m/sec) (lO^g-m^/cm^-sec?)

W~l(a,b) 1.004 1489.3 3.615

W-2(a,b) 1.010 1499.0 3.438

W-3(a,b) 1.014 1504.9 3.352

W-4(a,b,c) 1.011 1500.4 3.422

W-5(a,b) 1.017 1508.9 3.415

W-6(a,b) 1.010 1498.5 3.391

W-7(a,b) 1.006 1494.1 3.505

S-l(a,b,c) 1.009 1499.4 3.327

S-2(a,b) 1.012 1501.1 3.267

S-3 1.008 1496.0 3.200

S-4 0.922 1367.1 3.402

S-5(a,b) 0.927 1375.4 3.519

S-6(a,b) 0.970 1441.9 4.054

laboratory sediment-to-water sound speed ratio.

Table VI. Acoustic Properties of Sediments

44

Sample

Mean Grain
Size
(0)

Sorting
(Deviation)

1.79

Sand
(%)

31.18

Silt
(%)

64.23

Clay
(M

4.59

Gravel

W-l(a,b)

5.27

0.00

W-2(a,b)

5.31

1.81

29.58

68.92

1.08

0.42

W-3(asb)

6.73

1.29

1.62

85.99

12.39

0.00

W-4(a,b,c)

6.72

1.28

0.0

82.84

17.16

0.29

W-5(a,b)

6.50

0.49

1.25

81 .6-9

17.05

0.00

W-6(a,b)

6.53

1.36

1.07

82.32

16.61

0.00

W-7(a,b)

5.78

1.10

2.79

90.18

7.04

0.00

S-l(a,b,c)

6.46

1.01

1.05

91.00

7.95

0.00

5-2(a,b)

6.43

0.91

1.15

92.10

6.75

0.00

5-3

6.32

0.98

1.57

91.12

7.31

0.00

5-4

1.40

4.01

51.18

14.03

5.94

28.84

5-5(a,b)

1.69

2.52

74.14

10.33

1.34

14.20

5-6(a,b)

4.55

2.48

50.92

35.15

12.68

1.25

Table VII. Textural Analysis of Sediments

45

CM

E
o
i

%

COL

1 1 1

1

1 1

1

First Mode

o

CO

-

o

o

CO

■•

•

"■

CN

-

-

o

CN

-

-

i2

o°

o

-

o

8 o

o

-

u->

o o
o

o

°§ °

o

o

-

1 1 1

<

1 1

1

1.4 1.5

1.6 1.7 1.8

DENSITY (g/cm3)

1.9 2.0

Figure 7. R. as a Function of Wet Density, First Mode

46

u

<

CM

E
o
i

D)

ac

1

1

1

1 1

1 1

Second Mode

CO

-

-

o

CO

-

__

•

o

CM

—

o

-

o°

o

12

©

o

o

O

-

o

o

-

m

o
o°

o

o
o

o

1

1

1

1 1

1 1

1.4 1.5

.6 1.7 1.8,

DENSITY (gAm3)

1.9 2.0

Figure 8. R, as a Function of Wet Density, Second Mode

47

CM

E
v

Di

1 1

1

1

1

1

Third Mode

lO
CO

-

-

o

o

CO

o

o
o

• o

CM

o
o

o

-

O
<N

o o

o

o

i£}

°o o

r

"

O

o

©

o

o
o

-

in

—

-

1 1

1

1 1

1

1

1.4 1.5 1.6 1.7 1.8 1.9 2.0

DENSITY (g/cm3)

Figure 9. R^ as a Function of Wet Density, Third Mode

48

CO

First Mode

o

CO

CM

.8

CM

E
o

i

O
CM

G£ IO

o

o

©

LO

o

1

O °

i

60
POROSITY (%)

70

o
o

50

80

Figure 10. Rl as a Function of Porosity, First Mode

49

in

CO

o

CO

in

CM

<

CN

E
o

o

o

CN

a. ir>

o _

in -

■a

1

1

1

Second Mode

-

o

- -

-

-

o

o o

o

o

o

•

o

o

-

o

O QD
©©

o
o

1

I

1

50

60

70

POROSITY (%)

Figure 11. R. as a Function of Porosity, Second Mode

80

50

CO

o

CO

CM

o

CM

CN

E
o

i

D)

an co _

O -

uo -

-

1

~l

1

Third

Mode

-

o
o

o

—

o

-

-

o

o
o

-

-

o

o °

-

-

«

o

-

-

-

o o
°§o

o

1

-

o

1

1

50

60

70

POROSITY (%)

Figure 12. RL as a Function of Porosity, Third Mode

80

51

E
o
i

ai

1375

1400 1425 1450 1475

SOUND SPEED ( m/sec )

1500

Figure 13. R| as a Function of Sound Speed, First Mode

52

CO

o

CO

CM

o

CN

<

csi

E
o
i

cc 10

o -

m -

1

i

1 i

1 1

Second Mode

-

-

o

-

o

@

2

o

—

-

o

o
o o

-

o°

5000-

0
0

•

i

1 1

1 1

1375 1400 1425 1450 1475 1500

SOUND SPEED ( m/sec )

Figure 14. R|_ as a Function of Sound Speed, Second Mode

53

o

cm

E
o

i

O

Q£

CO

o

CO

10

o

in

10 -

1

1

J

1

! 1

Third Mode

-

- o

--

-

o

o

—

o

o
o

o

© -

o

o
°o o

-

00 -

8© °

-

o

1

'

i

1 1

1375 1400

1425 1450 1475

SOUND SPEED ( m/sec )

1500

Figure 15. R. as a Function of Sound Speed, Third Mode

54

.8

CM

E
o

i

CO

OC

1

1

1

1

1

o

First Mode

m

CO

~

MM

o

O
CO

"

•

CN

-

o

CN

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-

if2

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o

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o

© o

IT)

o °

o

o
o

o

o -

1

^

1

i

1

32

34 36 38

oC2 ( I05 g-m2/cm2-sec2 )

40

Figure 16. RL as a Function of the Product of Met Density and
Sound Speed Squared, First Mode

55

<?C2 ( I05 g-m2/cm2-sec2 )

Figure 17

Ri_ as a Function of the Product of Wet Density and
Sound Speed Squared, Second Mode

56

o

CM

E
o
i

1

1

1

1

1

0)

Third Mode

-

o

CO

o

o
o

o

-

CM

o

o

o

<N

o o

o

o

—

° o

o

o

o o

°B

o

o

-

m

-

^

1

1

1

1

1

32

Figure 18.

34

36

33

40

oC2 ( I05 g-m2/cm2-sec2 )

R[_ as a Function cf the Product of Wet Density and
Sound Speed Squared, Third Mode

57

CO

First Mode

o

CO

u
o

CM

£
u
l
O)

a:

O

CM

U")

m

19

o

t r

O

O

J.

jl

10 20 30 40 50 60

PERCENT SAND (%)

70 80

Figure 19. R^ as a Function of Percent Sand, First Mode

58

PERCENT SAND (%)

Figure 20. Rj_ as a Function of Percent Sand, Second Mode

59

o

V

E
o
i

at.

1

1

1 1

1

1 1 !

CO

_

Third Mode

-

o

CO

o

---

O

o
o

-

ex

o
o

o

-

s<

D

o

o

-

lO

«

o

i

D

?o

■

O

-

iO

—

1

1

i i

1

1 1 1

0 10 20 30 40 50 60 70 80

PERCENT SAND (%)

Figure 21. R, as a Function of Percent Sand, Third f^ode

60

CO

o

CO

CM

u

<

CM

E
o

O
CM

O)

o

MM

*- '

_J

i£2

10

PERCENT SILT (%)

Figure 22. RL as a Function of Percent Silt, First Mode

61

CM

E
o

i

Qi

10 20 30

40 50 60

PERCENT SILT (%)

70 80

Figure 23. RL as a Function of Percent Silt, Second Mode

62

CO

o

CO

CM

o

CM

u

<

cs

E
o
i

D)

<* £

U"> -

1

1

1 1

1

1 1 1

1

Third Mode

~"i

-

o

—

—

-

o
o

o

•

o

-

o

o
o

o

o
o

o -

o

o

-

.

©

o

-

o

-

1

• 1

1

1 1 1

1

10 20 30 40 50 60 70 80 90

PERCENT SILT (%)

Figure 24. Rj_ as a Function of Percent Silt, Third Mode

63

o
.8

CM

E
o

i

CO

PERCENT CLAY (%)

Figure 25. RL as a Function of Percent Clay, First Mode

64

<

CM

E
u

i

1

1

1

Second Mode

CO

"

o

CO

o

—

•

-

CM

■"

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o

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o o

-

u?

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o

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o

1

o
o

o
o

1

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° °°§

o
1

10

15

PERCE NT CLAY (%)

Figure 26. R^ as a Function of Percent Clay, Second

Mode

65

u

CN

E
o
i

oc

1

1

1

lO

Third Mode

CO

o

CO

o
o

- -

o

-

IT)
CN

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o

o

—

O
CN

o

o

o

Q

lO

o°

O

O

_ o

o

o

oo
o

m

1

1

1

10

15

PERCENT CLAY {%)

Figure 27. Rj_ 3S a Function of Percent Clay, Third Mode

66

1

1 1 1

o

1 1

10

CO

-

First" Mode

-

o

O
CO

-

CM

•

-

o

4)

<
CM

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o

O
CN

— —

D)

%

lO

—

o

-

52

JO
3

•

-

•o

-o

i

1 1 1

1 1

-

10

15

20

30 35

PERCF.MT GRAVEL (%)

Figure 28. RL as a Function of Percent Gravel, First Mode

67

CM

E
v

i

Q£

1

1

1

-■" ■ 1

1 1

CO

Second Mode

-

o

CO

o

•

-

10

CM

"

o

CM

-

o

-

to

o

o

-

o'

o

•

'O

0

•

-

1

1

1

1

1 1

10 15

20

25 30

PERCENT GRAVEL (%)

Figure 29. R|_ as a Function of Percent Gravel , Second .'lode

68

CO

O

CO

CM

u

0>

CM

O
CN

E
v

i

-J m

10

I

1

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1

1 1

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Third Mode

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-

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3

i

1

1

1

1 1

10

15

20 25

30

PERCENT GRAVEL (%)

Figure 30. RL as a Function of Percent Gravel, Third Mode

69

u

o
<

E
o

oc

0.1 0.2 0.3 0.4

VANE SMEAR STRENGTH ( lb/In2 )
Figure 31. RL as a Function of Vane Shear Strength, First Mode

70

.8

<N

E
v

i

cc

0.1 0.2 0.3

VANJE SHEAR STRENGTH ( lb/in2 )

Figure 32. R, as a Function of Vane Shear Strength, Second Mode

71

u

CN

E
o

i

C£

_ ., ,

1

I

- - 1

u">

Third Mode

CO

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o

CO

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0

o

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-

in

"™

-

1

1

1

•

0.1 0.2 0.3

VANE SHEAR STRENGTH ( lb/in2 )

0.4

Figure 33. R, as a Function of Vane Shear Strength, Third Mode

72

■

CN

E
o
i

or

3 4 5

MEAN GRAIN SIZE ( 0 )

Figure 34. R. as a Function of Mean Grain Size, First "'ode

73

in

CO

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IT)
CM

CM

E
u

o

o

CM

or zJ

ir, _

O

ir> -

1 1

1

1

I

1 1

Second Mode

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o

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12 3 4 5 6 7

MEAN GRAIN SIZE ( 0 )

Figure 35. Rj_ as a Function of Mean Grain Size, Second Mode

74

4)

CM

E
u
i

ac —

mm

"1

1

1 1

II 1

CO

Third Mode

-

o

CO

-

o
o

- -

8

10

CM

o

o

o

o

CM

o

o o -
o

in

-

ooo

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-

o ' o -

%

o

k->

1

1

1 1

1 1 1

12 3 4 5 6

MEAN GRAIN SIZE ( 0 )

Figure 36. R[_ as a Function of Mean Grain Size, Third Vodt

75

CM

E
o
i
o>

mm

i

1

1

o

1

1

CO

First Mode

-

o

O
CO

—

in

CM

-

,

-

o

CM

-

-

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%

o

-

o

©o

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m

o

mm

^^

°o°

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8

,°%

o

1

1

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•

0

SORTING

Figure 37. R. as a Function of Sorting, First Mode

76

■

<N

E
u
i

ac

—

1

1

1

1

1

CO

Second Mode

-

o

CO

- -

o

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CN

-

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0

SORTING

Figure 38.

Ri as a Function of Sorting, Second Mode

77

CO

o

CO

CM

0)

CM

E
o

i

O

O

CM

lO

C£

lO -

mm

1

1

1

1

■■ I

Third Mode

-

-

o
o

--

o
o

o

-

o

o

-

oo

o

-

-

o

a

o

-

-

o

o
o

o

-

-

o

-

1

1

1

1

1

0

Figure 39

SORTING

R[_ as a Function of Sorting, Third Mode

78

REFERENCES CITED

1. Akal , T., The Relationship Between the Physical Properties of Under-

water Sediments that Affect Bottom Reflection, Marine Geology, v. 13,
1972, pp 251-266.

2. Andrews, R. S. and 0. B. Wilson, Jr., Measurement of Viscoelastic

Properties of Sediments Using a Torsi onally Vibrating Probe, paper
presented at the Office of Naval Research Symposium on the Physics
of Sound in Sediments, Austin, Texas, April 1973. (paper submitted
for publ ication)

3. Beida, G. E., Measurement of the Viscoelastic and Related Mass-Physical

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

4. Bucker, H. P., J. A. Whitney, and D. L. Keir, Use of Stoneley Waves to

Determine the Shear Velocities in Ocean Sediments, Journal of the
Acoustical Society of America, v. 36, no. 5, 1964, pp 1595-1591.

5. Bucker, H. P., J. A. Whitney, G. S. Yee and R. R. Gardner, Reflection

of Low-Frequency Sonar Signals from a Smooth Ocean Bottom, Journal
of the Acoustical Society of America, v. 37, no. 6, 1965, pp 1037-
1051.

6. Cepek, R. J., Acoustical and Mass-Physical Properties of Deep Ocean

Recent Marine Sediments, M. S. Thesis, Naval Postgraduate School,
1972, 83p.

7. Cohen, S. R. , Measurement of the Viscoelastic Properties of Water

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

8. Ferry, J. D. , Viscoelastic Properties of Polymers, Wiley and Sons, Inc.

1970, 617p.

9. Gallagher, J. J. and V. A. Nacci , Investigations of Sediment Properties

in Sonar Bottom Reflectivity Studies, Underwater Sound Laboratory
Report No. 944, 1968.

10. Hamilton, E. L. , H. P. Bucker, D. L. Keir, and J. A. Whitney, Veloci-

ties of Compressional and Shear Waves in Marine Sediments Determined
In Situ from a Research Submersible, Journal of Geophysical Research,
v. 75, no. 20, 1970, pp 4039-4049.

11. Hamilton, E. L., Sound Velocity, Elasticity and Related Properties of

Marine Sediments, North Pacific, Part II; Elasticity and Elastic
Constants, Naval Undersea Research and Development Center Technical
Report No. 144, 1969.

79

12. Hutchins, J. R. , Investigations of the Viscoelastic Properties of a

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

13. Lasswell, J. B., A Comparison of Two Methods for Measuring Rigidity

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

14. Mason, W. P., Measurements of the Viscosity and Shear Elasticity of

Liquids by Means of a Torsionally Vibrating Crystal, Transactions
of the A. S. M. E., May 1947, pp 359-370.

15. McSkimin, H. J., Measurements of Dynamic Shear Viscosity and Stiffness

of Viscous Liquids by Means of Traveling Torsional Waves, The Jour-
nal of the Acoustical Society of America, v. 24", no. 4, 1952, pp 355-
365.

16. Morgan, J. H., II, Design of an Instrument to Measure the Shear Modulus

of Soft Sediments, M. S. Thesis, Naval Postgraduate School, 1972, 42p.

17. Walsh, W. F. , Jr., The Use of Surface Wave Technique for Verification

of Dynamic Rigidity Measurements in a Kaolinite-Water Artificial
Sediment, M. S. Thesis, Naval Postgraduate School, 1971, 42p.

18. White, J. E., Seismic Waves: Radiation, Transmission, and Attenuation,

McGraw-Hill Book Co. , 1965, pp 302.

80

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Naval Postgraduate School
Monterey, California 93940

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Department of Oceanography

Naval Postgraduate School
Monterey, California 93940

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Texas A&M University

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BEFORE COMPLETING FORM

1. REPORT NUMBER

2. GOVT ACCESSION NO.

3. RECIPIENT'S CATALOG NUMBER

4. TITLE (and Subtitle)

Measurement of Viscoelastic Properties
of Some Recent Marine Sediments by a
Torsi onally Oscillating Cylinder Method

5. TYPE OF REPORT & PERIOD COVERED

Master's Thesis :
September 1973

6. PERFORMING ORG. REPORT NUMBER

7. AUTHORfaj

Steven Barker Kramer

6. CONTRACT OR GRANT NUMBERfs)

S. PERFORMING ORGANIZATION NAME AND ADDRESS

Naval Postgraduate School
Monterey, California 93940

10. PROGRAM ELEMENT. PROJECT, TASK
AREA 4 WORK UNIT NUMBERS

II. CONTROLLING OFFICE NAME AND ADDRESS

Naval Postgraduate School
Monterey, California 93940

12. REPORT DATE

September 1973

13. NUMBER OF PAGES

84

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Naval Postgraduate School
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IB. SUPPLEMENTARY NOTES

19. KEY WORDS f Continue on reverse aide It necessary and Identify by block number)

Marine Sediments Shear Modulus Sediments
Properties Marine Sediments Dynamic Rigidity Sediments
Acoustic Reflection Coefficient

20. ABSTRACT (Continue on reverse side If necessary and Identity by block number)

A torsional ly oscillating cylindrical probe method, opera tinq in the
frequency range of 0.8 to 3.3 kHz was employed for measuring the viscoelastic
properties of 13 marine samples collected by Shipek grab from shallow water
regions of Monterey Bay, California. Other mass physical properties such as
wetdensity, porosity, sound speed, sand-silt-clay-gravel percentages, mean
grain size and sorting were also measured. Limited precision of impedance

L

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measurements permitted only the determination of the mechanical resistance
due to the probe contact with the sediment. The observed values for various
sediments ranged up to a value 65 times the lowest value. Correlations
between mechanical resistance and mass physical properties are studied by
graphical means with results indicating that water content of sediments is
a determining factor in the mechanical resistance of a sediment. A dependence
of mechanical resistance upon frequency is observed.

DD Form 1473 (BACK)

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84

Thesis
K8485 Kramer

1

6109

Measurement of viscoe-r^
lastic properties of some
recent marine sediments
by a torsional 1y oscillat-
ing cylinder method.

Thesis

K8485

c.l

146109

Kramer

Measurement of viscoe-
lastic properties of some
recent marine sediments
by a torsional ly oscillat-
ing cylinder method.

thesK8485

Measurement of viscoelastic properties o

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