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DYNAMIC PROPERTIES OF FROZEN
GRANULAR SOILS
By
John Chien-Chung Li
A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Civil Engineering
1979
ABSTRACT
DYNAMIC PROPERTIES OF FROZEN
GRANULAR SOILS
By
John Chien-Chung Li
The dynamic properties of frozen granular soils
under earthquake loading conditions was the subject of
this investigation. The materials studied included commer—
cially available Ottawa sand and small-sized pea gravel
which is categorized as very coarse sand in the Unified Soil
Classification System. These materials, with adequate
amounts of distilled water, were artificially frozen into
cylindrical samples. Strain controlled cyclic triaxial
tests were performed on most of the samples to evaluate
their dynamic properties. The test parameters included the
following: axial strain ranging from 2)c10'3% to 43(10-2%,
confining pressures from zero to 1.378 MPa, frequency of
0.05 to 5.0 cps, and temperatures from -l°C to -10°C. In
addition to these variables, samples of different ice
saturation and salt content were tested to estimate the
influence of these factors. Some stress controlled tests
‘were also performed to investigate the creep behavior of
frozen Ottawa sand samples under dynamic loading conditions.
John Chien-Chung Li
Test equipment included (1) an MTS electrohydraulic
closed-loop testing system which applies the load to the
sample, (2) a triaxial cell completely immersed in a low
temperature coolant for temperature control, (3) a refrig-
eration unit for control of the coolant temperature and
constant coolant circulation, and (4) measuring devices
including an LVDT and a load cell together with recording
devices such as a digital multimeter, an oscilloscope, a
strip-chart recorder, and a mini-computer.
Test results indicated that the dynamic Young's
modulus increases with increasing frequency, confining
pressure, and sand content but decreases with increasing
strain and temperature. The damping ratio decreases with
increasing frequency, sand content, and lower tempera-
tures. The influence of confining pressures and axial
strain on the damping ratio are less explicit for the
ranges of test parameters considered. The reduced ice
saturation and increased salt content made the sample
softer and Young's modulus lower. Dynamic creep test
results indicate that an increase in the stress level
and/or a reduction in the degree of ice saturation both
increased the susceptibility to creep failure. A com-
parison between this study and test results from other
investigators shows a greater probability of creep
failure under dynamic loading conditions.
DEDICATION
to my beloved parents
ii
ACKNOWLEDGMENTS
The writer wishes to express his appreciation to
his major professor, Dr. 0. B. Andersland, Professor of
Civil Engineering, for his guidance, assistance and numer-
ous helpful suggestions during the preparation of this
dissertation. Thanks also to the members of the writer's
doctoral committee: Dr. Gilbert Y. Baladi, Assistant
Professor of Civil Engineering; Dr. William C. Taylor,
Chairman and Professor of Civil Engineering; Dr. William
A. Bradley, Professor of Civil Engineering; and to Dr.
Gary L. Cloud, Associate Professor of Metallurgy, Mechanics,
and Material Science. The writer also owes his apprecia-
tion to his former major professor, Dr. Ted S. Vinson,
Associate Professor of Civil Engineering, Oregon State
University, for his guidance during the initial stage of
this research. The writer also wishes to express his
gratitude to his wife, Ling, for her patience, encourage-
ment and assistance during the past several years.
Thanks are also due to the National Science Founda-
tion, the Division of Engineering Research, and the Depart-
ment of Civil and Sanitary Engineering for their financial
assistance which made this research possible.
iii
TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
LIST OF SYMBOLS
Chapters
1. INTRODUCTION
2. LITERATURE REVIEW
2.1 .Mechanical Preperties of Frozen
2.2
2.3
2.4
Granular Soils .
2.1.1 Unfrozen Water Content
2.1.2 Creep Behavior
2.1.3 Shear Strength
2.1.4 Cohesion
2.1.5 Saline Content
Fundamentals of Cyclic Stress and
Strain
2.2.1 Cyclic Loading
2.2.2 Hysteresis Loop
2.2.3 Energy Consideration
2.2.4 Cyclic Triaxial Test
Dynamic Properties of Unfrozen Soils
2. 3.1 Hardin and Drnevich' 8 Study
2.3.2 Seed and Idriss' Study
Dynamic Properties of Frozen Soils .
2.4.1 Dynamic Elastic Properties of
Frozen Soils
2.4.2 Damping Property of Frozen Soils
AND DATA REDUCTION
MATERIALS, SAMPLE PREPARATION, TEST PARAMETERS,
3.1 Materials Studied.
3. 2
Sample Preparation .
3.2.1 Low Mineral Content Samples
3. 2. 2 High Mineral Content Samples
3.2.3 Under-Saturated Samples
3.2.4 Saline Samples
iv
Page
vii
viii
XV
14
18
21
37
37
38
Page
Sample Installation in Triaxial Cell . . 41
Test Parameters . , , 42
3.4.1 Magnitude of Test Parameters
3. 4. 2 Application Sequence of Test
Parameters
3.5 Dynamic Creep Test . . . . . . 45
3y6 Data Reduction and Processing . . . . 45
um
J-‘UJ
SAMPLE DATA AND EXPERIMENTAL RESULTS . . . 55
4.1 Sample Data . . . . . 56
4.2 Stress- Strain Behavior and Test
Parameter Effects . . . . . . 56
Axial Strain Effect
Confining Strain Effect
Temperature Effect
Frequency Effect
Mineral Content Effect
Ice Saturation Effect
Saline Content Effect
y Absorbing Behavior and Test
eter Effects . . . . . . 61
Axial Strain Effect
Confining Pressure Effect
Temperature Effect
Frequency Effect
Mineral Content Effect
Ice Saturation Effect
Saline Content Effect
4.4 Creep Behavior of Frozen Sand Samples
Under Cyclic Loading Conditions . . . 65
4.3
00 NO‘U-L‘WNH
935‘
mâ€.......
B
b-bbkb-P-F’Ut’ibbbF-bF-P
wwwwwwwfl (D NNNNNNN
\lO‘U‘I-L‘WNH
DISCUSSION . . . . . . . . . . . . 130
.1 Mineral Volume Fraction and Dynamic
Behavior of Granular Soils . . . 130
Ice Saturation and Dynamic Behavior of
Frozen Sand . . . 132
Saline Content and Dynamic Behavior of
Frozen Sand . . . . . . 133
Tension Failure and. Effects on
Experimental Results . . . 135
Application Sequence of Test Parameters
and EffEct on Experimental Results . . 136
Comparison of Experimental Results with
Previous Data . . . 137
Dynamic Creep Behavior of Frozen Sand . 141
MUIU'IU'IUIU'lU!
“0“!!wa
6. SUMMARY AND CONCLUSIONS
REFERENCES
APPENDICES
A. Test Equipment and Recording Devices
B. Dynamic Young's Modulus for Frozen Sand
Samples
C. Damping Ratio for Frozen Sand Samples
D. Dynamic Young's Modulus for Frozen Gravel
Samples
E. Damping Ratio for Frozen Gravel Samples
F. Data for Under-Saturated Frozen Sand Samples
G. Data for Saline Frozen Sand Samples
vi
Page
164
170
177
178
193
221
249
277
305
312
Table
3.
NHO‘U’l-L‘UDNH
1
LIST OF TABLES
Mineral Content for Frozen Sand and Frozen
Gravel Samples
Application Sequence of Test Parameters for
Frozen Granular Soils
Frozen Sand Samples
Under-Saturated Frozen Sand Samples
Saline Frozen Sand Samples
Frozen Sand Samples Used in the Creep Tests
Frozen Gravel Samples
Experimental Data of Creep Tests
Testing Sequence for 81-102 Through SI-106
Values of Pseudo-Instantaneous Strains and
Creep Strain Rates
Comparison of Creep Strength Under Static
and Dynamic Testing Conditions
vii
Page
53
54
66
67
68
69
70
123
158
159
162
Figure
2.1
LIST OF FIGURES
Constant-stress creep test (after
Andersland, et a1., 1978)
Frozen frictional soils (after Ladanyi,
1972) .
(a) Straight- -line approximation of the
failure envelopes
(b) Dependence of creep strength on
confining pressure
Volume concentration of Ottawa sand and
peak strength (after Goughnour, and
Andersland, 1968) . . . .
Volume of water freezing out as a function
of temperature (after Yong, et. a1., 1978)
Cyclic stress-strain plot of elastic be-
havior (after Sandor, 1972)
Development of the hysteresis loop (after
Sandor, 1972) . . . . .
Hysteresis loops obtained in cyclic triaxial
tests on frozen soils . . . . .
Stress condition during a cyclic triaxial
test . .
Shear moduli of sands at relative density of
about 75% (after Seed and Idriss, 1970) .
Damping ratio for sands (after Seed and Idriss,
1970)
Effect of void ratio on complex shear modulus
(after Stevens, 1973) .
Effect of ice saturation on complex shear
modulus (after Stevens, 1973)
Effect of temperature on complex moduli,
E* or G*; frequengy = 1 KHz, dynamic
stress = 0.7 KN/m . . . . .
viii
Page
25
26
27
28
29
29
29
30
31
32
33
33
34
Figure Page
2.12 Effect of frequency on complex shear
modulus (after Stevens, 1973) . . . . . 35
2.13 Effect of dynamic stress on complex
shear modulus (after Stevens, 1973) . . . 35
2.14 Effect of temperature of damping property
(after Stevens, 1973) . . . . . . . 36
2.15 Effect of frequency on damping property
(after Stevens, 1973) . . . 36
3.1 Teflon molds and a set of base and cap
units . . . . . . . . . . . . . 49
3.2 Samples being frozen in a freezer box . . . 50
3.3 A fresh sample just extruded from mold . . 50
3.4 A typical strip chart record . . . . . . 51
3.5 Computation of damping ratio . . . . . . 52
4.1 Dynamic Young's modulus vs. confining pres-
sure for frozen sand samples of 20% sand
content . . . . . . . . . . . . 7].
4.2 Dynamic Young's modulus vs. confining pres-
sure for frozen sand samples of 45% sand
content . . . . . . . . . . . . 72
4.3 Dynamic Young's modulus vs. confining pres-
sure for frozen sand samples of 65% sand
content . . . . . . . . . . . . 73
4.4 Dynamic Yount's modulus vs. confining pres-
sure for frozen gravel samples of 24%
gravel content . . . . . . . . . . 74
4.5 Dynamic young's modulus vs. confining pres—
sure for frozen gravel samples of 42%
gravel content . . . . . . . . . 75
4.6 Dynamic Young's modulus vs. confining pres-
sure for frozen gravel samples of 59%
gravel content . . . . . . . . . 76
ix
Figure
4.7
4119
4.20
Dynamic Young's modulus vs. temperature
for frozen sand samples of 20% sand
content . .
Dynamic Young's modulus vs. temperature
for frozen sand samples of 45% sand
content . . . . .
Dynamic Young's modulus vs. temperature
for frozen sand samples of 65% sand
content . . . . .
Dynamic Young's modulus vs. temperature
for frozen gravel samples of 24% gravel
content . . . . . . . . .
Dynamic Young's modulus vs. temperature for
frozen gravel samples of 42% gravel con-
tent . . . . . . . . . .
Dynamic Young's modulus vs. temperature for
frozen gravel samples of 59% gravel con-
tent . . . . . . . . . .
Dynamic Young's modulus vs. frequency for
frozen sand samples of 20% sand content .
Dynamic Young's modulus vs. frequency for
frozen sand samples of 45% sand content -
Dynamic Young's modulus vs. frequency for
frozen sand samples of 65% sand content .
Dynamic Young's modulus vs. frequency for
frozen gravel samples of 24% gravel
content . . . .
Dynamic Young's modulus vs. frequency for
frozen gravel samples of 42% gravel
content . . . .
Dynamic Young's modulus vs. frequency for
frozen gravel samples of 59% gravel
content . . . . .
Dynamic Young's modulus vs. sand content of
frozen sand samples at 0.345 MPa confining
pressure
Dynamic young's modulus vs. sand content for
frozen sand samples at 0.3 cps frequency
X
Page
77
78
79
80
81
82
83
84
85
86
87
88
89
90
Figure Page
4.21 Dynamic Young's modulus vs. gravel content
for frozen gravel samples at 0. 345 MPa
confining pressure . . . . 91
4.22 Dynamic Young's modulus vs. gravel content
for frozen gravel samples at 0. 3 cps
frequency . . . . . . . . . . . 92
4.23 Influence of degree of ice saturation on
dynamic Young s modulus for frozen Ottawa
sand at 0.345 MPa confining pressure . . 93
4.24 Influence of degree of ice saturation on
dynamic Young s modulus for frozen Ottawa
sand at 0.3 cps frequency . . . . . . 94
4.25 Influence of salt content on dynamic Young's
modulus for frozen Ottawa sand at 0. 345
MPa confining pressure . . . - 95
4.26 Influence of salt content on dynamic Young's
modulus for frozen Ottawa sand at 0. 3 cps
frequency . . . . . . . . . . . 96
4.27 Damping ratio vs. confining pressure for
frozen sand samples of 20% sand content . 97
4.28 Damping ratio vs. confining pressure for
frozen sand samples of 45% sand content . 98
4.29 Damping ratio vs. confining pressure for
frozen sand samples of 65% sand content , 99
4.30 Damping ratio vs. confining pressure for
frozen gravel samples of 24% gravel content 100
4.31 Damping ratio vs. confining pressure for
frozen gravel samples of 42% gravel content 101
4.32 Damping ratio vs. confining pressure for
frozen gravel samples of 59% gravel content 102
4.33 Damping ratio vs. temperature for frozen
sand samples of 20% sand content . . . 103
4.34 Damping ratio vs. temperature for frozen
sand samples of 45% sand content . . . 104
4.35 Damping ratio vs. temperature for frozen
sand samples of 65% sand content . . . 105
xi
Figure Page
4.36 Damping ratio vs. temperature for frozen
gravel samples of 24% gravel content . . . 106
4.37 Damping ratio vs. temperature for frozen
gravel samples of 42% gravel cOntent . . . 107
4.38 Damping ratio vs. temperature for frozen
gravel samples of 59% gravel content . . . 108
4.39 Damping ratio vs. frequency for frozen sand
samples of 20% sand content . . . . . . 109
4.40 Damping ratio vs. frequency for frozen sand
samples of 45% sand content . . . . . . 110
4.41 Damping ratio vs. frequency for frozen sand
samples of 65% sand content . . . . . . 111
4.42 Damping ratio vs. frequency for frozen gravel
samples of 24% gravel content . . . . . 112
4.43 Damping ratio vs. frequency for frozen gravel
samples of 42% gravel content . . . . . 113
4.44 Damping ratio vs. frequency for frozen gravel
samples of 59% gravel content . . . . . 114
4.45 Damping ratio vs. sand content for frozen sand
samples at 0.345 MPa confining pressure . . 115
4.46 Damping ratio vs. sand content for frozen sand
samples at 0.3 cps frequency . . . . . 116
4.47 Damping ratio vs. gravel content for frozen
gravel samples at 0.345 MPa confining pres-
sure . . . . . . . . . . . . . 117
4.48 Damping ratio vs. gravel content for frozen
gravel samples at 0.3 cps frequency . . . 118
4.49 Influence of degree of ice saturation on
damping ratio for frozen Ottawa sand at
0.3 cps frequency . . . . . . . . . 119
4.50 Influence of degree of ice saturation on damping
ratio for frozen Ottawa sand at 0.345 MPa
confining pressure . . . . . . . . 120
4.51 Influence of salt content on damping ratio for
frozen Ottawa sand at 0-3 cps frequency . 121
xii
Figure Page
4.52 Influence of salt content of damping ratio
of frozen Ottawa sand at 0.345 MPa .
confining pressure . . . . . . . . . 122
4.53 Dynamic creep curve of samples CSI-9 and CST-4 126
4.54 Dynamic creep curve of samples CSI-2, CSI-5,
and CSI—7 . . . . . . . . . . . . 127
4.55 Dynamic creep curve of samples CSI-6 and CSI-3 128
4.56 Number of cycles needed for frozen sand
samples to deform from 0.15% strain to 0. 50%
strain in a dynamic creep test - - . - 129
5.1 Comparison of test results saturated and par~
tially saturated frozen sand samples . . . 147
5.2 Influence of degree of ice saturation on dyna-
mic Young's modulus at -4°C expressed in
terms of corresponding temperatures . . . 148
5.3 Comparison of salt content effect and % volume
of water frozen at -10°C on the dynamic
Young's modulus . . . . . . . . . . 149
5.4 Comparison of test results for fresh water and
saline frozen sand samples . . . . . . 150
5.5 Influence of saline content to dynamic Young's
‘modulus at -10°C expressed in terms of cor-
responding temperature . . . . . . . 151
5.6 ‘Bent hysteresis loops . . . . . . . 152
(a) An oscilloscope picture
(b) Definition of terms
5.7 Influence of test frequency on D and Ed for
frozen sand samples tested at -4°C 153
5.8 Influence of test sequence on D and Ed for
frozen sand samples tested at -1°C 154
5.9 Dynamic properties of several frozen soils
(a) Longitudinal velocity vs. temperature
(b) Damping ratio vs. temperature . , , , 155
5.10 Dynamic properties of several frozen soils at
°C 156
(a) Longitudinal wave velocity vs. loading.
frequency
xiii
Figure Page
(b) Damping ratio vs. loading frequency
5.11 Dynamic Young's modulus and damping ratio of
frozen soil vs. confining pressure , , , 157
5.12 Log-log plot of 5(1) and é(c) vs. applied
stress (ice saturation = 92%) 160
5.13 Log-log plot of 8(1) and é(c) vs. applied
stress (ice saturation = 40%) . . 161
5.14 Comparison of creep strength under static
and dynamic testing conditions . , , , , 163
A.1 Cyclic triaxial test system . . . . . . 186
A.2 Triaxial cell inside the cold bath . . . . 187
A.3 Schematic of anti-tilt device . . . . . . 188
A.4 Sample with anti-tilt device installed . . . 188
A.5 Hydraulic pump . . . . . . . . . . . 189
A.6 Actuator and cold bath . . . . . . . . 189
A.7 Storage oscilloscope and MTS controller , . 190
A.8 Electrohydraulic closed-loop test system , , 190
A.9 Schematic of cold bath . . . . . . . . 191
A.10 Refrigeration and circulation unit . . . . 191
A.1l Strip-chart recorder . . . . . . . . . 192
A.12 Mini-computer system . . . . . . . . . 192
xiv
LIST OF SYMBOLS
area of a hysteresis loop
area of the work capacity triangle
cohesion intercept
effective cohesion
damping ratio
maximum damping ratio
average diameter of soil particles
dynamic Young's modulus
void ratio
frequency
shear modulus
maximum shear modulus
acceleration of gravity
the total ion content of ion 1 in the soils
c cot ¢
damping parameter
coefficient of lateral stress at rest
dynamic strength parameter
creep parameter
molar latent heat of fusion
equivalent of the ion "1"
XV
PIC/30350
('1'0
molecular weight of solvent
number of loading cycles
_ 1 + sin¢
flow value - m
creep parameter
number of moles of discrete particles per
equivalent
gas constant
specific surface area, m2/g
degree of saturation
temperature, °C
freezing point of pure solution
time
loading duration to failure
longitudinal wave velocity
unfrozen water content
unit weight of a material, kN/m3
shear strain
phase lag angle
engineering strain
proof strain for creep equation
'maximum strain
peak strain
strain rate
creep strain rate
xvi
('7).
strain rate parameter for creep equation
negative temperature, °C
freezing point depression shift, °C
density of a material, kg/m3
density of soil particles, kg/m3
uniaxial normal stress
proof stress for creep equation
deviator stress
creep failure stress
peak stress
principal normal stresses
effective mean principal stresses
effective principal normal stress
effective principal normal stresses
shear strength
maximum.shear strength
angle of internal friction
effective angle of internal friction
angular frequency
xvii
CHAPTER 1. INTRODUCTION
In recent years, the discovery and exploitation of
natural resources in the cold regions north of the 60th
parallel has called attention to places like Alaska,
northern Canada, Siberia, etc. Many large engineering
projects have been completed and more are planned in
these areas. Thus, knowledge of the mechanical properties
of frozen ground has become essential for engineering
purposes. In addition, some of these cold regions are
located in the world's most active seismic zones. This
makes an understanding of the ground surface motions,
caused by earthquakes, important for design of massive
and expensive structures in these areas.
It is now generally accepted that ground surface
motions, which occur during an earthquake, are influenced
to a large extent by the dynamic properties of the under-
lying soil deposit (Idriss and Seed, 1968; Seed and Idriss,
1969). The soil properties used in analytical techniques
presently available for prediction of ground surface
motions (Streeter, wylie and Richart, 1974; Schnabel,
Lysmer and Seed, 1972) include the dynamic shear modulus
and damping ratio. The dynamic shear modulus represents
an elastic property and the damping ratio reflects the
energy absorbing property of the soil. These dynamic
properties of frozen soils have been evaluated with
various vibratory test devices at very low strains, up to
10-3%, and relatively high frequencies by several inves-
tigators (Kaplar, 1969; Nakano et a1., 1972; Nakano and
Arnold, 1973; Stevens, 1973 and 1975). A review of their
research will be provided in Chapter 2. However, at
greater strains and lower frequencies, those associated
‘with moderate to strong earthquake motions, experimental
data has not been available because vibratory testing
techniques were not feasible.
Several previous investigations of dynamic
properties of unfrozen soils (SW-AJA, 1972) have suggested
the use of three kinds of cyclic load tests to simulate
the greater strain amplitude and lower frequency ranges
chacteristics of seismic loading conditions. These
testing techniques included (1) the cyclic triaxial test
(Seed and Lee, 1969; Schroeder and Schuster, 1968); (2)
the cyclic simple shear test (Peacock and Seed, 1968;
Converse, 1961; Thiers and Seed, 1968; Sowers, 1963); and
(3) the cyclic torsional shear test (Hardin and Drnevich,
1972a).
Each of the above tests were discussed briefly by
SW-AJA (1972) and in detail by several other references.
The cyclic triaxial test was chosen for this research
project for the following reasons:
(1) equipment availability from an earlier
project;
(2) easy sample preparation;
(3) convenient and more accurate tempera-
ture control; and
(4) more information available about the
testing devices and techniques.
The cyclic triaxial test is a repeated loading
test which can be used to determine the dynamic Young's
modulus and damping ratio of the soil specimen tested.
A review of this test will be presented in Chapter 2 and
the project equipment will be described in Appendix A.
Once the dynamic Young's modulus and damping ratio
are determined, they can be converted into other dynamic
elastic properties and energy absorbing properties with
the help of conversion equations compiled by Vinson (1978).
These conversions require representative values of
Poisson's ratio which for the one-size ice saturated
Ottawa sand, falls in the range of 0.24 to 0.38 with an
average value close to 0.30 (Stevens, 1975).
As part of a larger study of the dynamic proper-
ties of frozen soils under simulated earthquake loading
conditions, work on artificially frozen clays, silts and
ice has been completed by Chaichanavong (1976) and Czaj-
kowski (1977)-
The current effort covers the evaluation of the
dynamic properties of frozen granular materials under
cyclic triaxial loading conditions. The granular materials
tested in this study included a one-sized Ottawa sand and
a uniform pea-gravel. A detailed description of these
materials is presented in Chapter 3.
Parameters which may influence the dynamic proper-
ties of frozen granular soils included axial strain,
loading frequency, temperature, confining pressure, saline
content, degree of ice saturation, and mineral volume
fraction. The experimental data are presented in Chapter
4 and the discussion of the influence these parameters
have on the dynamic properties is given in Chapter 5.
Also, the problem of creep behavior under cyclic
loads was considered in the later part of this research.
A preliminary study was launched and the test results and
a discussion have been included in Chapter 4 and Chapter
5, respectively.
CHAPTER 2. LITERATURE REVIEW
This chapter reviews mechanical properties of
frozen granular soils, fundamentals of the cyclic triaxial
test, earlier studies on the dynamic properties of
unfrozen soils, and previous investigations on the dynamic
properties of frozen soils based on vibratory testing
techniques. This background information provides a frame-
work for presenting the current study on the dynamic prop-
erties of frozen granular soils under cyclic triaxial
loading conditions.
2.1. Mechanical Properties of
Frozen Granular Soils
2.1.1. Unfrozen Water Content
Frozen soils can be considered as a multi-phased
system composed of soil particles, polycrystalline ice,
unfrozen water, and entrapped vapor and/or air. Unfrozen
water content (wt), the major factor affecting the mechan-
ical properties of frozen fine-grained soils is believed
to be a function of the specific surface area of the soil.
Anderson et a1. (1973) introduced an expression corre-
lating unfrozen water content to specific surface area:
1nwï¬ = 0.2618 + 0.55191nS - 1.4493'0-2541ne (2.1)
5
where wt = unfrozen water content (gH20/g soil)
S = specific surface area (m2/g soil)
_ 6
a")
s s
6 = negative temperature (°C) = 273 - T(°K)
and d8 = average soil particle diameter (m)
08 = density of soil particles (gm/m3)
Thus, for frozen granular soils, unfrozen water content
would be negligible due to its relatively larger particle
size and smaller specific surface area. Scott (1969)
made this conclusion in an earlier study.
2.1.2. Creep Behavior
Creep is the time-dependent deformation of
materials which occurs under constant stress and temper-
ature. It is believed that the pressure developed between
soil particles and between soil particles and ice in the
vicinity of contact points causes melting of the ice.
Differences in water surface tensions move the unfrozen
water to regions of lower stress,where it refreezes. The
process of ice melting and water migration is accompanied
by a breakdown of structural bonds, by displacement of
particles, and by deformation of pore ice. At the same
tflme, there is a regrouping of particles, a recrystalli-
zation of the pore ice, and re-establishment of bonds.
As the process continues, it leads to a time dependent
deformation (creep) of frozen soils.
A typical creep curve for frozen soil and the
strain rates corresponding to each point on the curve
are shown in Figures 2.1a and 2.1b. Three stages of
creep are usually observed in the creep process. The
creep rate decreases in the first stage, remains constant
in the second stage and increases in the third stage.
These three stages are commonly designated as primary,
secondary, and tertiary creep. For relatively low loads,
the second and the third stages may not develop. Once
creep enters the second stage, a creep failure will occur
for sure. Creep failure is usually defined as the point
where creep rates increase or at the beginning of tertiary
creep. The stress at the point of creep failure is usually
defined as the creep strength or long-term strength of the
frozen soil. For secondary creep, the strength after a
long time interval at a constant temperature can be
expressed as
of = o (. ) (2.2)
where of = creep failure stress,
0c = proof stress,
cf = creep failure strain,
E = arbitrarily selected creep rate,
tf = time to failure,
n = exponent in the creep equation.
The stress-strain-time relationship of creep behavior can
be expressed as
e = %+ ekooflgk + $531)“ (2.3)
c
where s = total strain,
0 = uniaxial normal stress,
E = Young's modulus,
8k = arbitrary small strain,
0k = proof stress in the stress-strain equation
and other notations are as previously defined. For a
detailed discussion of these power relationships, refer
to Ladanyi (1972) and Andersland, et a1. (1978).
2.1.3. Shear Strength
Shear strength of soil has been traditionally
defined by the Mohr-Coulomb failure theory as the sum of
a cohesion component and a frictional component. The Mohr-
Coulomb theory has also been applied to define the shear
strength of frozen soils (Vyalov, 1959). A straight line
approximation of the Coulomb-Mohr envelopes has been intro-
duced by Ladanyi (1972) for the expected range of normal
pressures. Such an approximation is shown in Figure 2.2a,
within which the shear strength is defined by:
T = c(t,6) + otan¢ (2.4)
or T = [H(t,e)+o]tan¢ (2.5)
where H(t,0) = c(t,6)cot¢ (2.6)
t = load duration to failure,
9 = negative temperature (°C) = 273 — T(°k),
c = cohesion intercept,
o = normal stress,
¢ = angle of internal friction,
and C(t,9) = W (2.7)
The flow value, N¢, is defined by
_ 1 + sin
N¢ - 1———:—-"'1_ 31nd) (2.8)
and Ofu is the creep failure stress for uniaxial compression
conditions.
Alternatively, in terms of principal stresses,
the stress difference at failure
10
(c1 - o3)f = ofu(t,0) + 03(N¢ — l) (2.9)
For practical interest, the angle of internal friction
depends little on time and temperature and the effects
appear to be primarily concentrated in the value of ofu'
A set of Mohr-Coulomb envelopes corresponding to Equation
2.2 for a constant temperature and different times to
failure are shown in Figure 2.2a. Alternatively, a set
of creep strength curves based on Equation 2.9 for
constant temperature and different confining pressures are
shown in Figure 2.2b. It is interesting to note that for
an infinitely slow creep rate, a finite value for a purely
frictional threshold strength agrees well with experimental
values of unfrozen granular soils. The deviator stress
at failure increases with an increase in confining
pressure. This behavior is related to the higher fric-
tional and dilatancy effects at higher confining pressures
for the granular soils.
Goughnour and Andersland (1968) showed that a
bilinear relationship exists between sand volume concen-
tration and peak strength as shown in Figure 2.3. Pure
ice samples have no long-term strength; i.e. they flow
under very small loads. The addition of dispersed sand
particles in the sand-ice structure increases the strength
of the sample. The strength increase is proportional to
11
the volume concentration of sand in the sample. When a
critical concentration of sand, about 42%, is reached a
rapid increase in shear strength was observed. It is
believed that at this point, sand particles begin to contact
each other, and friction and dilatancy starts to contri-
bute to the strength of the frozen sample.
Thus, the strength of frozen granular soils can be
concluded as a function of temperature, strain rate,
mineral concentration, confining pressure, and the shape
or angularity of soil particles.
2.1.4. Cohesion
Dry sand has no unconfined shear strength. When
wet sand is subjected to subfreezing temperature and
frozen, a substantial increase in unconfined strength will
be observed. The increase in strength due to the cementing
action of the ice matrix is called cohesion.
In general, cohesion in frozen soils may result
from three causes (Vyalov, 1962):
(1) Intermolecular cohesion due to attrac-
tion between particles, i.e., electro-
static and electromagnetic attractions.
(2) Structural cohesion resulting from geo-
logical origin of soil or that devel-
oped during the weathering process of
soil, e.g., geological texture, chemical
bonding, chemical cementation, etc.
12
(3) Cohesion due to cementing action of
the ice matrix (ice cementation).
For frozen granular soils, it is reasonable to
assume that the first two are negligible due to the rela-
tively large particle sizes. Therefore only the cohesion
due to ice cementation is important for frozen granular
soils.
2.1.5. Saline Content
The salinity found in some natural polar soils
CTedrow, 1966; Brown, 1969) introduces the need for an
understanding of the effect of salt content on frozen soil
behavior. Yong, et a1. (1973) proposed use of the theory
of pure solutions to describe the properties of pore water
containing salts. The presence of sodium chloride in a
freezing solution reduces the temperature at which freezing
is initiated, but not all of the water will freeze at that
temperature. Exclusion of the dissolved solute by the
growing ice crystal increases the concentration in the
surrounding water, thus freezing will not continue unless
the temperature is further reduced. Banin and Anderson
(1974), using the same theory, developed expressions for
a freezing point depression shift 6' applicable to many
dissolved species. Their expressions for 9' include:
l3
(1) for a wide range of ion concentrations
RT 2
u _ O b
9 ‘ ' 1.f lnl(1000 emu +1.3] (2'8)
and (2) for dilute solutions only
6 = 1000 a e/wu - ae/wu (2.9)
— freezing point depression shift (°K),
unfrozen water content (gm per gm),
2
RTo /Lf-b,
gas constant (cal. per deg. mole),
freezing point of pure solvent (°K),
molar latent heat of fusion (cal. per mole),
6
10 lene’
molecular weight of the solvent,
number of moles of descrete particles per
equivalent,
n
igfgi/Mi) .
the total ion content of â€1" ion in the solids
(mg per gram) .
the equivalent weight of the ion "i" (mg per
milliequivalent), and
1000a'.
14
The relationship between volume of water freezing
out as a percentage of the total volume of solution and
temperature for various concentrations of salinity is
summarized in Figure 2.4. Since the theory of pure
solutions was employed to develop the expressions, the
effect of the diffuse double layer on the soil particle
surface has been neglected. This is more acceptable for
frozen granular soils, due to their relatively large
particle sizes and low specific surface area.
2.2. Fundamentals of Cyclic
StreSs and Strain
2.2.1. Cyclic Loading
Cyclic loading means periodic and uniformly
repeated loading conditions. Sinusoidal, triangular or
square functions are normally used to control the appli-
cation of either force, stress, displacement or strain.
The control of one of the above variables is repeated in
such a way that the peaks are constant from cycle to
cycle. Variables other than the controlled one are
allowed to vary according to the character of the material
being tested. Stress control and strain control are com-
monly referred to in publications, but force control or
displacement control is easier to apply in practical
tests .
15
2.2.2. Hysteresis Loop
The cyclically changing stress and strain (or
force and displacement) at every instant of time may be
plotted on stress versus strain coordinates. Figure 2.5a
shows such a plot of an idealized linearly elastic material.
However, a â€hysteresis" loop, shown in Figure 2.5b, is
more likely to be observed due to the phase lag between
stress and strain caused by the inherent plastic behavior
of commonly tested materials. For frozen and unfrozen
soils tested under cyclic triaxial loading conditions,
which means greater strain and lower frequency, sharp tips
may disappear and blunted loops may appear (Figure 2.5c).
These loops are usually obtained when the cycling is
slow, the temperature is close to the melting point of
the material, or the stress amplitude is high enough to
cause creep. In this case, the material has time to relax
the peak stress toward zero stress before the load
reversal occurs. Immediately after the reversal, the
stress is still high enough to cause a little further
relaxation, which distorts the unloading path. The total
plastic strain per cycle has to include creep strains,
since relaxation in the high-stress region increases the
loop width (Sandor, 1972).
16
2.2.3. Energy Consideration
Assume that the hysteresis loops shown in Figure
2.5c are obtained in a test with a loading frequency
f = w/2n where w is the angular frequency and 6 is the
phase lag angle between stress and strain. The work done,
or reciprocally, the energy dissipated is given by the
integral of o(t)de over the stress cycle, that is
AB = [Zn/m
0 cos wt-e w sin(mt - 6)dt
o o 0
Integration gives
AE = we 0 sin6
o o
where so is the peak strain and Go is the peak stress.
Usually, the phase lag angle 6 is small, hence -
sin 6 2 tan 6 2 6, so that the energy dissipation is
proportional to 6 (Kennedy, 1962).
2.2.4. Cyclic Triaxial Test
Strain controlled cyclic triaxial testing is the
most popular and widely used testing technique to evaluate
dynamic stress-strain characteristics of soils (Silver and
Park, 1975). In this test, longitudinal compression and
extension stresses are applied to a solid cylindrical-
shaped sample (Figure 2.6a), in addition to the all-around
17
confining pressure. The resulting stress-strain character-
istics are measured directly. The major principle stress
direction rotates 90° in each stress cycle. Mohr's stress
circle representation, shown in Figure 2.6b, may not
exactly represent the field case. In the field, the major
principal stress is normally perpendicular to ground
surface but rotates through a small angle as cyclic shear
stresses (under earthquake loads) are applied to the soil.
Before the deviator stress is applied, the isotropic
confining pressure differs from the actual anisotropical
situation in the field.
Still another condition which prevents correct field
simulation, is the fact that the laboratory triaxial
specimen undergoes some deformation in each of the three
principal stress directions. Presumably, the soils in
the field under earthquake motions are deformed primarily
in simple shear, or unidirectionally.
Although this test has a number of shortcomings,
it does have the advantage of being adaptable to the prepar—
ation and testing with ease of all types of disturbed and
undisturbed soils. Also, precise control over strains
and stresses and the ready availability and familiarity
of numerous laboratories with the equipment are strong
advantages for this test.
18
2.3. Dynamic Properties of Unfrozen Soils
2.3.1. Hardin and Drnevich's Study
A comprehensive study of the factors affecting
the shear moduli and damping ratios of unfrozen soils was
undertaken by Hardin and Drnevich (1972, a and b). They
concluded that the primary factors affecting moduli and
damping ratios included:
strain amplitude, 7;
effective mean principal stress,
o'm = l/3(o'1 + 0'2 + 0'3);
void ratio, e;
number of loading cycles, N; and .
degree of saturation (for cohesive soils), S.
Less important factors included:
octahedral shear stress;
overconsolidation ratio, OCR;
effective stress strength parameters, c
and ¢'; and
time effects.
They presented relationships for computing the maximum
shear modulus (at essentially zero strain) and the variation
of modulus values with strain for all soils. The expres-
sion for evaluating the maximum shear modulus for angular
sand particles is,
2
cm1x = 14750 (2%? g e) (o'm)1/2 (2.10)
19
r
whe e Gmax
e is the void ratio, and
o'm is the mean principal effective stress in psf
is the maximum shear modulus in psf,
The modulus value, G, at a strain level, y, is
then evaluated as:
Gmax
her
w e max
max
11+ K6 2 1 - K6 2 1/2
Tmax = {(——2-——)o'vsin¢' + c'coso') - (_—2_—_)O'v) }
,
Ko = the coefficient of lateral stress at rest,
o'v = vertical effective stress, and
c', ¢' = static strength parameters in terms of effec-
tive stress.
Similar relationships were also presented for
evaluating the damping ratio, D, at a strain level, y,
thus
D ax'Y/Y
= m r
D 1 + Yer (2.12)
where Dmax is the maximum damping ratio corresponding to
very large strains. For clean sand, D
‘max (1n percent)
20
is evaluated by:
Dmax = K - 1.510g10N (2.13)
where K equals 33 for clean dry sand and 28 for saturated
clean sand, and N equals the number of stress cycles.
2.3.2. Seed and Idriss' Study
Seed and Idriss (1970) compiled results of previous
studies from which they concluded that the shear moduli
for sand is strongly influenced by confining pressure
(expressed in terms of o'm), strain amplitude, y, void
ratio e, and not so significantly influenced by variation
in grain size characteristics.
In general, the shear modulus for unfrozen sand
can be expressed by the equation:
1/2
G = 1000-K2(o'm) (2.13)
where K2 is a parameter introduced to reflect the influ-
ence of the various factors other than o'm. A typical
curve of K2 versus shear strain for sand is shown in
Figure 2.7, and a relationship for damping ratio of sand
to shear strain is shown in Figure 2.8. From design
curves similar to these and Equation 2.13 one can estimate
the dynamic properties of a given unfrozen sand with known
strain and stress conditions.
21
2.4. Dynamic Propgrties of Frozen Soils
The dynamic properties of frozen soils have been
studied by Kaplar (1969) and Stevens (1973) with the
resonent frequency method and Nakano and Froula (1973)
with the ultrasonic method. Stevens (1973) provided a
detailed discussion on the dynamic properties of frozen
soils, which will be summaried in the following paragraphs
with emphasis on frozen granular soils, the topic of the
current research.
2.4.1. Dynamic Elastic Properties
of Frozen Soils
The parameters which may influence the dynamic
elastic properties include stress and/or strain amplitudes,
frequency of loading, temperature, void ratio or water
content, and degree of ice saturation. Each parameter
will be reviewed.
Void Ratio Effect. The relationship between com-
plex shear modulus and void ratio at a temperature of
-9.4°C is summarized in Figure 2.9 for several frozen
soils with ice saturation greater than 90%. The stiffness
increases with decreasing void ratio and the modulus of
all frozen soils is greater than or equal to that of ice
(about 3.1 GN/mz). Granular soils generally have a higher
modulus. Each soil has a tendency to reach a peak modulus
22
as the void ratio approaches the minimum for that soil.
For finer soils the void ratio may increase beyond 1.0.
When the volume of pore ice becomes larger than the volume
of the soil solids, the modulus tends to approach that of
ice.
Ice Saturation Effect. The degree of saturation
strongly affects the shear modulus as shown in Figure 2.10.
However, there is a considerable difference in the rela-
tionship depending on soil type. For frozen granular
soils and ice saturation greater than 50% there is little
effect of ice saturation on modulus. At lower values of
ice saturation the modulus decreases significantly,
approaching that for dry unfrozen soil with no ice satur-
ation.
Temperature Effect. The temperature effect on
both Young's moduli and the shear moduli are summarized
in Figure 2.11 for both frozen and unfrozen soils. The
frozen soil moduli fall in the range of 100 to 2500 MN/mz,
and that of unfrozen soils in the range of 2.2 to 22 MN/mz.
Considering only the frozen soil, it is shown that the
modulus increases with decreasing temperature but tends
to level off at temperatures below -10°C. Temperature
has a greater effect on fine-grained soils as compared to the
23
coarse-grained soils. The modulus for frozen Ottawa sand
decreased only slightly in the range of -18°Ctx>-4°C.
Frequency Effect. The effect of frequency, from
1 to 1000 kHz, on the shear modulus is shown in Figure 2.12.
While the overall effect of frequency on stiffness is less
significant in the range considered, it is still apparent
that the shear modulus increases with increasing frequency.
The rate of increase is greatest in the range of 1 to 5
kHz. This suggests that a significant decrease in shear
modulus may result if a vibratory load were imposed at a
much lower frequency.
Dynamic Stress Effect. The decrease in complex
modulus with increasing dynamic stress is small, at least
up to a peak stress of 34.5 KN/mz, as shown in Figure 2.13.
The effect of stress is greatest at warmer temperatures
and lower frequencies. The shear modulus is almost indepen-
dent of stress level to 34.5 KN/m2 at a temperature of
-18°C. At about -4°C, a significant non-linearity with
increasing stress starts at about 7.0 KN/m2 with the
greatest rate of decrease at lower frequency loads.
2.4.2. Damping Property of Frozen Soils
Stevens (1973) expressed the damping property as a
tangent function of the stress-strain phase lag angle 6.
24
Effects of temperature and frequency on the values of tan
6 are summarized in the following paragraphs.
Temperature Effect. The influence of temperature
on tan 5 is shown in Figure 2.14. A definite trend is
difficult to define due to the random data points. In
general, the values of tan 6 do not change significantly
for a given soil from the unfrozen state to frozen state
as temperature decreases. Stevens suggested that the
mechanism causing damping of a stress wave may be different
for the two states and by chance, the tan 6 values are
close. It is interesting to observe that tan 6 values of
frozen Ottawa sand were slightly higher than that for the
unfrozen state.
Frequency Effect. The large effect of frequency
on tan 6 is shown in Figure 2.15. The values of tan 6
decrease as frequency increases, and this effect is more
significant for Ottawa sand than for the fine-grained silt.
This obvious trend indicates that damping in frozen soil
‘may resemble a viscous or dashpot type behavior suggesting
that the pore ice governs the damping of frozen soils.
25
‘I ————————————————————— c
I
I
I
.‘c‘ '
.5. a I
m
l I
a» --_4 ............. 4
I
: I
l : In
to A l I
'r Timer
I I
I I
«a I ‘ : : .
g ' I : ’
g V \' ' l
a l I
l f I/
0 I I II I III
I, Tim:
Figure 2.1 Constant-stress creep test (after
Andersland, et a1., 1978)
(a) typical creep curve
(b) true strain rate vs. time
26
Nomalma
‘0' - 03,"
(b)
Figure 2.2 Frozen frictional soils (after
Ladanyi, 1972)
(a) straight-line approximation of
the failure envelopes
(b) dependence of creep strength on
confining pressure
Peck axial stress. MN/m’
27
*- 3, - 2.66 x 10" min"
7" '12.03°C
l, - 1.33 x 10" min"
7" '12.03°C
a/
___ -—-D
I'D-——-—"u n \
l, - 2.66 x 10" min"
b T- '3.85°C
1 1 l 1 L L I I
0 10 20 30 40 50 60 70
Parent and by volume
Figure 2.3 Volume concentration of Ottawa
sand and peak strength (after
Goughnour and Andersland, 1968)
of the Total Volume of Solution
Volume of water Freezing Out as a 8
§
90-
80..
70-
60-
50-
40-
30
20
IO
28
Saline Content
(by weight)
2%
3%
5%
7%
Data points based
on Eq. (2-8)
-lo L ~13: ' -iF—'_='2'2
Temperature, T(°C)
Figure 2.4 Volume of water freezing out as a function of
temperature (after Yong, et al. 1978)
29
stress vs. lime
Figure 2.5a
Cyclic stress-strain
plot of elastic
behavior
(after Sandor, 1972)
A
Figure 2.5b
Development of the
6 hysteresis loop
(after Sandor, 1972)
////
Figure 2.5c Hysteresis loops obtained in
cyclic triaxial tests on frozen soils
30
Extension
“0
Compression
0'1
01 + at
‘ 1rnumnuu
' l m
x “
—-c- \ .— 8 - G
‘ oz 03 I 03 ‘flfcb
t 1'uusnmu
u'I""'o 03
(b)
c1
0 - deviator stress
I shear stress
(after Cho, gt g_l_ 1976)
Figure 2.6 Stress condition during a cyclic
triaxial test
31
'00 ' 1
G t’lOOO KID-"9'69“
90_ El Weissmon and Hort ((960 .4
A Richart, Hall and Lysmer (I962)
0 Drnevich, Hall and Richorl 0966)
80 0 Seed 09680)
A Silver and Seed (I969) —
V Hardin ond Drnevich (I970)
70—
60 T“
K2 50",
40
30-
20
IO—
0
I0“ I0'3 0‘2 I0" I
Shear SIroin-percenl
Figure 2.7 Shear moduli of sands at relative
density of about 75%
(after Seed and Idriss, 1970)
32
Aommp .mmwcua use ummm cmummv
mucmm toe owner newaEmo w.~ mcamwm
.coucoeasocï¬. coogm
19.2.23...» uco 3.5.x
AOhm: £03050 98 50.0...
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80m: 26m 6:0 .326
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Lammmc tacoE pen :0: £2350
80m: :65...
com: to: pen eoEmflo;
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33
Growl
Memo
Honchoâ€.
Honour 8m
New sm
sm
ï¬â€”r I 1 I I I I I | I I I ‘ï¬
m: "..‘% 4
7% Is nous -
C
0 fl cl
'2 '4
° ° as ‘
! :741i:\£naut .
3
cl
3 s
-° “33—— 30: .
(n s l s l sl 1 l l A l s
' 0.5 to so ‘ o
s. Void Iotlo
Figure 2.9 Effect of void ratio on complex shear
modulus (after Stevens, 1973)
Point Soils
4
Palm ‘ (
Fm. Sons a
I Manchester sm l -3.!
A 20°me Sons
SI"
0 IOOO-IO
I2]
I ~64
'U'I'I 1 ' I'U‘I" T ' I'V'Vv]
moms
fl-“
. ID to
{mucus-sun. sun-f
Figure 2.10 Effect of ice saturation on complex
shear modulus (after Stevens, 1973)
34
Design.
on _
oeo e'zo-ao Ono-o Send
97.2 - 0.73
- 9|.4 0.73
96.9 - 0.63
- 99.4 0.95
E'mmm sm
E'sooench Clay
- 93.3 0.60 o'zo-so Oiionn Send
G'flonchsslsr sm
6' Goodrich Clny
nnnmqquqoqnans
(D
0
I
O
U
U
'2 \ '1
Z I'- d
3 _ +
3 I. \ d
:,dn ‘\*
f E
g . I
‘o I . T
a .___e_
“ L .
Id; 5%;
t '-------C' J
——_E‘—.o‘
I- “—0"
F r 4‘1
-"‘1ir‘=nr*=t-‘=t-“1s 4 6’ ï¬â€˜LIs
. Wehmflc
Figure 2.1] Effect of temperature on complex
modulu, E* or 6*; frequency = 2
lkHz, dynamic stress = 0.7 kN/m
(after Stevens, 1973)
35
1 ' I'I'I'] T ' I'I'I"_-T 'I'T‘I"
20-30 Ofloeo Send
I «417 _
' -.9«:
I2 -
r -I
Honorer-Momhesier Sill
8 - 47.733 4'
.. = W 4"
e'cmmpnusnurauuuwe.ound'
dynamic peak stress = 0.7kN/
1 . 1.1.1.1 1 . 1-1-r-l 1 11-1-1-1
4
l «r K?
Frequency. III-ls
Figure 2.12 Effect of frequency on complex shear modulus
(after Stevens, 1973)
mam: --IOIII-Iz
I T I F I ‘1‘1 ' I i
â€0.53
J L lelelnj A I ‘
«f
Dynornle Stress kN/m'
o. -so one" Send. sorurored
6" Complex Sheer Modulus. cum!
5
'I‘I'l I ' I 'I'I" I..o‘.73I
% A n
-l7.7{.i_ __ ' ,
“ '9‘““""'~t:jb
9
Q“ Maegan—o.
-e.4{ —.. ‘
a d
b d
{'0 ___aemmurmm*
,p-ae‘_g : ï¬â€˜_4
. I...‘;! l "1A.A.$ 1 er]
0:, Dynomlc Stress su/m'
e. Iononeerer sm. mirrored
Figure 2.13 Effect of dynamic stress on complex shear
modulus -
(after Stevens,1973)
Figure 2.14
Ton I (Torsional)
Ton IlLordludnel)
Ton I (Torsionol)
.0
IT
36
Desire, 3'
A. 20-30 Olioeo Sond Dry
6 Honchesler SIII 95.8
c Goodrich Clay 98.4
0 20-30 Oilorro Sand 9L4
Frequency
= 1 kHz
Dynamic StEess
' = 0.7 kN/m
O
§
,0
O
b
0.02
-5
Temperature °c
do
*Ԥ*
Effect of temperature on damping property
(after Stevens, l973)
’ —Ilonchesrer 3m
-- 20-30 Otter-o Sons
ï¬r.
r dull
Fromm, has
'0'
I n lLL‘ll
Io'
Figure 2.l5 Effect of frequency on damping property
(after Stevens, 1973)
CHAPTER 3. MATERIALS, SAMPLE PREPARATION,
TEST PARAMETERS, AND DATA REDUCTION
Materials studied, sample preparation, sample
installation, testing procedures, and data reduction pro-
cedure are described in this chapter.
3.1. 'Materials Studied
Two materials, standard Ottawa sand and pea-gravel,
were used on this project. Standard Ottawa sand, which is
commercially available, was used in all frozen sand
samples. The sand was composed of uniform sub-angular
quartz particles with a specific gravity of 2.65. To
insure a uniform gradation, only particles between the No.
20 (0.84 mm) and the No. 40 (0.42 mm) U.S. Standard Sieve
sizes were used. This uniformity helped eliminate
variables caused by particle composition and gradation.
A series of tests was also run on frozen gravel
samples. The material used was a commercially available
pea-gravel, which passed the No. 4 (4.76 mm) and was
retained on the No. 6 (3.36 mm) U.S. Standard Sieves.
According to the Unified Soil Classification System (ASTM
designation D-2487), this material falls in the category
37
38
of a very coarse gravelly sand with no fines and is poorly
graded. The particles ranged from round to angular and
consisted of mixed mineral composition with an average
specific gravity of 2.74. For convenience, this material
was labeled as â€gravel" instead of "very coarse gravelly
sand" throughout this dissertation.
3.2. Sample Preparation
Samples with three different mineral-ice composi-
tions were tested for both the sand and the gravel materials.
The mineral-ice combinations were expressed as sand or
gravel content by volume. For the sand-ice materials,
samples of 20%, 45%, and 65% sand (by volume) were tested.
For gravel-ice materials, samples with 24%, 42% and 59%
gravel (by volume) were tested. The calculated water
contents for different mineral-ice composition are listed
in Table 3.1.
All test.samples were prepared by placing an alu-
minum base unit, sand or gravel, water, and an aluminmm
cap unit into a cylindrical Teflon mold and placement into a
freezer box for at least 24 hours at a temperature of
about -20°C. The samples, after extrusion from the mold,
were ready for tests. Detailed sample preparation proce-
dures are given in the following paragraphs.
39
3.2.1. Low Mineral Content Samples
The preparation procedure for low mineral content
samples (20% and 45% for sand, 24% and 42% for gravel)
were as follows:
(1) A hollow cylindrical Teflon mold (7.11 cm
inner diameter), with the sample base inserted in one end,
and a sample cap were placed in a large freezer box main—
tained at -20°C for at least one hour. The Teflon molds,
with a set of the cap and base units, are shown in Figure
3.1. Both the cap and base units have "coupling" devices,
consisting of an a1uminum.p1ate and four Allen head screws,
which permit tensile stresses to be applied to the sample.
(2) Air dried Ottawa sand or pea-gravel, precooled
to a temperature below 0°C, was mixed with loose, dry,
clean snow, which had been screened through a No. 4 sieve.
The amount of solids and dry snow to be mixed were con-
trolled by weight to give the desired mineral-ice compo-
sition.
(3) The Teflon mold was filled to within 50 mm
from the top with the mixture prepared in step (2) and
then left in the freezer for another hour.
(4) Precooled distilled water, close to 0°C, was
poured into the mold from the top up to the surface of the
mixture and the sample cap unit was inserted and hammered
into contact with the solid-snow-water mixture.
(5) The mold was placed in the freezer maintained
at a temperature of -20°C for at least 24 hours (Figure
3.2). Next, the samples were extruded from the mold using
a hydraulic jack.
The prepared samples were classified as SP, Vs
(Linnell and Kaplar, 1966). The samples contained inter-
mittent layers of mineral particles and ice, yet, none of
40
the layers with a lower sand or gravel content had a
thickness over 25 mm. An extruded sample is shown in
Figure 3.3.
3.2.2. High Mineral Content Samples
The 65% sand and 59% gravel content (by volume)
samples were prepared in a somewhat different way from
above. The procedure is as follows:
(1) A hollow cylindrical Teflon mold, with sample
base inserted and the sample cap were placed in a large
freezer box maintained at -20°C for at least one hour.
(2) Air dried Ottawa sand or pea-gravel was
immersed into and saturated with distilled water.
(3) The Teflon mold was filled with the solid-
water mixture (from step (2)) to within 50 mm from the
top.
(4) The saturated solids in the mold were then
compacted by vibration to obtain the desired maximum
density, and the cap was inserted and hammered into contact
‘with the sand or gravel. Excessive water would drain
through a small hole close to the top of the mold.
(5) The mold was placed in the freezer, at a
temperature of -20°C, for at least 24 hours.
Samples prepared in this way were classified as SP, Nb.
There were no visible ice lences in any direction.
41
3.2.3. Under-saturated Samples
The preparation of partially saturated samples was
basically the same as for high mineral content samples
introduced in Section 3.2.2 except for step (2). The
Ottawa sand was mixed thoroughly with a calculated amount
of distilled water and then poured into the mold. Control
of the exact water content was difficult due to some
gravity flow of pore water to the bottom of the sample.
After extrusion and inspection, samples with a poor distri—
bution of water were discarded.
3.2.4. Saline Samples
The preparation of saline samples was the same as
high mineral content samples except that pure distilled
‘water was replaced by distilled water with a specific
saline content. The saline water was prepared in the lab
by mixing preweighed.amounts of sodium chloride into
distilled water. Two different concentrations of sodium
chloride solution were prepared, 1.5% and 3.0% by weight.
The frozen saline samples showed a whiter and cloudier
appearance in comparison with samples with no salt.
3.3 Sample Installation in Triaxial Cell
The sample installation procedure is outlined
below:
42
(1) The sample was extruded from the Teflon mold
and then measured for length and weight. The quality of
the sample was determined by the length and density.
(2) The rubber membranes were applied to the
surface of the sample and then rubber bands were used to
secure the membranes to both the cap and base units of
the sample.
(3) The sample, with attached anti-tilt device
(Figures A.3 and A.4), was mounted in the triaxial cell
(Figure A. 2) .
(4) The LVDT (Linear Voltage Differential Trans-
former) was attached and then both LVDT and load cell were
adjusted to their null point.
(5) The thermistor bracket with two thermistors
attached, was then clamped to the sample.
(6) The top plate of the cell was closed and
tightened. A steel ram, which transmits load action
from the actuator to the sample, was then brought into
position and connected to the sample.
(7) The cell temperature usually rose about 1°C
during sample installation. One additional hour was
usually sufficient for the sample and the cold bath to
return to the desired test temperature based on thermistor
data.
(8) The actuator was then moved into position
and connected to the top of the steel ram using a split
brass connector ring. The sample and equipment was now
ready for testing.
3.4. Test Parameters
The test parameters considered in this investiga-
tion included temperature, strain amplitude, frequency
43
and confining pressure. The magnitude and application
sequence of each parameter may influence not only the
reliability of the data but also the amount of data which
can be gathered from each sample before its failure.
Ideally, more sample tests give a better statistical
average, but the cost would be higher and the time needed
would be much greater. In comparison, if only a small
quantity of samples are tested, the cost may decrease
and the time needed would be shorter but the overall
accuracy of the data would be reduced. Thus, reasonable
decisions on the magnitude and the application sequence of
test parameters were necessary so as to provide as much
accurate data as possible for the time available and a
limited number of test samples.
3.4.1. Magnitude of Test Parameters
The range and magnitude of test parameters chosen
included most field conditions and loadings anticipated
for frozen soil deposits subjected to strong motion earth-
quakes (Vinson, 1975). They included the following:
Temperature. A given sample was tested at only
one temperature. Tests at three temperatures, -l°, -4°,
and -10°C were accomplished on duplicate samples of similar
mineral-ice composition while other conditions were held
constant. Tests on a given mineral-ice combination and
44
temperature were repeated at least once; in most cases,
twice or more.
Strain Amplitude. Axial strain amplitudes ranged
3
from.2.0 x 10- % to 4.0 x 10-2%. The maximum strain ampli-
tude was usually limited by tensile failure of the sample.
ConfiningPressure. Three confining pressures,
0, 0.345, and 1.378 MPa (0, 50, and 200 psi), were applied
to the sample during each test.
Frequency. In general, four loading frequencies
were applied. They included 0.05, 0.3, 1.0, and 5.0 Hz
(cycles per second). At 5.0 Hz, the axial strain was
reduced due to the non-linear frequency response of the
loading system. This would not influence thetesting
result except that the data were obtained at a lower
strain.
Number of Cycles. For each frequency samples were
subjected to only 20 cycles or less. Damping ratio and
dynamic Young's modulus were usually calculated on the
basis of data recorded for the fifth or tenth cycle.
3.4.2. Application Sequence of Test Parameters
The stage testing technique (Silver and Park,
1975) has become the most popular method currently used
45
by practicing engineers to obtain dynamic properties of
soils for earthquake problems. A similar testing sequence,
used throughout this study, is summarized in Table 3.2.
The establishment and acceptance of this testing
sequence was justified in a previous study by Chaichanavong
(1976). A more detailed discussion on the effect of
testing sequence on test results will be presented in
Chapter 5.
3.5. Dynamic Creep Test
A preliminary study of the creep behavior of
frozen sand samples under dynamic loading conditions has
been part of this research. Frozen sand samples, with
several degrees of saturation, were subjected to static
loads at the beginning of each test until an axial strain
of, 0.07% was reached. Next, a 22168.36kN/m2 dynamic load
at 0.05 Hz was cycled about the original static load,
until a final axial strain of 0.5% was achieved. The
initial static load was a variable and the time (or number
of cycles) needed to achieve the final strain was recorded.
A zero confining pressure and a temperature of -4°C was
used for all samples so as to simplify test conditions.
3.6. Data Reduction and Processing
The dynamic Young's modulus and damping ratio were
evaluated from strip chart records of load and deformation
46
and oscilloscope photographs of hysteresis damping loops.
A typical strip chart record is shown in Figure 3.4 and a
typical oscilloscope picture of hysteresis loops was
shown in Figure 2.5c.
The dynamic Young's modulus was computed as
follows: using the sample's cross-sectional area and
length, the dynamic Young's modulus,
E = max. deviator stress
d max. axial strain
or
(0 -0)
Ed = 18 3 max (3.1)
max
The damping ratio, D, which represents the energy
absorbing behavior of the sample, is
D=m (3-2)
where AL is the area of the hysteresis loop and AT is the
area of the shaded triangle illustrated in Figure 3.5.
The computed Ed and D values all relate to a
temperature, mineral-ice composition, confining pressure
and loading frequency for different axial strains. A
linear regression analysis provided a correlation between
Young's modulus or damping ratio and peak axial strain.
47
A linear function may not be the true relationship between
dynamic properties and axial strain, but for the limited
axial strain range considered in this investigation, it
appeared to be acceptable. 7
A general expression for this correlation is
y=a+blnx (3,3)
where y = dynamic Young's modulus or damping ratio,
x = peak axial strain,
a = intercept for the least square fit line, and
b = slope of the least square fit line.
From Equation 3.3, values of dynamic Young's
modulus and damping ratio corresponding to a peak axial
strain of 1.0 x 10-2% were evaluated. The effect of each
variable on the dynamic properties of frozensoils pre-
sented in the next chapter was estimated at a peak axial
strain of 0.01%. This strain level was selected arbi-
trarily for convenience in comparison.
For frozen sand samples and frozen gravel samples,
the linear regression analysis was handled with the MSU
CDC6500 computer. Data points and least square fit lines
were plotted for all test conditions. These computer
output plots are presented in Appendices B, C, D and E.
For under-saturated and saline sand-ice samples, the
regression analyses were handled with a programmable hand
48
calculator and the original data are tabulated in Appen-
dices F and C, respectively.
49
Figure 3.1 Teflon molds and a set of base and cap units
50
Figure 3.2 Samples being frozen in a freezer box
DANU‘
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51
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52
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CHAPTER 4. SAMPLE DATA AND
EXPERIMENTAL RESULTS
Sample data, experimental results, and some imme-
diate interpretations of the results are presented in this
chapter. Experimental results presented can be categorized
into two parts. The first part consists of (1) original
computer plots of data points with least square fit lines
on a dynamic properties versus axial strain coordinates
for both frozen sand and frozen gravel samples, and (2)
tables of data obtained in tests on saline samples and
under-saturated samples. The second part includes cross-
plots, which demonstrate various parametric effects on
dynamic properties of frozen granular soils, and test
results obtained in dynamic creep tests. To compare the
first part with the second part, data and curves,in their
relatively primitive form.ar€tgiven in the Appendices as
supplemental information. The second part is presented
within this chapter with some immediate interpretations on
the meaning of the curves.
55
56
4.1."Sample Data
The sample data includes sand or gravel contents
(percent volume concentration) and sample densities calcu-
lated from the sample dimensions, the weight before the
test and the weight of soil solids after oven drying.
Other information has been included for samples tested for
different purposes. All the descriptive sample data are
tabulated in Tables 4.1 through 4.5.
Each sample was assigned a specific number with a
heading descriptive of the group to which it belongs.
The headings are explained as follows:
(1) SI-series--frozen sand samples.
(2) G-series--frozen gravel samples,
(3) SALT-series--sa1ine frozen sand samples,
(4) US-series--under-saturated frozen sand
samples, and
(5) CSI—series--frozen sand samples for
dynamic creep tests
Samples in the SI-series and G—series were tested
for three temperatures, -1°, -4° and -10°C. The US-series
and CSI-series samples were tested only for -4°C and the
SALT-series samples were tested only for -10°C.
4.2. Stress-Strain Behavior and Test
*Parameter Effects
The stress-strain behavior of frozen granular
soils is represented in this study by the dynamic Young's
modulus (Ed). The effects of axial strain, confining
57
pressure, temperature, frequency, and mineral content on
the dynamic Young's modulus has been investigated for both
frozen Ottawa sand and frozen pea-gravel samples. The
degree of ice saturation and saline content effect were
investigated only for frozen sand samples.
4.2.1. Axial Strain Effect
The dynamic Young's moduli for various test condi-
tions were plotted against axial strain using the MSU CDC
6500 computer. These plots are shown in Appendices BandD
for frozen sand and gravel samples, respectively. The
dynamic Young's modulus generally decreases while the
strain increases from approximately 2 x 10-3%
to approxi-
‘mately 4 x 10-2%. Axial strain has more influence for
samples tested at lower temperatures, higher frequency,
and higher sand content. '
The relationship between dynamic Young's modulus
and confining pressure, frequency and temperature can be
established by interpolation of the results presented in
Appendices B and D at a specific strain amplitude. A
strain amplitude of 1.0 x 10-2% was selected for conven-
ience. Another strain amplitude could have been selected
without a significant change in the conclusions reached in
the following paragraphs.
58
4.2.2. Confining PresSure Effect
The correlation of dynamic Young's modulus with
confining pressure for frozen sand samples is shown in
Figures 4.1 to 4.3. The same correlation for frozen gravel
samples is shown in Figures 4.4 to 4.6. The dynamic
Young's modulus decreases with decreasing confining
pressure. At higher confining pressures it appears that
the ice microfissures cannot open as easily resulting in
a stiffer structure. Also, at higher confining pressures,
‘more frictional resistance may develop between mineral
particles, which contributes to the strength of the
frozen soil system.
.Some curves shown in the figures of this section
and in other sections of this chapter have dashed portions,
which indicates either an unexpected drop of dynamic
Young's modulus or an unexpected rise of damping ratio.
The original data points were replaced by a dashed line,
which conforms with the trend of other curves shown in the
same figure. These unexpected changes of dynamic proper-
ties were most often caused by tension failure of the
sample and this will be discussed in detail in Chapter 5.
4.2.3. Temperature Effect
The correlation of dynamic Young's modulus with
temperature is summarized in Figures 4.7 to 4.9 for frozen
59
sand samples and in Figures 4.10 to 4.12 for frozen
gravel samples. The dynamic Young's modulus increases
generally with decreasing temperatures. For low mineral
content (ice rich) samples, the strength increase at
lower temperatures is believed to be due to the stiffer
dynamic elastic properties of ice (Chaichanavong, 1976).
It is well established that the dynamic elastic
properties of unfrozen cohesionless soils increases
with increasing confining pressure (Seed and Idriss, 1970)
owing to the increased stress at the contact points
between particles.
The ice matrix of a high mineral content sample
would be strengthened at lower temperatures. The larger
confining force on the soil particles would increase the
friction at particle contact points and thereby contribute
to an increased dynamic Young's modulus for high mineral
content samples at the lower temperatures.
4.2.4. Frequency Effect
The dynamic Young's modulus increases, in general,
‘with increasing frequency of loading as shown in Figures
4.13 to 4.15 for frozen sand samples and in Figures 4.16
to 4.18 for frozen gravel samples. The rate of increase
of the dynamic Young's modulus appears to be independent
of temperature.
60
4.2.5. Mineral Content Effect
The effect of mineral content on the dynamic Young's
modulus is summarized in Figures 4.19 and 4.20 for frozen
sand samples, and in Figures 4.21 and 4.22 for frozen
gravel samples. Figures 4.19 and 4.21 show the results
obtained at a single confining pressure, 0.345 MPa, for
various frequencies and temperatures. Figures 4.20 and
4.22 show the results obtained at a single frequency, 0.3
cps, for various confining pressures and temperatures. It
is shown that the dynamic Young's modulus increases with
increasing mineral content for -4°C and -10°C. For
samples tested at -l°C, the modulus changes very little with
change in mineral content for frozen gravel samples and
decreases with increasing mineral content for frozen sand
samples.
4.2.6. Ice Saturation Effect
The effect of ice saturation on the dynamic Young's
modulus at a single confining pressure, 0.345 MPa, and
various frequencies is shown in Figure 4.23. The effect
of ice saturation on the dynamic Young's modulus at a
single frequency, 0.3 cps, and various confining pressures
is shown in Figure 4.24. It is apparent that the dynamic
Young's modulus increases with increase in degree of ice
saturation. The data points for 93% ice saturation were
61
obtained from Figure 4.15 and the data points for lower
degrees of saturation were evaluated at an axial strain
of 1.0 x 10-2% from the data shown in Appendix F.
It is reasonable to believe that the increase in
ice saturation strengthens the ice bonding effect on the
sand particles and thus increases the total strength of
the sample. The effect of degree of ice saturation was
evaluated only for frozen sand samples.
4.2.7. Saline Content Effect
The effect of saline content on the dynamic Young's
modulus was evaluated only for frozen sand samples. The
correlation of modulus with saline content for tests run
at a confining pressure of 0.345 MPa is shown in Figure
4.25. The same correlation for a constant frequency, 0.3
cps, is shown in Figure 4.26. I
The data show that the dynamic Young's modulus
decreases with increase in saline content. This is due
to the increase in unfrozen water content (Yong, et al.,
1973; Banin and Anderson, 1974), which reduces the strength
of the sample.
4.3. yEnergyAbsorbing Behavior and
Test Parameter Effects
The damping ratio represents the energy absorbing
behavior of frozen soils and has been expressed as the
62
percentage energy absorbed per stress cycle. The effect
of axial strain, confining pressure, temperature, frequency,
and mineral content on the damping ratio have been inves-
tigated for both frozen sand and frozen gravel samples.
The effect of degree of ice saturation and saline content
were investigated only for frozen sand samples.
4.3.1. Axial Strain Effect
The computer output plots presented in Appendices
C and E for frozen sand and frozen gravel samples,
respectively, indicate a random relationship between
damping ratio and axial strain. The damping ratio may
increase, decrease or remain constant with respect to
increasing axial strain. Values of damping ratio evaluated
at an axial strain of 1.0 x 10-2% was selected to serve
for the purpose of comparison. The following paragraphs
are based on the comparison at this strain level.
4.3.2. Confining Pressure Effect
The relationship of damping ratio with confining
pressure is not explicit from the curves shown in
Figures 4.27 through 4.29 for frozen sand samples and
Figures 4.30 through 4.32 for frozen samples. However,
it appears that the variation of damping ratio with
respect to confining pressure over the range of consider-
ation is not significant.
63
4.3.3. Temperature Effect
The correlation of damping ratio with temperature
for frozen sand samples is shown in Figures 4.33 to 4.35,
and in Figures 4.36 to 4.38 for the frozen gravel samples.
Generally, the damping ratio decreases with a decrease in
temperature.
To compare the effect of temperature on both
modulus and damping ratio, it is obvious that damping ratio
drops when the modulus increases. It is reasonable to
conclude that samples tested at lower temperatures are
stiffer and act more elastic with less energy absorbed.
4.3.4. Frequency Effect
The effect of frequency on damping ratio is
summarized in Figures 4.39 to 4.41 for frozen sand
samples and in Figures 4.42 to 4.44 for frozen gravel
samples. The damping ratio decreases as the frequency
increases. A higher frequency means higher strain rates,
which in turn make the samples tested act more elastically
and absorb less energy.
4.3.5. Mineral Content Effect
The mineral content effect on damping ratio is
summarized in Figures 4.45 and 4.46 for frozen sand samples
and in Figures 4.47 and 4.48 for frozen gravel samples.
64
Figures 4.45 and 4.47 show the results obtained at a
single confining pressure, 0.345 MPa, for various frequen—
cies and temperatures. Figures 4.46 and 4.48 show the
results obtained at a single frequency, 0.3 cps, for
various confining pressures and temperatures.
The data show that the relationship between
damping ratio and mineral content is not constant. For
samples testedan:higher temperatures, the damping ratio
generally increases with increase in mineral content; but
for lower temperature tests, the damping ratio increases
to a peak and then decreases along the mineral content
scale.
4.3.6. Ice Saturation Effect
The effect of degree of ice saturation was inves-
tigated only for frozen sand samples. From Figures 4.49
and 4.50, note that the damping ratio decreases with
increase in ice saturation. The scatter in data points
fall within a relatively narrow band with the damping ratio
decreasing with increasing degree of ice saturation.
4.3.7. Saline Content Effect
The effect of saline content on damping ratio is
shown in Figures 4.51 and 4.52. Damping ratio increases
with respect to saline content to a peak around 1.5% and
65
then decreases. The effect of saline content on the
damping behavior was evaluated only for frozen sand samples.
4.4. Creeprehavior of Frozen Sand Samples
under Cyclic Loading Conditions
Seven high sand content samples with several degrees
of ice saturation were tested for their creep behavior
under cyclic loading conditions. Experimental results
are tabulated in Table 4.6. Creep curves are presented
in Figures 4.53 to 4.55. The descriptive sample data
with the initial static loading for each sample is shown
in Table 4.4. The creep curves show that the secondary
creep appears to have developed in all samples. In the
strain range of 0.15% to 0.5% each creep curve shows a
relatively constant slope (or creep rate). The number of
cycles needed for each sample to deform from 0.15% strain
to 0.5% is plotted in Figure 4.56 versus the initial
static stress level, which is also the mean stress level
during the cyclic loading period.
It is shown that for a given degree of ice satur-
ation, the higher the stress level, the less cycles are
needed to develop a certain strain level. For samples
with a lower degree of ice saturation, the number of
cycles to achieve a given strain level is less than that
for the higher degree of ice saturation sample.
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no.N ow.mm H noc.N No.oo oN nm.H mN.wN cm ONI
om.N «N.om mm coo.N NN.N< mN mm.N nn.NN mN
.<.z o~.wm 0H No.N HN.H¢ mN om.N mw.MN NN
.<.z mq.mm a No.a No.H< «N cm.H on.nN NN NI
No.N oN.mn mm ome.a NN.N¢ NH
oo.N Nm.mm on oN.N mo.mo on cm.a oN.NN CN
mm.N oN.mm MN ON.H mc.No ma om.N 0N.mN ma
.<.z om.mm NH oN.H mm.Ne «N on.H hm.mN ma HI
muamnon NMMMHW<N oHeamm unencua HMMHWW<N oaeanm huwmcon NMWMHW<N magnum
8 use
am No SN eununuonaoa
AoESHo> he ucoonoov ucoucoo Ho>muo vouooexm
Amoï¬nmmlov moHnEmm Ho>muw couonm m.q manna
71
“E 25- Axial Strain=l.0xlO-2% ‘<; 25- Axial Strain=l.0xlO-2%
E? =_1 deg c E; T=—4 deg C
8 8
,0 (a) ,0 (b)
m 20I- “J 20"
a?
a
'2
g 15. 15.
2:
(D
g Frequency
8 10' Frequency lOI' (cps) 5 O
’5‘ (6138) . '
o 5.0 1.0
-.-I 1.0 //_ 0.3
E .
g 5.- 0.3 5:- 4 0.05
E' —g 0.05
O. l L l l O '- I I l I
O 0.5 1.0 1.5 0 0.5 1.0 1.5
Confining Pressure (MPa) Confining Pressure (MPa)
. . -2
of‘ 25, Ax1al Strain=1.0x10 7
.E T=—1O deg C
2:
53
L5on- (C)
a?
D
H
a
B 15' Frequency
r" (CPS)
U)
m 5.0
g 10- 1.0
:3 0.3
0 0.05
"E
2 5'
>.
c:
0 1 L l l
0 0.5 1.0 1.5
Confining Pressure (MPa)
Figure 4.1 Dynamic Young's modulus vs. confining pressure for
frozen sand samples of 20% sand content.
72
25' Axial Strain=.Ul% 25" Axial Strain=.01%
,\ T=-1°C of“ T=—4°C
N E
ii ( ) E; ( )
a 0 b
55/ 20- v 20. _
'o
'u m
m
g 15_ 15b Frequency
H (CPS)
-€ _ 5.0
: Frequency
g (C S) 1.0
U) lor- P 10-
E? 5.0 0.3
g 1.0 0.05
w 5. 0,3 .5“ .,/vâ€"â€â€˜ï¬‚'———____-_.
â€:1" '//4:0.05
s /â€
i 0
Q J l l I O- I a l l
0 0.5 1.0 1.5 O 0.5 1.0 1.5
Confining Pressure (MPa) Confining Pressure (MPa)
25 F Axial Strain=.01%
A =-10°C
N
E
E3 20 F (C)
"D
LIJ
J , Frequency
3 13 P ‘
.3 (CPS)
'P 5.
1.8
0.3
U) I p
10 10 ,. 0.05
G I
a
0
>4
.3 5 r
6
c
>.
a
O b 1 l L l
0 0.5 1.0 1.5
Confining Pressure (MPa)
Figure 4.2 Dynamic Young's modulus vs. confining pressure
for frozen sand samples of 45% sand content.
73
25 ’ Axial Strain=.01% 25' Axial Strain=.01%
A ="'1°C N’: T='4°C
N a
E \
2 (a) 6 (b)
£3 20 ' " 20' ,
:6 Frequency
IND ‘3 (cps)
" 5.0
3 15 r 15’
'3' 1.0
'o
o
2 Frequency 0.3
g) ———o 0.05
5 5.0 W
>9 1.0
g, 5 " 0.3 5*
S: 0.5
e
>.
Q o . o. . J
0 0.5 1.0 1.5 0 0.5 1.0 1.5
Confining Pressure (MPa) Confining Pressure (MPa)
25} Axial Strain=.01%
N: T=-10°C
é; Frequency
0 (C) c
V 20» ( pg)—
'6 5.0
m 1.0
a?
H315)- 0.3
'U 0.05
o
2
Jâ€
«a 10’
c
s
o
>.
o r
°r-i J...
E
E
E
.2
0r
l l l I
0 0.5 1.0 1.5
Confining Pressure (MPa)
Figure 4.3 Dynamic Young's modulus vs. confining pressure
for frozen sand samples of 65% sand content.
74-
,‘ Axial Strain=.01% ,\ Axial Strain=,01%
N
=-1°C 9‘ T=—4°c
E 23- E 25-
2: z
53 (a) 53 (b)
m†zu- .3†20-
c5
.3 .
a 15- 15.
-u
.8
m Frequency
E? 10" Frequency 10' (CPS)
9 (CPS)
3 5.0 / a 1.8
U 5'- 1.0 5'- :‘ O 3
«4 —0 0.3. f —e o 05
E 00.03
E, -
'3 U1: 1 L l 1 0'- I l l I
0 0.5 1.0 1.5 O 0.5 1.0 1.5
Confining Pressure (MPa) .Confining Pressure (MPa)
25 r Axial Strain=.01%
=-10°C
N
C
l
Dynamic Young's Modulus, Ed (GN/mz)
15 -
Frequency
(CPS)
1" h 5.0
. .I-g
5 - t===:-——--II-I"'"""-> 0:05
0
a 1 l
0 0.5 1.0 1.5
Confining Pressure (MPa)
Figure 4.4 Dynamic Young's modulus vs. confining pressure
for frozen gravel samples of 24% gravel content.
75
NA NA
5 25 - Axial Strain=.Ol°/. g
a T=—l c a
'U (a) '0
id 20 r m
6‘
3
H _
.3 15 -
.2
{g 10 _ Frequency
é (cps
>‘ i_;; 5.0
:3 5 " .4vâ€."———— 1.0
_ - ().3
g {EEEEEEEE—————————_:;i(0.05
>.
G O '- 1 I l I
H
U)
0 0.5 1.0
Confining Pressure (MPa)
20
15
10
Axial Strain=.01%
,=-4°c
(b)
Frequency
(CPS)
5.0
/ 1.0
/ 0.3
/" 0.05
.,.—Ar—-—"“"_—_—.
L L
0 0.5 1.0 1.5
Confining Pressure (MPa)
Axial Strain=.01%
Frequency
(CPS)
5.0
0
OCH
3
.05
NA
E
g 25 -
c, T=-lO°C
:30
Q 20 L (C)
CD
:)
H
53
9‘ 15 "
.5â€
CD
5 10
0
>4
:5 s -
G
n
c
5‘
O I. l l
0 0.5
1.0
1.5
Confining Pressure (MPa)
Figure 4.5 Dynamic Young's modulus vs. confining pressure
for frozen gravel samples of 42% gravel content.
76
NA N“
S 25 â€Axial Strain=.01% E 25 " Axial Strain=.01%
8 T=’1°C c2: T=-4°c
“SD 20 - (a) Law 20 - (a)
0; Frequency
:5
"‘ (CPS)
«3‘: 1: P 15 -
>1 5.0
0) Frequency 1.0
’3; 10 - (cps) 10 - 0.3
8 5.0 ./——. 0.05
g 5 ' 0.3 5 -
E —e 0.05
m x
c:
5‘ 0 o
I J l 1 J l I l
0 0.5 1.0 1.5 0 0.5 1.0 1.5
Confining Pressure (MPa) Confining Pressure (MPa)
NA
E
E 25' Axial Strain=.017o
8 T=—lO°C
Frequency
m“ 20 . (cps)
U; ........ _. 500
D " 1.0
H
g 15 . f: 0.3
2: 0.05
_m
00 10 -
c:
:1
0
>4
0 5 -
"3‘:
E5
:3
>.
£3 0 L.
1 l l J
O 0.5 1.0 1.5
Confining Pressure (MPa)
Figure 4.6 Dynamic Young's modulus vs. confining pressure
for frozen gravel samples of 59% gravel content.
25
A
N
E
E? 20
O
V
'0
LL}
.5 15
:1
H
:3
“U
0
E
m 10
.00
C
:3
o .
>‘ 5
U
â€-1
E
to
C‘.
5; 0
77
- Axial Strain=.01% 25-Axial Strain=.01%
Confining Pressure=0 MPa Confining Pressure=0.345 MPa
(a) “E (b)
. E; -
E3 20
'o
m
h 15 1-
Frequency
(cps)
Frequency
' 10 - 5
(CPS) 1.8
0.3
0.05
. 5 .
0 b L L
-l -4 —7 —10 -l -4 -7 -10
Temperature (°C) Temperature (°C)
25' Axial Strain=-Ol%
Confining Pressure=1.5)8 MPa
~;
22 (C)
53 20'
vs
:1
a. 15_ Frequency
.3 (Cps)
:
E
z 1.0
.9 10. 5.0 0.3
on --
g 0.05
o
w -
D I
u
'H
5
g,
a O '- A +
-l -4 -7 —10
Temperature (°C)
Figure 4.7 Dynamic Young's modulus vs. temperature for
frozen sand samples of 20% sand content.
78
25' Axial Strain=.01% 25 ‘Axial Strain=.01%
,\ Confining Pressure=0 MPa Confining Pressure=0.345 MPa
2 (a) ; (b)
8 20‘ a 20'
'U V
m w
x
‘3 15- 15-
H
5 Frequency
3 Frequency CPS
T (CpS)
J†10' 10' 5.0
‘0: ' o 1 o 3133
5 . . .
,--- 0.3 .
>9 0.05 5
o 5- 5-
-H
E
m
a
>
a
O I 1 I l A 1 1 I n 1 0’- I l l l l L J L I L
-l —4 -7 -10 —l -4 —7 —10
Temperature (°C)
25
A
N
E
E
U 20
v
'U
71-}
u? 15
:J
r—4
:1
"U
a
R-a
m 10
09
I:
:J
O
>‘ 5
U
-H
E
m
S.
=2 0
Temperature (°C)
’ Axial Strain=.01%
Confining Pressure=l.378 MPa
(C)
Frequency
- (CPS)
5.0
1.0
. 0.3
0.05
-l —4 -7 -10
Temperature (°C)
Figure 4.8 Dynamic Young's modulus vs. temperature for
frozen sand samples of 45% sand content.
25 r Axial Strain=.01% 25- Axial Strain=.01%
,\ Confining Pressure=0 MPa ,\ Confining Pressure=0.345 MPa
NE < > NE ( >
a a
g 20. (E 20-
Freauenc
ï¬n Frequency ï¬n (cps) y
g 15. (CPS) 15-
g ’5.0 1,0
3 †5,0 ’ 0.3
E ’ 1.0 0 05
_"’ 10' 10'
w .3
'5 0.5
o
>
U 5 - 5-
d
t:
m
c
3
0 A I I I I J I I J L 0 1 I k I l I I A A +
-l -4 -7 -10 —l -4 -7 -10
Temperature (°C) Temperature (°C)
' F Axial Strain=.OlZ
Confining Pressure=l.378 MPa
(c) Frequency
(CPS)
N
U
N
C
l
. , 2
Dynamic Young's Modulus, hd (UN/m )
H H
O U:
I I
c> c; 1a
0 :5 o
L"
U1
I
O
I I A
-l —4 -7 -10
Temperature (°C)
Figure 4.9 Dynamic Young's modulus vs. temperature for
frozen sand samples of 65% sand content.
80
NA NA
8 E
E; 25- Axial Strain=.01% E§25’ Axial Strain=-Ol%
xx Confining Pressure=0 MPa \/ Confining Pressure=0-345 MP3
ï¬t 13°
20. (a) 20- (b)
6
a
H
£3 15, 15.
o
2 Frequency Frequency
.01 (cps) (CPS)
g 10- 10'
0 5.0
V 5 O 1.0
.3 5» (1, 9 5- 8'8-
c
>.
O t) 0
-l -4 -7 -10 —1 -4 -7 ~10
Temperature (°C) Temperature (°C)
“2
E 25 - Axial Strain=.Ol°/.
g Confining Pressure =l.378 MPa
:5“ 20 , (C)
J
5
F4 -
_§ 13 _ Frequency
g (CPS)
.9
39 10 ' 5.0
g / 5'0
.3
w r
'd
K:
m
E.
2 0
-1 -4 ‘ -7 -10
Temperature (°C)
Figure 4.10 Dynamic Young's modulus vs. temperature for
frozen gravel samples of 24% gravel content.
81
NA NA
{-3
i: 25 * Axial Strain=.01% E? 25’
8 Confining Pressure=o MPa 8
r5020 . (a) 1211,20-
m“
.3 _
'3 15 _ Frequency 13_
o (CPS)
El
.0)
w 10 - 10'
c
a
o
>~
o 5 - 5,
-H
E
a
2.
a O O
Axial Strain=.01%
Confining Pressure=0.345 MPa
(b)
Frequency
(Cps)
-1 -4 —7 -10
Temperature (°C)
N
U‘
I
Confining Pressu
1- (C)
N
O
p.»
UW
U
-1 -4
Temperature (°C)
-7
Axial Strain=.Ul% -
re=1.378 MP
Frequency
(CPS)
Dynamic Young's Modulus, Ed (GN/mz)
O
T
Temperature (
Figure 4.11 Dynamic Young's modulus vs.
‘0
09:00
Oc)
temperature for
frozen gravel samples of 42% gravel content.
82
â€5 NE
5 25 'Axial Strain=.01z g 25' Axial Strain=.01%
~I Confining Pressure=0 MPa ‘1 Confining Pressure=0.345 MPa
Q“ av Frequency
. 20 -(a) Frequency 20' (b) (CpS)
‘3 (CPS) 1.0
'3
E 15 . 15- 0.3
.01 0.05
an 10 _ 10.
a
a
o
>
3 5 - 5.
E
m
a
5‘
U A I A A A I A 141— o A A A A A A A L
—1 —4 -7 ~10 —1 -4 —7 —1o
Temperature (°C)
NA
i: ZJ- Axial Strain=.01%
53 Confining Pressure=l.378 MPa
U Frequency
"J 20- (CPS)
J 5.0
3 1.0
g 15_ 0.3
§ 0.05
(I)
1m 10-
a
a
0
>4 .
u 5.
'H
E':
m
a
>
3 0
—l —4 -7 -10
Temperature (°C)
Figure 4.12 Dynamic Young's modulus vs. temperature for
frozen gravel samples of 59% gravel content.
83
25 )Axial Strain=.01% 25 - Axial Strain=.01%
Confining Pressure=0 MPa C<>nfining Pressure=0.345 MPa
°f‘ a °{: b
8 53
'U -u
:2 m
A 15 - 15 * Temperature
8 Temperaure (°C)
'3‘ (°C)
'6
;§ 10 - 10 '
m -10
- o
g --- -10 //° -1
~14
E
2 J
3 O F l A A A o I A J L
0.05 0.3 1.0 5.0 0.05 0.3 1.0 5.0
Frequency (cps)
N
U1
7
(C)
N
O
I
H
U1
l
l-J
O
I
Dynamic Young's Modulus, Ed (GN/mz)
u:
7
Frequency (cps)
Axial Strain=.Ol%
Confining Pressure=l.378 MPa
Temperature
(°C)
-10
-4
oIrrz’,,r4*â€"'°——————-° —1
0.05 0.3
1.0 5.0
Frequency (cps)
Figure 4.13 Dynamic Young's modulus vs. frequency for
frozen sand samples of 20% sand content.
84
L Axial Strain=.Ol%
25 ’ Axial Strain=.01% 25
Confining Pressure=0 MPa Confining Pressure=0.345 MPa
“2 “2
2 20 _ (a) 2 201- (b)
8 8
'0 'U
a: m
. _ . Temperature
3 15 Temperature 15 (°C)
'3 (°C)
'o
-2
m 10 ' 10*
co
g .—-————_'.---- 10 ’4
o 5 h -1 5
W4
E /-—_.
m
E.
Q U h A A A A 0" A A J A
0.05 0.3 1.0 5.0 0.05 0.3 1.0 5.0
Frequency (cps)
Frequency (cps)
25 ~Axia1 Strain=.01%
Confining Pressure=l.378 MPa
“2
E? (C)
8 20 '
Temperature
A5" (°C)
a? 15 -
3 _-1o
{3’ I" -4
o
21
.m 10 ' -l
on
a
a
:53
o 5 L
H
E
m
a
>.
2‘ o ’ . . . .
0.05 0.3 1.0 5.0
Frequency (cps)
Figure 4.14 Dynamic Young's modulus vs.
frozen sand samples of 45%
frequency for
sand content.
85
25-Axial Strain;.01% 25"Axial Strain=.Ol%
Confining Pressure=0 MPa Confining Pressure=0.345 MPa
(a) NE (b)
20. z 20 '
8
Temperature an Temperature
(°C) ‘ (°C)
15'
1.4
O
I
2
Dynamic Young's Modulus, Ed (GN/m )
O
O
1
0.05 0.3 1.0 5.0 0.05 0.3 1.0 5.0
Frequency (cps) Frequency (cps)
25- Axial Strain=.01%
Confining Pressure=l.378 MPa
0:\ Temperature
g (c) (°C)
8 20 -10
“U 0
{d
d .15P -4
s
H
a
-u
.9
fl 0
m 10"
on
g —l
>9
5 P
u
.a
E
m
a
5‘
0 . 1 . .
0.05 0.3 1.0 5.0
Frequency (cps)
Figure 4.15 Dynamic Young's modulus vs. frequency for
frozen sand samples of 65% sand content.
86
NA
~E 25 “Axial Strain=.01%
5 Confining Pressure=0 MPa
ï¬n 20 -(8)
i
a
3' 15 -
'v
.2
H Temperature
:0 10 _ (°C)
cJ
:
a
0
>4
0
-H
E
m
c
>.
:3
O
1
0.05 0.3 1.0 5.0
Frequency (cps)
20 1- (C)
10 '
Dynamic Young's Modulus, Ed (GN/mz)
u
C
0.05 0.
I
3
Ed (GN/mz)
25
20
15
10
’Axial Strain=.01%
Confining Pressure=0.345 MPa
-(b)
Temperature
_ (°C)
-10
0.05 0.3 1.0 5.0
Frequency (cps)
25 P Axial Strain=.01%
Confining Pressure=l.378 MPa
Temperature
I
(°C)
-10
/ -4
—l
J
1.0 5.0
Frequency (cps)
Figure 4.16 Dynamic Young's modulus vs. frequency for
frozen gravel samples of 24% gravel content.
25
20
15
10
Dynamic Young's Modulus, Ed (GN/mz)
U1
0
I
0.05
NA
E
prial Strain=.01% 2 25
Confining Pressure=0 MPa EB
an
,(a) 20
p 15
Temperature
(°C)
p 10
—10
87
-Axial Strain=.01%‘
Confining Pressure=0.345 MPa
.(b)
Temperature
(°C)
-10
.fl:
L I L
A 1 A I
0.3 1.0 5.0
Frequency (cps)
0.05 0.3 1.0 5.0
Frequency (cps)
NA
g 25~ Axial Strain=.01% ,
£3 Confining Pressure=l.378 MPa
La" 20. (c)
£‘
'3 Temperature
0
3 15- (C)
.2
.24
:0 -10
ca 10' -4
‘5‘
>9
0 51- / -l
'2
ES
3
0L . 1 .
0.05 0.3 1.0 5.0
Frequency (
cps)
Figure 4.17 Dynamic Young's modulus vs. frequency for
frozen gravel samples of 42
Z gravel content.
88
NA NA
~E 25-Axial Strain=.01% .E 25
5 Confining Pressure=0 MPa 5
:JU 20_(a) Temperaure bf, 20
. (°C)
w
,3 I, —10
.8 15* ,«' 15
.23 . °
w
an 10 P / ‘4 10
a
0
>4
.3 5 b /a -1 5
E
m
c
E? 0 o
0.05 0.3 1.0 5.0
Frequency (cps)
-Axia1 Strain=.01%
Confining Pressure=0.345 MPa
.(b) Temperature
(°C)
0.05 0.3 1.0 5.0
Frequency (cps)
Confining Pressure=0.378 MPa
Temperature
(°C)
-10
NA
E
E; 25"Axia1 Strain=.01%
L9
kit, 20 - (c)
6‘
a
'3
“U 15 "'
o
2:
U)
so 10-
c
s
0
>4
0 5 c
H
E
m
E.
o 0
0.05 0.3 1.0 5.0
Frequency (cps)
Figure 4.18 Dynamic Young's modulus vs.
frequency for
frozen gravel samples of 59% gravel samples.
89
25 ~Axial Strain=.01 25-Axial Strain=.01
Temperature=—1°C Temperature=-4°C
°i§ ( ) °£§ (b)
a
220. E 201-
8 8
:4“ {Au Frequency
Q (Cps)
u) 15" 15"
D
2 5.0
:3 1.0
A
m 10 _ Frequency 10A 0.3
in (CPS)
c n 0.05
D -
o
>" 5_ “5'0 5-
“: \100
30+ '0
10 20 3O 4O 50 6O 10 20 3O 4O 50 60
Sand Content (Percent by Volume) Sand Content (Percent by Volume)
25'Axia1 Strain=.01
F‘ Temperature=~lO°C
NE
E; (C)
<9 20‘
c, Frequency
:5“ (Cps)
a? 15-
,3 1.0
'8 0.3
2 0.05
I†10-
CO
5
,8
U 5.
~g
a
a
>.
E 0
10 2‘0 ‘36 ‘4'0 '50 60
Sand Content (Percent by Volume)
Figure 4.19 Dynamic Young's modulus vs. sand content of
frozen sand samples at 0.345 MPa confining pressure.
9O
25-Axia1 Strain=.01% 25- Axial Strain=.01%
,\ Confining Pressure=0 MPa ,\ Confining Pressure=0.345 MPa
Na NE
E (a) E (b)
53 20* £3 20’ .
,4“ Temperature :5“ Temperature
. (°C) (°C)
9 15- 15b
'3‘
“U ‘10
ï¬g
J†10- ‘10 10- —4
co ‘4
a
3
0
>4
U 5 " 5 "
-H
E
CU ‘— 4N \\
i —1 -1
=3 o o.
10 20 3O 4O 50 6O 10 20 30 4O 50 60
Sand Content (Percent by Volume) Sand Content (Percent by Volume)
N
U1
-Axial Strain=.01%
Confining Pressure=l.378 MPa
(c) Temperature
(°C)
N
O
I
H
U.
I
F \
Dynamic Young's Modulus, Ed (GN/mz)
uz
«
u
0+-
10 "26 A 35 40 50 60 ‘
Sand Content (Percent by Volume)
Figure 4.20 Dynamic Young's modulus vs. sand content for
frozen sand samples at 0.3 cps frequency.
91
“2 4 “E
E; .25 â€Axial Strain=.01% g; 25*Axial Strain=.01%
£3 Temperature=-1°C £3 Temperature=—4°C
m“ 20 .(a) .3†20%)
c5
,3 Frequency Frequency
53’ 15 ’ (CPS) 15' (CPS)
m 5.0
to 10 ~ 10' 1.9
g 0.3
0 .
W 5.0 / 0 05
o 5 r 1.0 5'
"a g; 0.3
E, v, - v 0.05
Q 0 r L A A A L A I L A A O L A AA; A A A A A
10 20 1M) 40 50 6O 10 20 30 40 50 60
Gravel Content(% by Volume) Gravel Content (% by Volume)
NA
5
E 25'Axial Strain=.01%
" Temperature=—10°C
:3“ Frequency
. 20'(C) (cps)
S 1.0
H
a
'8 15- 0.3
:1
m 0.05
g) 10. ,
D I
0
>4
:5 5-
t:
m
a
>.
a 0
10 20 30 40 50 60
Gravel Content (2 by Volume)
Figure 4.21 Dynamic Young's modulus vs. gravel content for
frozen gravel samples at 0.345 MPa confining pressure.
92
Na 25pria1 Strain=.01% Ne
E Confining Pressure=0 Mpa 2
8 8
(a)
In." 20' Temperature sic
* (°C)
(D
3 15
S —10
o
2:
go 10.
?=° —4
s
0
>2 5" /
:4) - 3 —: -l
E f'
2
g‘O#ALL4LALIIIIII_
10 20 30 4O 50 6O
Gravel Content (2 by Volume)
NC
3 25
z
53
15° 20 .(c)
m0
3
a 15 _
'o
.9
A
U)
a
s
0
>1
0 5 .
H
E
CO
5.
a O
25
20
15
10
0
~Axial Strain=.01%
Ccuifining Pressure=0.345 MPa
_(b)
Temperature
(°C)
. —10
9
n
I I I I I I I I I I L
10 20 30 4O 50 60
Gravel Content (Z by Volume)
LAxial Strain=.01%
Confining Pressure=l.378 MPa
Temperature
(°C)
-10
I I I
10 20 30 40 50 60
Gravel Content (Z by Volume)
Figure 4.22 Dynamic Young's modulus vs. gravel content for
frozen gravel samples at 0.3 cps frequency.
Dynamic Young's modulus, Ed (GN/mz)
16
14
12
10
93
Frequency
Temperature =—4 5.0 cps
Sand content = 65Z by volu<://
Confining pressure = O. 345 a
Axial strain = 1.0x10 Z
.3 cps
V1 Eq 6-19, Richart, Hall
and Woods (1970)
VZEq 5.6, SW—AJA (1972) 05 cps
°/
0!
0
{h
j A A I A A A I I
10 20 30 40 50 60 70 80 90 100
Degree of ice saturation (Z)
Figure 4.23 Influence of degree of ice saturation on
dynamic Young's modulus for frozen
Ottawa sand at 0. 345 MPa confining pressure
Dynamic Young's modulus, Ed (GN/mz)
16
H
I.‘
H
N
H
O
(D
V20.345 MPa,
Hall and
94
Temperature = -4°C Confinin
Sand content = 65Z by volume g
Frequency = 0.3 cps pressure
P Axial strain = 1.0 x 10'2Z 1.378 MPa
v1 1.378 MPa, Eq 6-19, Richart
Hall and Wood (1970)
Eq 6-19, Richart 0.345 MPa
Wood (1970)
0 MPa
L
*-
V71
V72
0 10 20 3O 40 50 60 7O 80 90 100
Degree of ice saturation (Z)
Figure 4.24 Influence of degree of ice saturation on
dynamic Young's modulus for frozen
Ottawa sand at 0.3 cps frequency
16
H
b
H
N
10
Dynamic Young's modulus, Ed(GN/m%
Temperature - -4°C
Sand content = 65%
\\ Confining pressure = 0.345 MPa
‘ Axial strain - .OlZ
Frequency
5 cps
I A I I I I L I I
0 1.0 2.0 3.0 4.0
Salt content (Z by weight)
Figure 4.25 Influence of salt content on dynamic
Young's modulus for frozen Ottawa
sand at 0.345 MPa Confining pressure
Dynamic Young's modulus, Ed (GN/mz)
96
16 -
14 Temperature = -10°C
Sand content = 65Z by volume
Frequency = 0.3 cps
Axial strain 1.0 x 10-2Z
Confining
pressure
1.378 MPa
0.345 MPa
0 MPa
0 A A I I A A I A I A
0 1.0 2.0 3.0 4.0
Salt content (Z by weight)
Figure 4.26 Influcence of salt content on dynamic
Young's modulus for frozen Ottawa
sand at 0.3 cps frequency
97
Axial Strain=.01Z :2 Axial Strain=.01Z
.25 ~Temperature =-1°C .25-Temperature=-4°C
Frequency
_ c . Fre uenc
(a) ( p8) 5,0 (b) ‘1 Y
(CPS)
.20 _ .201
b D
1.0 5.0
. // .15.
p- u-
0.3 .. :1-0
RAW/’9 .101' I
' " W 440.3
.05 D .\\.0.05 .05.
H
U1
H
O
V
Damping Ratio, D
\
F P 40.05
.00 . A ‘ 1 A '00. A A J L
O 0.5 1.0 1.5 O 0.5 1.0 1.5
Confining Pressure (MPa) Confining Pressure (MPa)
Axial Strain=.OlZ
.25 *Temperature=-10°C
'(C)
.20 '
Frequency
9 r (cps)
5?: .
g .15
m P ï¬:5.0
â€a ' " ——-—.l.0
E E’F—i
m .
E 0.3
.05 . #— flo.05
.00 >
I I A I
0 0.5 1.0 1.5
Confining Pressure (MPa)
Figure 4.27 Damping ratio vs. confining pressure for
frozen sand samples of 20Z sand content.
98
Frequency
:3
Axial Strain=.01%
=_ 0
.25 _ N .25_Temperature 4 C Frequency
5.0 _ (b) (cps)
.20- /â€'\.1 0 .20- °-——°f 45.0
Q
0
0H
H
CO
of.
00 P
c:
-H
D. I
E .10 -
In
G .
\0.05
.05 P AXial Strain=.01%
.00 , (a)
l
0
0.5
Temperature==l°C
J
1.0 1.5
Confining Pressure (MPa)
.25
.20
Q
.2 . 15
‘4
TU
05
g> .10
"-4
Q.
E
(U
Q
.05
.00
. (c)
.05’
.00v
1 l
0 0.5 1.0 '1.5
Confining Pressure (MPa)
Axial Strain=.01%
Temperaure=-10°C
Frequency
(Cps)
/ A500
b ---4p_, s—+ol.0
./——-—-————.0o3
--—¢——— 4——90.05
L
0 0.5 1.0 1.5
Figure 4.28 Damping ratio vs. confining pressure for
frozen sand samples of 45% sand content.
Dumping Ratio, D
99
Frequency Q
-£CPS)
.25 r ~“‘-05.0 .
n /—\1.0
.20.
'- /—\0.3
.10 ' Axial Strain=.01Z 0'05-
Temperature=~l°C
.05 . (a)
.00
L J L
0 0.5 1.0 1.5
Confining Pressure (MPa)
Axial Strain=.
.25
b
(e)
.20 -
.15 ~
Dumping Rat io , D
.00
I
0 0.5
Axial Strain=.01%
Temperature=~4°C
25»
(b) Frequency
, (CPS)
.20. 9\\\~‘¥________fl_’fl',,.5.0
.15- .~“‘ï¬r——~ ’_____°1.0
10» ' ~a;0.3
Oï¬- ‘\\\“o~__________——’—'*’0'05
0 0.5 1.0 1.5
Confining Pressure (MPa)
01%
Temperature=-10°C
Frequency
(Cps)
5.0
1.0
.10 h /
_ 0.3
'05 F ::::::::::::::::::::::: 0.05
1.0 1.5
Confining Pressure (MPa)
Figure 4.29 Damping ratio vs. confining pressure for frozen
sand samples of 65% sand
content.
Damping Ratio, D
.25
.20
.15
.10
.00
h
100
Axial Strain=.01Z Q Axial Strain=.01Z
Temperature=-1°C
=_o
.25 Temperature 4 C
(a) 5'0 _(b) Frequency
Frequency (cps)
(CPS) .20-
1.0 I. /——\o 5.0
// .15â€
0.3 _ _ _ 1.0
A I
0 0.5 1.0
Confining Pressure (MPa)
4.; 0.05 .05'
* A 0.05
. .00* . . . ‘
1.5 0 0.5 1.0 1.5
Confining Pressure (MPa)
Axial Strain=.OlZ
25, Temperature=—10°C
20 (C) Frequency
° (CPS)
a .
.9.“ .15-
39 ~ 5.0
gJ 10 -
'3‘ : 4—#o 1.0
E o
g .05 .. .___—.—7 4 .3
00 P .__.._7‘ n l 4‘0.05
0 0.5 1.0 1.5
Confining Pressure (MPa)
Figure 4.30 Damping ratio vs. confining pressure for
frozen gravel samples of 24% gravel content.
101.
Frequency
(a) (cps)
~3d' ,/°"* ‘0 5.0
D
.25-
} 'Iâ€J*,.——— ~—_o 1.0
‘3 .20-
o. D
'3 .._¢ a 0 3
m .15.
m
00 L
.3 0
a. .1 '
SE; _ "—’ ——o 0.05
9 Axial Strain-.017.
.05' Temperature-=1°C
.OOF . .
0 0.5 1.0 1.5
Confining Pressure (MPa)
Axial Strain=.OlZ
Temperature-=4°C
Fre enc
(b) (2:5) y
.25’
. oz/zâ€"—’f ‘_*' 5.0
.20L
~—o 1 0
.15_ .’,.4r—__i
’ o 0.3
o—"""’
.10'
.05“ r—Af ‘0 0.05
.00b
0 0.5 1.0 1.5
Confining Pressure (MPa)
Axial Strain=.01Z
. _= o
.25_Temperature 10 C
’(C)
D .20-
o“ .
H
L)
32.15“
g? ' \ ________.——-. 5.0
3.10.
Q In
’ O
.05- -3
00: o—-—¢f a 0.05
0 0.5 1.0 1.5
Confining Pressure (MPa)
Figure 4.31 Damping ratio vs. confining pressure for
frozen gravel samples of 42% gravel content.
102
Frequency
(a) (CPS)
i_; 5.0
.30r W ,
Axial Strain=.OlA
' C: Temperature=—4°C
.25b 1 0 .25’(b) Frequency
. W ‘3 ° (CPS)
g .20" .20" 5.0
. r k: ‘0 0.3 . /
o
'3 .15. .15- 1.0
g b L //——'o
w 0.3
5‘. .10- °""+ ‘0 0.05 .10' .//—°
2' _ Axial Strain=.01°/. ,
‘g ‘ Temperature=-1°C
05+ .05~ â€/0..— 40.05
- r
.00- . . . . .00- . . L A
0 0.5 1.0 1.5 0 0.5 1.0 1.5
Confining Pressure (MPa) Confining Pressure (MPa)
Axial Strain=.01%
.25 ~ Temperature=ulO°C
' (c)
Q .20 -
a _ Frequency
".1
u (CPS)
i9 .15 r
00 P
:
â€Ã©. .10 . / ——o 5.0
m
‘3 h ‘//â€.’__f ‘_—“‘ 1.0
.05 ’ W i. 0.3
’ N/ 0.05
.00 . . .
0 0.5 1.0 1.5
Confining Pressure (MPa)
Figure 4.32 Damping ratio vs. confining pressure for
frozen gravel samples of 59% gravel content.
103
Axial Strain=.OlZ Q Axial Strain=.01Z
.25-Confining Pressure—O MPa .25-Confining Pressure—0.345 MPa
'(8) ’(b)
.20†20- '
Frequency
D V * (cps)
,3 '15" Frequency '15)
E .. (CPS) . 5.0
on .
.5 .10- 1.0 .10. 1.0
g‘ ———o
.05. \ .05. °
_ ----- -o.05 _ 0-05
.00 .00
1 44 l l l l l J J_ 1 l 1 1 L 1 1 1 I n
-l -4 -7 -10 -l -4 -7 -10
Temperature (°C) Temperature (°C)
Axial Strain=.01Z
.25†Confining Pressure=l.378 MPa
_ (C)
.20.
9 Frequency
. - (Cps)
.2
u .15-
‘E . 5.0
co
.5
E‘.10~ 1.0
m
U ' o 3
~05 . 0.05
.00
f]- l l —ZI l l -i L L_llO
Temperature (°C)
Figure 4.33 Damping ratio vs. temperature for
frozen sand samples of 20% sand content.
104
ial Strain=.01%
Temperature (°C)
Q Axial Strain=.01Z
Confining Pressure=0 MPa Confining Pressure=0.345 MPa
.25 - .25'
(a)
.20 _ Frequency .20, Frequency
(CPS) (CPS)
Q I-
. . 5.0
.2 .15 ,. 5.0 .15-
J.)
:2 ,_ \\‘ P.
\
2° .10 . x ‘x. .10 1'0
‘H x 1'0 F o 3
g I. \ “O 3 . \F .
Q 4____,_.—o
.05 _ s‘ .05- 0 05
“0.0S °
- r
.00 L .OOt
-1 —4 -7 -.O -l -4 -7 ~10
Temperature (°C)
Axial Strain=.01%
.25 r Confining Pressure=l.378 MPa
. (C) Frequency
(CPS)
.20 -
‘3 5.0
.9. .15 -
U
9
‘1‘ 1.0
21°
«4 .10 '
9.
E3 r- 0.3
D \ M
.05 ' 0.05
000 h 1 1 l L 1 l L A J A
-1 —4 —7 -10
Temperature (°C)
Figure 4.34 Damping ratio vs. temperature for frozen
sand samples of 45% sand content.
1105
Axial Strain=.01% 9 Axial Strain=.01Z
Confining Pressure=0 MPa Confining Pressure=0.345 MPa
.25 - .25L
\ (a) (b)
.. \ .
\\‘ Frequency \
20 - ‘ (cps) ‘20- \\ Frequency
o _ _ (CPS)
6‘
'3 15 ’ .15'
w
m _ .
on
.5 .10 . .10-
Q.
E
m . .
a
.05 ~ .05.
0.05 0.05
.00 f .00 . . 44g
-1 -4 -7 -1O -1 -4 -7 -10
Temperature (°C) Temperaure (°C)
Axial Strain=.01Z
Confining Pressure=l.378 MPa
.25 '
(C)
.20 â€
O _ Frequency
55 (CPS)
u .15 .
5.9
a? ’
'3 .10 . 5.0
S
Q r 1.0
.05 . 0.3
. 0.05
'00 14 n n . n n J_I ;
-l —4 -7 -10
Temperature (°C)
Figure 4.35 Damping ratio vs. temperature for frozen
sand samples of 65% sand content.
106
Axial Strain=.01% Cl Axial Strain=.01%
25 Confining Pressure=0 MPa 25 Confining Pressure=0.345 MPa
(a) b h (b)
CI'ZO ' Frequency '20’ Frequency
3 (cps) + (cps)
:0 .15 r .19
E†' ' 5.0
.H :-
§-.10 ' .10
g _ 5.0 . 1.0
1.0 O 3
.05 0.3 '05. \\ .
.00.L44l4__‘1‘0.05.00£‘ 0.05
-1 -4 -7 -1o -1 -4 -7 -10
Temperature (°C) Temperature (°C)
Axial Strain=.Ol% ,
h_Confining Pressure=l.378 MPa
(C)
.25
Q .20 ' Frequency
.3 . (CPS)
u
32 .15 '
g3 - 5.0
I; 10 ’
5‘3 ' 1.0
a D
.05 t 0.3
.00 . 0.05
-l -4 -7 -10
Temperature (°C)
Figure 4.36 Damping ratio vs. temperature for frozen
gravel samples of 24% gravel content.
l-‘
UI
.10
Damping Ratio, D
.00
107
Axial Strain=.01Z
Confining Pressure=0 MPa
(3)
Frequency
(Cps)
-10
Temperature (°C)
.15 '
.10 '
Damping Ratio, D
.05
.00 >
.30
.25
.20
.15
.10
.05
.00
-7
Temperature (°C)
Axial Strain=.01Z
Confining Pressure=0.345 MPa
(b)
Frequency
(Cps)
Temperature (°C)
Axial Strain=.OlZ
Confining Pressure=l.378 MPa
(C)
Frequency
(Cps)
5.0
1.0
0.3
0.05
-10
Figure 4.37 Damping ratio vs. temperature for frozen
gravel samples of 42% gravel content.
.30
.25
N
O
o
H
U1
Damping Ratio, D
L O
c:
O
U1
C
O
Axial Strain=.01%
(a)
(CPS)
.30 F
N
U1
N
O
l'-‘
U1
.10 »
Damping Ratio, D
.05 r
.00
Confining Pressure=
108
0 MPa
Frequency
(C)
Q
.30
.25
.20
.15
.10
.05
.00
Axial Strain=.01Z
Confining Pressure-0.345 MPa
(b)
Frequency
(CPS)
b 5.0
L-
1.0
' 0.3
L.
L 0.05
-1 —4 —7 -10
Temperature (°C)
Axial Strain=.01%
Confining Pressure=l.378 MPa
Frequency
(CPS)
Temperature (°C)
Figure 4.38 Damping ratio vs. temperature for frozen gravel
samples of 59% gravel content.
109
. Axial Strain=.01Z Q Axial Strain=.01%
Confining Pressure=0 Mpa Confining Pressure=0.345.MPa
25 ’ .25'
(a) _ (b)
.20 ’ .20’
a - '
5.15 _ .15.
-H
u
m
m ' '
21° .10 _ .10,_
H
O.
E . p
m
c:
.05 . .05-
.00 .00-
0.05 0.3 1.0 5.0 0.05 0.3 1.0 5.0
Frequency (cps) Frequency (cps)
Axial Strain=.01%
.25» Confining Pressure=l.378 MPa
(C)
.20-
c:
.0“
S .15r
g D
es
c
21.10*
E
m
c:
.05.
p
.00
0.05 0:3 150 5.0
Frequency (cps)
Figure 4.39 Damping ratio vs. frequency for frozen
sand samples of 20% sand content.
110
Axial Strain=.01Z c: Axial Strain=.01%
Confining Pressure=0 MPa Confining Pressure=0.345 MPa
.25. (a) .25+ (b)
r b
.20- .20»
o - ~
.3 .15» .15’
U
m
m - *
°° L
.S .10†.10
Q.
E". .
m P
c:
.05“ .05'
.00 .00
1.0
Frequency (cps)
1:0 5.0 0.05 0.3
Frequency (cps)
0.05 0.3
Axial Strain=.01Z
Confining Pressure=l.378 MPa
.25b (c)
.20'
Q P
o“ .15-
H
.5.)
g F
2° .10-
H
9..
a .
m
::
.05P
.00
1.0
0.3
Frequency (cps)
0.05 5.0
Figure 4.40 Damping ratio vs. frequency for frozen
sand samples of 45% sand content.
lll,
Axial Strain=.01Z :: Axial Strain=.01Z
25 ’Confining Pressure=0 MPa 25_Confining Pressure=0.345 MPa
(3) (b)
Temp
.20 _ Temp .20_ (°C)
(°C)
a
6.15 .. -l .15_
H
4H
g .
5:"
'H .10 ' .10.
O.
E
m D
c:
.05 ’ .05’
‘ ’ -10
.00 .OOL
0.05 0.3 1.0 5.0 0.05 0.3 1.0 5.0
Frequency (cps) Frequency (cps)
Axial Strain=.OlZ
Confining Pressure=l.378 MPa
.25“ (c)
y.
.20.
c:
.3 .15-
4.)
£2 .
co
:3. .10-
a
(U )-
c:
.05-
.OOr 4L
0.05 0.3 1.0 5.0
Frequency (cps)
Figure 4.41 Damping ratio vs. frequency for frozen sand
samples of 65% sand content.
.25
.20
Damping Ratio, D
112
Axial Strain=.01%
Confining Pressure=0 MPa
(a)
.00
_ Temp.
(°C)
' —l
-4
L .‘10
0.05 0.3 1.0 5.0
Frequency (cps)
.25
.20
.15
.10
.05
Axial Strain=.01%
Confining Pressure=0.345 MPa
(b)
,
P
’ Temp.
. (°C)
b
h -l
- -4
. I l l l -10
0.05 0.3 1.0 5.0
Frequency (cps)
Confining Pressure=l.378 MPa
—1
-4
-10
l
Axial Strain=.01Z
(C)
.25,
a .20.
6 .
‘3
o .15-
a:
on
E.
3.10P
o
O I
.05'
.00 P
0.05
0.3 1.
O 5.0
Frequency (cpS)
Figure 4.42 Damping ratio vs. frequency for frozen gravel
samples of 24% gravel content.
H N
C UI
Damping Ratio, D
L- a.
c> U!
0
U:
C)
C
113
Axial Strain=.01%
Confining Pressure=0 MPa
(a)
L.
Temp.
' (°C)
' -1
—4
-10
0.05 0.3 1.0 5.0
Frequency (cps)
.15)
.10
Damping Ratio, D
.00"
:1
Axial Strain=.01%
Confining Pressure=0.345 MPa
.30- (b)
.25"
. Temp.
.10
(°C)
.05
.10- _1
p.
.05 -4
.00. ~10
0.05 0.3 1.0 5.0
Frequency (cps)
Axial Strain=.01%
Confining Pressure=l.378 MPa
0105
033
110
Temp.
(°C)
-1
—4
-10
5:0
Frequency (cps)
Figure 4.43 Damping ratio vs. frequency for frozen gravel
samples of 42% gravel content.
114
Axial Strain=.01% :1 Axial Strain=.01Z
Confining Pressure=0 MPa Confining Pressure=0.345 MPa
.30 - .30-
(a)
25 ' .25'
o . .
.9. .20 t .20'
u . Temp. #
£3 (°C)
00 15 - .15â€
a
H b
a .
E -1
g .10- -1 .10b
' F
' - a ' _
.05 _4 .05 4
.00 - -10 .00- . . . -10
0.05 0.3 1.0 5.0 0.05 0.3 1.0 5.0
Frequency (cps) Frequency (cps)
Axial Strain=.01%
30* Confining Pressure=l.378 MPa
.25'
5‘ .20'
.2 i
4..)
£2 .15
:0 I
.5
a. .10’
E
m b
a:
.05†-4
' -10
.00‘ .
0.05 0.3 1.0 5.0
Frequency (cps)
Figure 4.44 Damping ratio vs. frequency for frozen gravel
samples of 59% gravel content.
115
(a
Frequency
", (CPS)
.
N
U?
\ V
O C
F4 F1 n:
O U1 Q
\
U1 0
° C
O
0.05
O
(.0
Damping Ratio, D
c.
Ln
Axial Strain=.01Z
Temperature=—1°C
.00
10 20 30 40 50 60 70
Sand Content (% by Volume)
A
:3 Axial Strain=.01‘Z
Temperature=-4°C
.25 r(b) Frequency
. (CPS)
.20. I /\ 0.05
.15 /\ 003
.10 . ¢//////â€,,o——————“0 1.0
.05 r- /‘—_\O 5.0
P
.00 l l A A l l
10 20 30 40 50 60 70
Sand Content (% by Volume)
25 Axial Strain=.01%
' Temperature—=10°C
20 _ (C) Frequency
(CPS)
::
o“ .15
SH
3.)
a ./â€,,——4L___—..i\\\u 0.05
2’ 10 _
.H oâ€â€â€™â€”——‘_-——““\\.
2‘ 0.3
‘3
05 . 1.0
5.0
.00
10 20 30 40 50 60 70
Sand Content (Z by Volume)
Figure 4.45 Damping ratio vs. sand content for frozen sand
samples at 0.345 MPa confining pressure.
.25
.20
.10
Damping Ratio, D
.00
.15 .
p
b-
b
Axial Strain=.01%
_Confining Pressure=0 MPa
Temp
(°C)
(a)
A L A l J.
10 20 30 40
Sand Content (% by Volume)
Damping Ratio, D
1116
70
.25
.20
.15-
.10
.05’
.00
Axial Strain=.01Z
.Confining Pressure=0.345 MPa
Temp
*(b) (°c) -1
p
A -10
I J
10 20 30 40 50 6O 70
Sand Content (% by Volume)
Axial Strain=.OlZ
Confining Pressure=l.378 MPa
.25†Temp
(°C)
(C) _1’
.20‘
.15. _4
.10. M/‘Hlo
.05-
.00 I 1 A j A A A I A A
10 20 30 50 60 70
Sand Content (% by Volume)
Figure 4.46 Damping ratio vs. sand content for frozen
sand samples at 0.3 cps frequency.
.30
Damping Ratio, D
La k: R:
U1 c> u.
0
U!
C
O
H
O
117
Frequency
(a) (CPS) ‘3 Axial Strain=.OlZ
0-05 '._ Temperature=-4°C
’ .30
L (b)
Frequency
' .25' (cps)
0.3 , .
p .20. ‘/////—o~\\\\\~
1-0 r 0.05
' .15' 0.3
L
5.0 .10» /_\° 1'0
Axial Strain=.01Z 05L
Temperature=-1°C ° N 5.0
.,..l . - . a. . . L,. .00’ . . .. . . . . . l .
10 20 30 40 50 60 70 10 20 30 40 50 60 70
Gravel Content (Z by Volume)
.30
Damping Ratio, D
L: L: k;
UI 0 Ln
H
O
O
U1
10
Gravel Content (Z by Volume)
Axial Strain=.01Z
Temperature=-10°C
(C)
Frequency
(CPS)
“ 0.05
V—‘N 0.3
A 1.0
A 5.0
A A A j A A A A A A A
20 30 40 50 60 70
Gravel Content (Z by Volume)
Figure 4.47 Damping ratio vs. gravel content for frozen
gravel samples at 0.345 MPa confining pressure.
.30
.25
Q 20
6‘
«4
g .15
Ct.
00
.E
9. .10
I:
('0
c:
.05
.00
F
b
b
P
10
2118
Axial Strain=.OlZ
Confining Pressure=0 MPa
(8)
Temperature
(°C)
—1
))
-10
A A 4 A A 1
20 30 40 50 60 70
Gravel Content (Z by Volume)
I l A
.30 L
~ (C)
N
L}:
.30F
.25
.20
.15-
.10‘
.05'
.00
L
L
L
b
Axial Strain=.OlZ
Confining Pressure=0.345 MPa
(b)
Temperature
(°C)
-1
'/,/â€"_-““u i-a
""—"\o -10
l A l J A A A l l J
10 20 30 40 50 60 70
Gravel Content (Z by Volume)
Axial Strain=.OlZ
Confining Pressure=l.378 MPa
Temperature_
(°C)
-1
a
0.20 '
0
.,.q _
‘3
cm .15 ’ d//,/â€â€˜P_-“‘ -4
00
a b
-H
2‘ 10 ~
m .
a _ oâ€'—_‘L“~\\°
-10
05 P
.00 .
A A A A A
A l A
A l L
10 20 30 40 50 60 7O
Gravel Content (Z by Volume)
Figure 4.48 Damping ratio vs. gravel content for frozen
gravel samples at 0.3 CpS frequency.
Damping ratio, D
.28
.26
.24
.22
.20
.18
.16
.14
.12
.10
.08
.06
.04
119
Temperature = ~4°C
Sand content = 65Z by volume
Frequency = 0.3 cps
Axial strain = 1.0 x lO'ZZ
<> 1.378 MPa
0 0.345 MPa
[3 0 MPa
(>1Damping ratio of dry sand
(sw—AJA, 1972)
< 03=1.378 MPa
F
0 10 20 30 40 50 60 70 80 90 100
Degree of ice saturation (Z)
Figure 4.49 Influence of degree of ice saturation on
damping ratio for frozen Ottawa sand
at 0.3 cps frequency
Damping ratio, D
120
Temperature = -10°C
’28 ’ Sand content 8 65% by vol.
£5 Confining pressure = 0.345 MPa
.26 P Axial strain = .OlZ
Frequency:
.24 . <> 5.0 Cps
SAX (D 0.3 cps
22 , A\ A 0.05 cps
' \\ 9 ()1 SW-AJA, P143, Fig. 574
\ \ \ (1972)
.20 - A \ \
.18 - \\ ‘~ .g “_
\\ .05 cps
. ‘\
16 \é; \\
\x
‘\
.14-1, ‘\
é> \ 0\
o \ \
.12 ~ \ o \
\\ “~‘\
10 ’ \ 0\
. \ .3 CPS
08 \\\\
<> \\
\
.06» ‘\ ‘\~
(>\
.04 L 4 4 1 1 k ‘ J L 5 CPS
0 10 20 30 40 50 60 70 80 90 100
Degree of ice saturation (Z)
Figure 4.50 Influence of degree of ice saturation on
damping ratio for frozen Ottawa sand
at 0.345 MPa confining pressure
Damping ratio, D
121
.22L
.20-
.18.
Temperature = -10°C
Sand content = 65Z by volume
.16- -
Frequency - 0.3 cps
14 Axial Strain = 1.0 x 10’2Z
Confining Pressure
0 MPa
0.345 MPa
1.378 MPa
.04-
.02’
0 1.0 2.0 3.0 4.0
Salt content (Z by weight)
Figure 4.51 Influence of salt content on damping
ratio for frozen Ottawa sand at
0.3 cps frequency
Damping ratio, D
.24
.22
.20
.18
.16
.14
.12
.10
.08
.06 "
.04
.02
122
Temperature = ~10°C
Sand content = 65Z by volume
Confining pressure = 0.345 MPa
Axial Strain 1.0 x 10’2Z
Frequency
A 0.05 CPS
P 0.3 cps
1.0 cps
L A 1 l
1.0 2.0 3.0 4.0
Salt content (Z by weight)
Figure 4.52 Influence of salt content on
damping ratio of frozen Ottawa
sand at 0.345 MPa confining pressure
Table 4.6 Experimental data of creep tests
123
040010 «0. 051-2 001:3 051-4
2 5400 04.0 03.0 03.7
ICE
0410041100 92.0 90.0 95.2
121
0000111 1007001 «.4. 2. 2.03
1011141
514110 1040 1300 090 2070
(KN/Hath)
1100 510410 1100 510410 1100 010410
0147500 0140500 0142550
(0001 1x0.0121 (0501 (10.0121 (5001 (40.0111
0 0.0 0 0.0 o 0.0
10 1.40 00 0.045 10 2.712
42 4.03 130 1.009 34 5.750
0 100 0.03 170 2.130 52 7.305
x 170 7.75 250 2.545 100 11.159
0 310 10.07 310 2.004 194 15.000
E 450 11.09 452 3.500 300 19.240
0 004 14.31 504 3.909 434 23.444
1 724 15.170 732 4.410 554 27.132
0 709 15.752 952 5.109 000 30.929
0 1100 19.910 1172 5.709 020 34.740
0 1730 24.747 1454 0.409 900 30.300
1 2100 20.450 1732 7.055 1120 42.332
A 2090 32.245 1950 7.010 1274 45.930
L 3290 30.304 3512 11.419 1410 49.347
4050 41.212 5372 14.940 1550 52.574
0 5030 40.730 7472 10.400 1720 50.304
4 5710 50.509 9332 21.191 1000 50.110
1 0390 54.100 11032 24.004
A 13724 27.002
15020 29.002
10420 32.019
21500 30.500
25114 40.237
20314 43.500
32200 47.340
35214 50.200
124
Table 4.6 (Continued)
SAHPLE N0. 881-5 881-6 851-7
2 SAND 63.6 64.3 64.5
ICE
SATURAlION 41.0 38.9 41.7
(2)
BENSITY (EH/CC) 1.83 1.84 1.86
INITIAL
STA1IC 1040 690 345 518
(KN/n10;
TIHE SFRAIN 116E SIRAIN TlflE STRAIN
ELAPSEU ELAPSED ELAPSED
(SEC) (X0.012) (SEC) (X0.011) (SEC) (X0.0121
0 0.0 0 0.0 0 0.0
16 4.182 12 4.57 2 1.433
30 10.364 46 5.65 22 3.851
E 66 13.841 86 6.26 6? 5.960
X 170 18.114 126 6.77 fl’2 7.807
P 330 22.124 186 7.37 282 11.754
E 510 25.446 266 8.00 462 14.783
R 778 29.182 546 10.717 682 17.649
I 1150 32.909 966 13.570 934 20.330
0 1534 36.237 1386 15.835 1342 23.710
E 2054 39.959 1886 18.142 1702 26.198
N 2690 43.782 2406 20.212 2282 29.631
1 3214 46.691 3066 22.531 2830 32.348
A 3950 50.241 3878' 25.062 3542 35.455
L 4750 53.632 5006 28.161 4282 38.247
5010 54.900 6166 30.925 4994 41.104
0 7306 33.439 5974 44.084
A 8826 36.546 6994 46.941
1 10266 39.217 8222 50.053
A 11766 41.829 8562 50.893
13234 44.254
14986 46.954
16566 49.270
18566 52.055
19126 $2.863
125
Table 4.6 (Continued)
D-ibu
SAMPLE N0. CSI-9
2 SAND 63.6
ICE
SATURATION 6.5
(1)
DENSITY (EH/CC) 1.71
INITIAL
STATIC LflAn 173
(KN/nxn)
TIHE STRAIN
ELAPSED
(SEC) (X0.011)
0 0.0
12 3.66
44 12.722
E 96 18.900
X 148 23.752
P 216 28.649
E 296 33.408
R 392 38.397
I 476 42.424
H 556 45.903
E 636 48.923
N
T
A
L
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CHAPTER 5. DISCUSSION
The dynamic behavior of frozen granular soils is
discussed in terms of mineral volume fraction, ice satur-
ation, and saline content in sections 5.1 through 5.3.
The effect of tensile failure and parameter application
sequence on the test results are explained in sections 5.4
and 5.5. Typical test results from studies of dynamic
properties of several types of frozen soils are compared
in section 5.6. The similarities and differences are
identified and discussed. This chapter ends with a
discussion on the dynamic creep behavior and a trial pre-
diction of dynamic creep strength using a power equation.
5.1. Mineral Volume Fraction and Dynamic
Behavior of Frozen Granular Soils
For temperatures at -l.2°C and above, there is a
rapid decrease in hardness of ice. ‘It appears that this
behavior is due primarily to the onset of pressure melting
(Barnes and Tabor, 1966). For samples with a low mineral
volume fraction, it appears that strength of the ice matrix
is the major factor controlling the strength of frozen
granular soils. As the mineral content increases, the
sand particles have more and more opportunity to contact
130
131
each other. An external load produces stress concentration
at contact points which result in pressure melting and
plastic flow of the ice in the vicinity of the contact
points (Goughnour, 1967) and reduce the shear strength for
samples tested at -l°C. The pressure melting process
appears to explain why the dynamic Young's modulus decreases
with increasing sand content for samples tested at -1°C.
For samples tested at -4°C and -10°C, the pressure
developed due to stress concentration has less influence
on pressure melting (Barnes and Tabor, 1966). The ice
matrix is stiffer at temperatures below the —1.2°C and
provides a stronger confinement to soil particles. As
the mineral volume fraction increases, the solids gain
more opportunity to contact each other with an increase
in friction between particles. This friction contributes
to the strength of the sample tested and contributes to an
increase in the modulus with increasing mineral content.
The mineral content at which soil particles first
have contact is approximately 42% by volume (Goughnour and
Andersland, 1968). The test results obtained in this
study show that the effects of pressure melting and
friction both become most obvious at mineral volume frac-
tions above 42%, which agrees with the earlier study.
132
5.2. Ice Saturation and Dynamic BehaVior
of Frozen sand
The dynamic Young's modulus increases with degree
of ice saturation as shown in Figure 4.23. The unsatur-
ated part of the voids was filled with air or vapor. For
granular soils essentially all water in the sample was
frozen at the test temperature of -4°C.
It is reasonable to assume that the available ice
bonding between sand particles would reduce as the ice
saturation decreases and thus the apparent strength of the
frozen sand mass would be reduced. As the ice saturation
goes to zero, the strength of the sample should approach
the strength of dry sand under a similar test condition.
The test results presented in Figure 5.1 show a decreasing
dynamic modulus with decreasing ice saturation. The dynamic
modulus appears to approach a constant value at lower
degrees of ice saturation. This fact agrees well with
the dynamic modulus values published by other investi-
gators (Richart, Hall and Woods, 1970; SW—AJA, 1972).
A comparison between Figures 4.23 and 4.9b is
presented in Figure 5.1. The line with arrows representing
a 707. ice saturated frozen sand sample with 657. sand
content and test temperature of -4°C, has the same
modulus as a saturated sample with the same sand content
tested at -2.2°C. This parallel relationship is presented
133
in Figure 5.2. From Figure 5.2, the modulus of an under-
saturated sample may be predicted by correlating to a
saturated sample with known properties. The influence of
testing frequency on the corresponding relationship
appears to be minor.
5.3. Saline Content and Dynamic Behavior
of Frozen Sand
The dynamic Young's modulus decreases with an
increase of saline content as shown in Figure 4.25. A
comparison of the saline content effect on both dynamic
strength of frozen sand and volume fraction of frozen water
is shown in Figure 5.3. The dashed line indicates the
volume fraction of frozen water as a function of saline
content. Data points on the dashed line were obtained
from curves shown in Figure 2.4 for a temperature of -10°C.
The relationship between percent volume of frozen water and
saline content appears to be linear whereas the dynamic
strength decreases non-linearly with increasing saline
content. The difference may have been caused by the non-
linear relationship between modulus and ice—saturation shown
in Figure 4.23. In Figure 4.25, dynamic Young's moduli
tend to approach a constant value in a range of salt
content from 2% to 4%‘WhiCh corresponds to an ice saturation
from 70% to 90%. In Figure 4.23, the dynamic Young's
moduli approach a constant value in a much lower range of
134
ice saturation. This observation leads to the fact that
the non-linear relationship between dynamic Young's modulus
and ice saturation cannot be the only reason which causes
a nonlinear relationship between modulus and salt content.
Weeks and Assur (1967), in their study of the
mechanical properties of sea ice, suggested that during
the formation of sea ice, salts are rejected and the salt
concentration increases in the water immediately in front
of the ice-water interface. When the salt concentration
is sufficiently high, the interface becomes unstable and
the salt is incorporated into the ice as brine pockets.
These brine pockets, if formed in the soil samples, would
influence the mechanical properties of the ice matrix in
the frozen saline samples.
The curves shown in Figure 2.4 were based on the
theory of pure solution. No consideration was given to
possible surface effects at the interface between soil
particles and saline pore water. The factor warrants
additional consideration in future projects.
A comparison between Figure 4.9b and Figure 4.25
is presented in Figure 5.4. The arrows in the figure
show that a 1.5% saline frozen sand sample tested at -10°C
will give approximately the same modulus as a fresh water
frozen sand sample tested at -2°C. Similar comparisons
between Figure 4.9b and 4.25 result in the curves shown in
135
Figure 5.5. From Figure 5.5, the modulus of a 65% mineral
volume fraction saline sample can be evaluated by corre-
lating its property to a fresh water frozen sample tested
at higher temperature. To fully establish these kinds of
correlations, more tests are required.
5.4. Tension Failure and Effects on
Experimental Results
All samples tested to failure failed with a tension
crack at the level of the aluminum coupling plates where
the sample's cross section was the smallest. For those
samples tested closetx>failure, a deformed or bent hyster-
esis loop (Figure 5.6) was observed on the oscilloscope.
This bent loop shows a reduced tensile load compared with
the compressive load, and leads to a reduced stress for
the same strain. Thus, the resulting dynamic Young's
modulus was reduced and the damping ratio increased. A
bent loop is a clear signal of the emergence of such a
failure plane. Failure of the ice matrix along the
direction of tensile stress may have started earlier in
the test. Failure of the ice matrix would influence test
results before the appearance of a bent loop. This tension
failure is believed to be the reason for some unexpected
drops in modulus data and rises of damping ratios for
tests run at colder temperatures, higher strains, lower
confining pressures and higher mineral volume fractions. A
136
combination of some of these conditions would be sufficient
to reduce the modulus and to increase the damping ratio.
All questionable data points were corrected and shown by
dashed lines in the figures presented in Chapter 4.
Tension failure prevented certain samples from being
tested at higher strains.
5.5. Application Sequence of Test Parameters
and Effects on Experimental Results
The stage testing technique (Silver and Park, 1975)
used in this study involved an application sequence of test
parameters as shown in Table 3.2. The application sequence
effect on the accuracy of the experimental results is still
under discussion by some researchers.
Several high mineral fraction frozen sand samples
were tested to verify the influence of the testing
sequence. The testing sequence for these samples,
numbered from SI-102 to 81-106, are tabulated in Table 5.1,
and typical experimental results are shown in Figures 5.7
and 5.8.
Each of these samples was first tested at the
lowest strain, highest confining pressure, and lowest
frequency to verify the initial character of the sample.
Due to difficulty in preparing duplicate samples having
the same void ratio and density, some samples may have
been somewhat stiffer or softer.
137
From.Figure 5.7, note that sample No. 102 shows the
modulus and damping ratio in the same range as those
obtained previously. Sample No. 106 (Figure 5.8) shows
the same modulus as those obtained before. Samples No.
103, 104 and 105 are relatively stiff by character
because of their higher modulus at the lowest strain. Data
points for higher strain levels are also generally higher,
but they follow the same trend (slope of best fit line) as
the one shown in the figure. The damping ratios for samples
No. 103 and 106 are generally higher. These results show
that the influence of test parameter application sequence
on the dynamic properties of frozen sand samples was minor.
5.6. Comparison of Expegimental Results
with’Previous Data
The dynamic properties of frozen granular soils
obtained in the present study are compared with data from
other investigators (Kaplar, 1969; Nakano and Froula, 1973;
Stevens, 1975; Chaichanavong, 1976; Czajkowski, 1977) for
several soil types in Figures 5.9 through 5.11. A legend
identifying the soil type and source has been included.
For the purpose of a direct comparison, the dynamic
properties obtained in all of the studies were converted
to common units. Thus, dynamic stress-strain properties
are presented in terms of longitudinal wave velocities and
damping properties are presented in terms of damping ratios.
138
Values of dynamic Young's modulus obtained in the present
study were converted to longitudinal wave velocities
using:
/2
vL = (Ed/o)1 (5.1)
<
11
where L longitudinal wave velocity,
Ed = dynamic Young's modulus,
p = mass density of the material = Y/g.
y = unit weight of the material, and
g = acceleration of gravity.
Values of damping ratio were calculated from phase lag
angles determined in previous studies using:
D = sin-g ‘ (5.2)
where D damping ratio
6 phase lag angle
Figure 5.9a shows that the longitudinal wave velocity (VL)
of frozen soils increases as temperature decreases. The
lower longitudinal wave velocities given by the cyclic
triaxial test data are related to the lower loading
frequencies and higher axial strains. The damping ratio
decreases with descending temperatures (Figure 5.9b) and
139
is higher for the frozen cohesionless soils as compared to
cohesive soils. Resonant column tests (Stevens, 1975) give
the lower damping ratios for the frozen Ottawa sand and
frozen silt, which is believed to relate to the relatively
higher frequency and lower axial strain amplitude.
Because of the larger particle size and the smaller
specific surface area, a frozen Ottawa sand system
contains much less unfrozen water compared to frozen silts
or clay at the same negative temperature (Dillon and
Andersland, 1966). In other words, almost all the
moisture in a frozen sand system freezes at a negative
temperature close to the freezing temperature of the
water. Therefore, a more abrupt change in longitudinal
wave velocities for frozen sand is seen in Figure 5.9a and
the velocities tend to approach a constant value after the
relatively abrupt deflection as the temperature decreases.
The relationship between wave velocity and temperature for
frozen gravel is somewhat different from above. An abrupt
change is not shown throughout the temperature range
studied. It is believed that the size of pore ice in a
frozen gravel system is larger than that in a frozen sand
system. Thus, the stiffness of pore ice in a frozen
gravel system contributes to the strength of the total
system more directly than the pore ice in frozen sand. As
140
the temperature decreases, the pore ice in frozen gravel
becomes stiffer, and so is the total system.
The effect of loading frequency on the longitudinal
wave velocity and damping ratio of several frozen soils
at -4°C is shown in Figure 5.10. Available data cover
only the lower and higher portions of the frequency
spectrum. The longitudinal wave velocity (Figure 5.10a)
increases gradually with increasing frequency and appears
to be relatively independent of soil types. The damping
ratio (Figure 5.10b) decreases with increasing loading
frequency. Damping ratios obtained with the cyclic
triaxial test are in general higher, which is believed to
relate to the higher strain and lower frequency.
The influence of confining pressure on dynamic
properties of frozen soils was investigated in the
current research only with cyclic triaxial techniques. A
comparison of confining pressure effects on various frozen
soil systems is shown in Figure 5.11. Generally, confining
pressure does not have a significant influence on either
the dynamic Young's modulus or damping property of frozen
soils. An increase of modulus with increasing confining
pressure for frozen granular materials is the only excep-
tion. For a frozen sand or a frozen graVel system.with a
high.mineral volume fraction, confining pressure greatly
increases the contact pressure between particles or between
141
particles and ice, thus the dynamic elastic strength of
the sample is increased. For the frozen silt or frozen
clay system tested in the previous studies, confining
pressure may only increase the pressure in the unfrozen
pore water and ice matrix with little or no increase in
effective contact pressure. Therefore, the effect of
confining pressure on frozen fine-grained soils would be
minor.
The dynamic prOperties of a frozen sand system
and a frozen gravel system.are very much comparable for
most of the cases. However, a direct comparison between
'these two systems is not appropriate due to the different
mineral composition and the different shape of particles,
which was not considered as a part of this research project.
5.7. Dynamic Creep Behavior of
Frozen Sand
Creep behavior of frozen soils is commonly domin-
ated by secondary creep. The strain developed in the
secondary-creep period is generally large compared with
the strain developed during primary-creep. The creep
curve for this case can be well approximated by adding a
steady state creep strain, €(c), to a pseudo-instantaneous
strain, 5(i), which occurs at time equal to zero (Figure
2.1a). The pseudo-instantaneous strain is the combination
of an elastic portion and a plastic portion, hence
142
8(1) = E(ie) + €(ip) (5.3)
The elastic portion, €(ie), can be expressed as
e‘ie) = €1ng (5.4)
where E(T) is a fictitious elastic modulus. It is smaller
than the instantaneous elastic modulus because €(ie) also
contains the delayed elasticity effect.
For the plastic portion, Ladanyi (1972) has written
(ip)
e as a power expression,
. k(T)
(1") = [ ° 1 (5.5)
E 6k okZTS
where Gk plays the role of a temperature dependent defor-
'mation‘modulus.
The slope of the straight line represents the
constant strain rate of the secondary creep, éCc), hence
( )
a“) = 94c};— (5.6)
This strain rate can also be written as a power
expression,
Eu.) n(T)
- o
- eclgzzfy] (5.7)
143
where oc(T) and n(T) are creep parameters, both dependent
on temperature. The proof stress oc (Hult, 1966) is the
uniaxial stress which would generate an arbitrarily selected
creep rate ac when applied to the frozen soil. Therefore,
the total strain can be summarized as
(2.3)
For frozen Ottawa sand samples subjected to cyclic
triaxial loads, creep curves were obtained as shown in
Figures 4.53 to 4.55. These creep curves conformed well
to those obtained in static creep tests. By extending the
straight line portion of each curve back to an intercept
time equal to zero, a pseudo-instantaneous strain €(i) and
a constant strain rate é(c) corresponding to the secondary-
creep period can be found. Assume €(ie) to be small and
let 8(1) = €(ip)’ then the total strain would be:
)n
_ c: k - o
e — €k(3;) + t€c(3_ (5.8)
C
when k, n, 0k, 0c can be determined experimentally.
Using the experimental results obtained from samples
CSI-Z, 3, and 4 for approximately 92% ice saturation, and
samples CST-5, 6, and 7 for approximately 40% ice saturation,
two creep strain constitutive equations can be established:
144
e = 1.0 x 10'3(§2)°-325 + t-1.0 x 10‘3(§7)1°66“ (5.9)
for 40% ice saturation, and
+ t-1.0 x 10’8(§gï¬)2-639 (5.10)
for 92% ice saturation.
The procedure for establishing these equations
included the following steps:
(1) Determine 5(i) and é<c> for each creep curve.
This can be accomplished by either a graphical method or
by statistical analysis of data poi t in thecstraight
line portion of the creep curve. 8 1 and e values
for CST-2 to CSI-7 are shown in Table 5.2.
(2) Plot 8(1)'s and é(c)'s versus axial stress
and then determine n and k graphically. Values of 9k
and 0 ‘were based on the graphs at a very small proof
strai e and a small proof strain rate é selected for
conveniehce (Figures 5.12 and 5.13). c '
(3) Substitute the values for n, k, oc, 0k, sk,
and so into Equation 5.8 to establish Equations 5.9 and
5.10.
For estimating the long term strength of frozen
soils, Vialov (1959) provided experimental data showing
that for time intervals greater than about 24 hours the
pseudo-instantaneous strain becomes less significant
compared with the creep strain, thus the first two terms
in Equation 2.3 can be neglected and the creep strain can
145
be expressed as
(5.11)
The creep strength, or the creep stress at failures can
then be written as
8f 1/
o = o (-,——) n (2.2)
f C e t
c f
This equation can be used to evaluate the long term strength
of frozen soil under cyclic loads. Using the creep
parameters determined experimentally, for an assumed failure
strain of 15%, a ten-year service life of a structure,
and a 92% ice saturated sand as subsoil, the creep strength
is
290 x ( -8 0.15 )1/2.639
1.0 x 10 x 10 x 365 x 86400
91.5 kN/mz
This creep strength represents the initial
static stress or the mean stress level during the cyclic
loading period. In each of the dynamic creep tests con-
ducted in this study, the samples were initially loaded
with a static stress to a certain level of strain and then
a cyclic load was added about the initial static load. An
146
immediate change or discontinuity of the creep curve was
not observed after the application of the cyclic stress.
Therefore, the cyclic stress may not have an immediate
effect on the creep behavior of the sample. The influence
of cyclic stress on long term creep behavior cannot be
easily identified because of lack of directly comparable
data. Information provided by Parameswaran (1979) and
Bragg (1979) can be used for a rough comparison. Such a
comparison is presented in Figure 5.14 and Table 5.3. The
"n" value, which represents the cotangent function of the
slope of a creep stress versus strain rate curve appears
to be a good indicator of creep strength. A steeper
slope or a lower "n" value signifies a higher susceptibility
to creep failure. From the comparison shown in Table 5.3,
it did suggest a much lower creep strength for cyclicly
loaded samples and led to a conclusion of higher possibility
of creep failure under dynamic loading conditions. The
effect of the frequency and magnitude of the cyclic load
was not studied.
To compare Figure 4.56 with Figure 2.2b, it is
obvious that the degree of ice saturation shown in Figure
4.56 plays the same role as the confining pressure in
Figure 2.2b. This serves as a basis for accepting the
confining effect of the ice matrix on the dynamic behavior
of the frozen granular soils.
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Corresponding Temperature (°C)
148
-8 _ Sand content = 65% by volume
03 3 0.345 MPa
81 = 0.0179
-6~
Frequency
4 0.3 Cps
- I 0.05 cps
-2-
0 , . . l, J
O 20 40 60 80 100
Degree of ice saturation (2)
Figure 5.2 Influence of degree of ice saturation on
dynamic Young's modulus at -4°C expressed
in terms of corresponding temperatures
2
Dynamic Young's Modulus, Ed (CN/m )
14
H
N
5.:
O
on
149
Volume of frozen water
as a function of salt
733‘. content at -lO°C
\\A\\ (Yong, et a1., 1978)
\
Frequency
(CpS)
5
OOH
Ob)
U‘I
[Figure 4.25]
Temperature = -10°C, Sand content = 65%
100
90
80
7O
60
03 - 0.345 MPa, 81 = 0.01%
1.0 2.0 3.0 4.0 5.0
Salt content (Z)
Figure 5.3 Comparison of salt content effect and
Z volume of water frozen at -10°C on
the dynamic Young's modulus
% Volume of water frozen
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151
Sand content = 65% by volume
03 = 0.345 MPa
61 = 0.01%
_ 0.05 cps
0.3 cps
1.0 cps
0 1.0 2.0 3.0 4.0
Saline Content (Z)
5.5 Influence of sailine content to dynamic
Young's modulus at -lO°C, expressed in
terms of the corresponding temperature.
152
////
(a)
Axial
stress, 01
_ Tension
Cc _ 8t (b)
0c > 0t 1?
/ $01: Axial
///l T% strain, 61
Compression
[<— 6c -—><——ct —>1
Figure 5.6 Bent hysteresis loops (a) an oscilloscope
picture (b) Definition of terms
Dynamic Young's Modulus, Ed (GN/mz)
Damping ratio, D
153
16 (a)
T = -4°C
14 f = .05 cps
102 03 = 1.378 MPa
9A A Sand content = 65% by volume
12
8
6
4
2
O
-3.0 -2.5 -2.0 -1.5 -1.0 -O.5 0.0
Log percent axial strain
.275h (b)
T = -4°C
.25 - f = .05 cps
G3 = 1.378 MPa
Sand content = 65% by volume
.225â€
A 102 #_
.20 . 0102 A A A
//—-i a
£5 £1
.175b
.15 ‘
.125 n s j n L n l
-3.0 -2.5 -2.0 -1.5 -l.0 -0.5 0.0
Log percent axial strain
Figure 5.7 Influence of test sequence on D and E for
frozen sand samples tested at -4°C d
Dynamic Young's modulus, Ed (GN/mz)
Damping ratio, D
154-
14 .
12 - (a)
T = -1°C
10- .f = .05 cps
°3= 1.378 MPa
8 Sand content - 65% by volume
6.
2182
O6 0105 104
106
2 r-
l 1 l l l I L
-3 O -2 5 -2 0 -l.5 -1 0 -0 5 0
Log percent axial strain
¢, 104
104
.30 " 105
.275-
.250-
T = -1°C
_225. f = .05 cps
03 = 1.378 MPa
sand content = 65% by volume
.20
.175 l l 1 j A I L
-300 -205 -300 -105 -100 -005 000
Log percent axial strain
Figure 5.8 Influence of test sequence on D and Ed for
frozen sand samples tested at -1°C
155
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Table 5.1 Testing Sequence for samples SI-102 through 51-106
Sample No. & Confining
(Temperature) Span* Pressure (MPa) Frequency (Hz)
2 1.378 I .05
(21196) 10 1.378 .05 -> 0.3 +1.0 + 5.0
10 0.345 .05 + 0.3 + 1.0
2 1.378 .05
#103 10 1.378 .05 +0.3 + 1.0 + 5.0
_ o
(‘0 m was ps+m3+L0+ao
10 0 .05 + 0.3 + 1.0 + 5.0
#104 2 1.378 .05
('1 C) 24 1.378 .054+ 0.3-+ 1.0
2 1.378 .05 + 0.3
#105 10 1.378 .05 + 0.3 + 1.0 + 5.0
_ o
(1†m mus 65+d3+L0+so
24 1.378 .05 + 0.3 +~l.0
#106 .
(-1°C) same as the regular sequence 1n Table 3.2
*"Span" is a nob setting on the MTS controller used to
indicate the relative amount of desired deformation
When sp
SP
SP
2 s
10 e
24 s
11
12
12
2.0 x 10'3%
2.0 x 10'2%
4.0 x 10‘2%
1.59?
6000 -
4000 > Degree of Ice Saturation = 922
1 Sand by Vol. - 64%
Testing Temperature - -4SB
~2
35 1000 _ z - cot 79.75° - 0.181
.. , k - 76.5 mm.2
‘1 600 . e ‘k - 10 x 10’2:
m .-
3 400 . " 1.0 x 10 3
h
V)
a.
3 200.
L:
U
100 r ‘\\\:9.75°
60 .
‘0 l L l l 4_ 4L 4 J
4 6 8 10 20 40 60 so 100
Pseudo-instantaneous Strain, 6(1) (xIO-ZZ)
p
6000 .
6000 » (b)
NA
E
E; 2000 -
O
,; 1000 -
8 r
I ° I
5 600 ’ 3 cot 20.752 2.639
a. c - 290 kN/m
§ ‘00 I 20.75° @ cc - .0001 x 10'22 sec‘1
° —— - 1.0 x 1o"8 «6’1
200 >
100 J A I J I k A I A A A A A 44
.0001 .0004 .001 .004 .01 .04 .1
Figure 5.12 Log-Log Plot of e
2
Z sec-1)
Creep Strain Rate, é(c) (x10-
(1) and é(c)
(ice saturation - 92%)
vs. Applied Stress
‘160
Table 5.2
Values of Pseudo-instantaneous strains and creep strain rates
Sample No. 0 2 5(i)_2 €13; _1 Ice Saturation
CSI-Series (kN/m ) (x10 %) (x10 % sec ) (%)
2 1380 17.761 .005727 92
3 690 14.932 .001005 90
4 2070 16.823 .022903 95
5 690 31.341 .004718 41
6 345 24.495 .001438 38.9
7 518 26.422 .002890 41.7
9 173 21.665 .043198 6.5
161
1°00 * Degree of Ice Saturation - 402
600 b 0 (a) 1 Sand by Vol. - 642
Testing Temperature - -4°C
1. 400.
N
e
\
5 k-cot 72°=0325
V 200 , '
c: °k - 22 k11/m2
m -2
§ 100. @Ek-10x10§
a . -110x;uf
Q 60 b
0
3
o 40 F 72°
20 .
10 I A L A L A 4 A
4 6 10 20 4O 60 100
Pseudo-instantaneous Strain, E(1) (x10-22)
2000 >
(b)
1000 ,
NA 1
E
SE 600 .
O.
o 400.
J
3 n - cot 31° - 1.664
3 200 2
a, CC I- 67 1614/11:
0 e - .0001 x 10 2 sec
6: 100 C -8 _1
o - 1.0 x 10 sec
60 »
40 .
30 a 4 _. A a - _.‘ 44.. s a a 4 A s
.0001 .0004 .001 .004 .01 .04 ..l
Creep Strain Rate, é(c) (x10-22 sec-1)
Figure 5.13 Log-Log Plot of 8(1) and 6(a) vs. Applied Stress
(ice saturation - 402)
162
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163
Curve No. Slope Proof Stress Temperature Creep Parameter
0c (kN/mz) (°C) "n"
l 4.2 10600 ~15 13.617
2 7.0 6400 - 6 8.144
4 8.0 5100 - 6 7.115
5 20.75 290 - 4 2.639
6 31.0 67 - 4 1.664
2.
-—-'_.—.—o_——-o._——o.——-“.——:—’o—:;:;—.â€-
10‘ ————— 1 ..’..____.o-::::_.â€__——-:“ “vâ€
:- -——-;.-,_--_.—.-.-..——;-;.——,r./ ’1...
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’0 t â€aâ€â€™
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E
z 2 .
35 Dynamic
b 103..
a 8 ’
g 6 ' ’4’"
a
a, ‘ P a"’
c. .:.’_'__.. 5 ’ —-— Parameswaran (1979)
E 2» ,z†"â€" Bragg (1979)
I
o 2 ,I’ —" Current Study
I
108: ’z" """ Extension of lines to
.sï¬â€” 6 _8 '1.
6 . 4 Proof stress é‘c) ' 10 83°
4 - ~ -..A - . - - L L. - - -4—
10" 2 4 6 s 10"7 2 4 6 s 10"6 2 I. 6 s 10"5
Strain Rate, é(c)(sec-1)
Figure 5.14 Comparison of creep strength under static and dynamic
loading conditions
CHAPTER 6. SUMMARY AND CONCLUSIONS
The dynamic properties of frozen granular soils
have been studied experimentally using strain-controlled
cyclic triaxial tests. Parameters investigated, which may
influence the dynamic properties of soils, included
mineral volume fraction, saline content and degree of ice
saturation of the frozen soils, temperature and confining
pressure of the ambient environment, and the strain
amplitude and loading frequency applied to the sample.
The materials studied included commercially available
Ottawa sand and small-sized pea gravel which is categorized
as very coarse sand in the Unified Soil Classification system.
These materials were combined with adequate amounts of
water and artificially frozen into cyclindrical samples.
The dynamic properties studied included elastic behavior,
energy absorbing properties, and creep behavior of frozen
granular soils.
Elastic Behavior
The strength of the ice matrix is a major compon-
ent of the strength of frozen granular soil systems.
'When the mineral volume fraction is high enough to allow
particle to particle contact, the inter-particle friction
164
165
and the interaction between particles come into effect
and contribute to the total sample strength.
The crystalline structure of the ice matrix is
very sensitive to temperature and impurities, hence, the
strength of the ice matrix can vary significantly. The
inter-particle stress is a function of mineral volume
fraction, temperature, and confining pressure. The ice
matrix provides the basic confinement to the solid grain
and confining pressure strengthens the confinement. Saline
content changes the water freezing temperature and thus
influences the stiffness of the ice matrix. The degree
of ice saturation alters the ice matrix volume and in
turn influences the dynamic strength of the frozen soil
system. Loading frequency and axial strain are believed
to influence the elastic and the dash-pot behavior of the
sample and thus affect the values of dynamic Young's
‘modulus.
Based on the experimental results, the following
conclusions can be made: the dynamic Young's modulus,
which represents the stiffness of the frozen samples:
(a) increases with increasing loading
fre uency, mineral volume fraction, and
con ining pressure;
(b) decreases with increasing axial
strain, higher temperatures, and increasing
saline content;
166
(c) increases with increasing ice content
for partially saturated samples but decreases
with increasing ice content for over-
saturated (ice-rich) samples.
Energy Absorbing Properties
Energy absorbing properties were represented by a
damping ratio, which is the fraction of energy absorbed
or dissipated per stress cycle. For frozen clay and silt
(Chaichanavong, 1976; Czajkowski, 1977), the damping ratio
decreased with an increase in the dynamic Young's modulus.
This was not always the case for frozen granular soils.
The damping ratio would increase, decrease, or remain
unchanged with respect to the increase of dynamic Young's
modulus which depends on changes in the test parameters.
This behavior appears to be a function of the larger-
sized particles in a granular soil system. The samples
acted more like a composite system of discrete materials.
Both loss of adhesive bonds between ice and soil grains
and relative movement between soil particles with respect
to the surrounding soil and ice lead to irrecoverable
loss of energy. The individual and irregular nature of
this type of energy loss made the change in damping ratio
with respect to certain parameters less predictable. The
following conclusions can be made from.the available test
results:
167
(l) The damping ratio, which represents
the energy absorbing properties of the sample,
(a) decreases with increasing loading fre-
quency and decreasing temperature, and (b)
decreases with increasing ice content for
samples of all degrees of saturation.
(2) The effect of axial strain, con-
fining pressure, solid content and saline
content on damping ratio are not explicit
from the data obtained in this study.
Creep Behavior
Dynamic creep tests involved frozen sand samples
with several degrees of ice saturation, a static load
until the axial strain reached 0.07%, and a stress-
controlled dynamic load (1168.4 kN/mz) thereafter at 0.05
Hz. The initial static load and the number of cycles
required to reach a final strain of 0.5% served as test
variables. The test temperature of -4°C and zero confining
pressure were constant for all samples.
This preliminary study of frozen sand creep
behavior under dynamic loading conditions permit several
conclusions to be made. The creep rate is dependent on
the initial stress state and degree of ice saturation.
The creep strength is a function of creep rate and in turn
is dependent on the degree of ice saturation. Based on
the test results, the creep rates increase with decreasing
ice saturation and increasing initial stress level. The
creep strength decreases with decreasing ice saturation
168
and increasing creep rate. A comparison with test results
from other investigators permits a conclusion of higher
susceptibility to creep failure under dynamic loading
conditions than under static loading conditions. The
creep behavior of frozen soil under dynamic loads may also
be influenced by temperature, the magnitude and frequency
of dynamic load, and confining pressure, but their
effects were not explored in this study.
REFERENCES
169
REFERENCES
Andersland, O.B., Sayles, F.H. and Ladanyi, B. (1978)
"Mechanical Pr0perties of Frozen Ground," Chap. 5
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McGraw-Hill Book Co., New York.
Anderson, D.M., Tice, A.R. and Mckin, H.L. (1973)
"The Unfrozen water and the Apparent Specific
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National Academy of Science, Washington, pp. 289-
295.
Banin, A. and Anderson, D.M. (1974)
"Effect of Salt Concentration Changes during
Freezing on the Unfrozen Water Content of Porous
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V01. 10:1.
Barnes, P. and Tabor, D. (1966)
"Plastic Flow and Pressure Melting in the Defor-
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pp. 878-882.
Bragg, R.A. (1979)
Personal correspondence.
Brown, J. (1969)
"Ionic Concentration Gradients in Permafrost,
Barrow, Alaska," Res. Rep. 272, 24 pp., U.S.A.
CRREL, Hanover, New Hampshire, 1969.
Chaichanavong, T. (1976)
"Dynamic Properties of Ice and Frozen Clay Under
Cyclic Triaxial Loading Conditions," unpublished
Ph.D. thesis, Michigan State University, East
Lansing, Michigan.
170
171
Cho, Y., Rizzo, P.C. and Humphries, W.K. (1976)
"Saturated Sand and Cyclic Dynamic Tests," selected
paper in "Liquifaction Problems in Geotechnical
Engineering,‘ ASCE National Convention, September
72 - October 1.
Converse, F.J. (1961)
"Stress-Deformation Relations for Soft Saturated
Silt Under Low-Frequency Oscillating Direct-Shear
Forces," Special Technical Publ. No. 305, Symposium
on Soil Dynamics, ASTM, pp. 15-19.
Czajkowski, R.L. (1977)
"The Dynamic Properties of Frozen Soils Under
Cyclic Triaxial Loading Conditions," unpublished
M.S. thesis, Michigan State University, East
Lansing, Michigan.
Dillon, H.B. and Andersland, O.B. (1966)
"Predicting Unfrozen Water Contents in Frozen
Soils," Can Geotech. Journal, 3(2):53-60.
Drnevich, V.P., Hall, J.R., and Richart, F.E., Jr. (1966)
"Large Amplitude Vibration Effects on the Shear
Modulus of Sand," Contract Report No. 3-161, U.S.
Army Eng. Waterways Experiment Station, Vicksburg,
Miss., Oct.
Goughner, R.R. (1967) ,
"The Soil-Ice System and the Shear Strength of
Frozen Soils," unpublished Ph.D. thesis, Michigan
State University, East Lansing, Michigan.
Goughnour, R.R. and Andersland, O.B. (1968)
"Mechanical Properties of Sand-Ice System,"
Journal of the Soil Mechanics and Foundations
Division, ASCE, Vol. 94, No. SM4, July.
Hardin, B.O. and Drnevich, V.P. (1970a)
"Shear Modulus and Damping in Soils; (1) Measure-
‘ment and Parameter Effects," Tech. Report UKY
26-70-CE-2, Soil Mech. Series No. 1, Univ. of Ky.,
College of Eng., July.
Hardin, B.O. and Drnevich, V.P. (1970b)
"Shear Modulus and Damping in Soils; (2) Design
Equations and Curves," Tech. Report 27-70-CE-3,
Soil Mech. Series No. 2, Univ. of Ky., College of
Eng., July.
172
Hardin, B.O., and Drnevich, V.P. (1972a)
"Shear Modulus and Damping in Soils, Measurement
and Parameter Effects,‘ Journal of the Soil Mech.
and Found, Div., ASCE, Vol. 98, No. 8M6, June.
Hardin, B.O., and Drnevich, V.P. (1972b)
"Shear Modulus and Damping in Soils: Design
Equations and Curves," Journal of the Soil Mech.
and Found, Div., ASCE, Vol. 98, No. 8M7, July.
Hult, Jan A.H. (1966)
"Creep in Engineering Structures," Blaisdell,
Waltham, Mass.
Idriss, I.M. and Seed, H.B. (1968)
"Seismic Response of Horizontal Soil Layers,"
Journal of the Soil Mechanics and Foundation
Division, ASCE, Vol. 94, No. SM4, July.
Kaplar, C.W. (1969)
"Laboratory Determination of Dynamic Moduli of
Frozen Soils and of Ice," Research Report 163,
USACRREL, Hanover, New Hampshire, January.
Kennedy, A.J. (1962)
"Processes of Creep and Fatigue in Metals,"
Edinburgh, Scotland: Oliver and Boyd.
Ladanyi, Branko (1972)
"An Engineering Theory of Creep of Frozen Soils,"
Can. Geotech. Journal 9(1):63-80.
Linell, K.A. and Kaplar, C.W. (1966)
"Description and Classification of Frozen Soils,"
Technical Report 150, USACRREL, Hanover, N. H.
Nakano, Y. and Arnold R. (1973)
"Acoustic Properties of Frozen Ottawa Sand," Journal
of water Resources Research, Vol. 9, No. 1, February.
Nakano, Y., and Froula, N.H. (1979)
"Sound and Shock Transmission in Frozen Soils,"
North American Contribution to the 2nd Interna-
tional Conference on Permafrost, National Academy
of Science.
173
Nakano, Y., Martin, R.J., and Smith, M. (1972)
"Ultrasonic Velocities of the Dilatational and
Shear Waves in Frozen Soils," Journal of Water
Resources Research, Vol. 8, No. 4, August, pp.
1024-1030.
Parameswaran, V.R. (1979)
Personal correspondence.
Peacock, W.H., and Seed, H.B. (1968)
"Sand Liquefaction Under Cyclic Loading Simple
Shear Conditions," Journal of the Soil Mech. and
Eggnd.8Div., ASCE, Vol. 94, No. 8M3, May, pp.
- 0 .
Richart, F.E., Jr., Hall, J.R., Jr., and Lysmer, J. (1962)
"A Study of the Propagation and Dissipation of
'Elastic' wave Energy in Granular Soils," Research
Report, Civil Eng. Dept., Univ. of Fla., Sept.
Richart, F.E., Hall, J.R., and Woods, R.D. (1970)
"Vibrations of Soils and Foundations," Prentice-
Hall, Inc., Englewood, N.J.
Sandor, B.1. (1972)
"Fundamentals of Cyclic Stress and Strain," The
University of Wisconsin Press, Madison, Wisconsin.
Schnabel, P.B., Lysmer, J., and Seed, H.B. (1972)
"SHAKE--A Computer Program for Earthquake Response
Analysis of Horizontally Layered Sites," Research
Report EERC 72-12, Earthquake Engineering Research
genter, University of California, Berkeley, Cali-
ornia.
Schroeder, W.L., and Schuster, R.L. (1968)
"Laboratory Simulation of Seismic Activity in
Saturated Sands," Special Technical Pub. No.
450, Symposium on Vibration Effects of Earthquakes
on Soils and Foundations, ASTM, pp. 57-70.
Scott, F.S. (1969)
"The Freezing Process and Mechanics of Frozen
Ground," Cold Regions Science and Engineering
Mbnograph ll-Dl, October 1969, USACRREL,
Hanover, New Hampshire.
Seed, H.B. (1968a)
Unpublished test results.
174
Seed, H.B. and Idriss, I.M. (1969)
"Influence of Soil Conditions on Ground Motions
During Earthquakes," Journal of the Soil Mech.
and Found. Div., ASCE, Vol. 95, No. SMl, January.
Seed, H.B. and Idriss, I.M. (1970)
"Shear Moduli and Damping Factors for Dynamic
Resonance Analysis,†Report No. EERC 70-10,
Univ. of California, Earthquake Eng. Research
Center, Berkeley, December, 1970.
Seed, H.B. and Lee, K.L. (1969)
"Pore-Water Pressure in Earth Slopes Under Seismic
Loading Conditions," Proc., 4th World Conference
on Earthquake Eng., Chile, Vol. 3, No. A5, pp.
1-11.
Silver, N. L. and Park, T.K. (1975)
"Testing Procedure Effects on Dynamic Soil
Behavior," ASCE, Journal Geotechnical Engineering
Division, Vol. 101, No. GTlO, October, 1975.
Silver, M.L. and Seed, H.B. (1969)
"The Behavior of Sand Under Seismic Loading Condi-
tions," Report No.-EERC 69-16, Univ. of Calif.,
Earthquake Eng. Research Center, Berkeley, Calif.
Dec.
Sowers, G.F. (1963) .
"Strength Testing of Soils," Special Technical
Pub. No. 361, Laboratory Shear Testing of Soils,
ASTM, pp. 3-31.
Stevens, H.W. (1973)
"Viscoelastic Properties of Frozen Soil Under
Vibratory Loads," The North American Contribution
to the 2nd International Permafrost Conference,
National Academy of Science, July.
Stevens, H.W. (1975)
"The Response of Frozen Soils to Vibratory Loads,‘
Technical Report No. 265, USACRREL, June.
Streeter, V.L., wylie, E.B., and Richart, F.E. (1974)
"Soil Motion Computations by Characteristic
Methods," Journal of the Geotechnical Engineering
Division, ASCE, Vol. 100, No. GT3, March.
175
SW-AJA (1972)
Tedrow,
Thiers,
Vinson,
Vinson,
Vyalov,
Vyalov,
Weeks,
"Soil Behavior Under Earthquake Loading Conditions"
State-of—the-Art Evaluation of Soil Characteristics
for Seismic Response Analysis," A joint adventure
of Shannon and Wilson, Inc., and Agbabian-Jacobsen
Associates, December. ~
J.F.C. (1966)
"Polar Desert Soils," Soil Science Soc. Amer.
Proc., 30, 381-387, 1966.
G.R., and Seed, H.B. (1968)
"Strength and Stress-Strain Characteristics of
Clays Subjected to Seismic Loading Conditions,"
Special Technical Pub. No. 450, Symposium on
Vibration Effects of Earthquakes on Soils and
Foundations, ASTM, pp. 3-56.
T.S. (1975)
"Cyclic Triaxial Test Equipment to Evaluate Dynamic
Properties of Frozen Soils," Report No. MSU-CE-
75-1, Division of Engineering Research, Michigan
State University, March, 1975.
T.S. (1978)
"Response of Frozen Ground to Dynamic Loading,"
Chapter 8 in Geotechnical Engineering for Cold
Regions, 0. B. Andersland and D. M. Anderson, editors,
McGraw-Hill Book Co. , New York.
S.S. (1959)
"Rheological Properties and Bearing Capacity of
Frozen Soils," USACRREL, Trans 74, (1965),
Hanover, N.H.
S.S. (1962)
"The Strength and Creep of Frozen Soils and Calcu-
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Translation 76 (1965) Hanover, New Hampshire,
1965.
W.F., and Assur, A. (1967)
"The Mechanical Properties of Sea Ice," U.S. Army
Cold Region Res. Eng. Lab. Monogr. II 63,
Hanover, N.H.
176
Weissman, G.F. and Hart, R.R. (1961)
Yong, R.
Yong, R.
"The Damping Capacity of Some Granular Soils,"
Special Technical Pub. 305, Symposium on Soil
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"Salt Migration and Frost Heaving of Salt-
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N., Cheung, C.H. and Sheeran, D.E. (1978)
"Prediction of Salt Influence on Unfrozen Water
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Bochum-Germany, 1978.
APPENDICES
177
APPENDIX A
TEST EQUIPMENT AND RECORDING DEVICES
178
TEST EQUIPMENT AND RECORDING DEVICES
The test equipment and recording devices included
(1) a triaxial cell completely immersed in a low temper-
ature coolant, (2) an MTS electrohydraulic closed-loop
testing system which applies the load to the sample, (3)
a cooling and circulation system for control of the
temperature and constant circulation of the coolant, and
(4) recording devices such as a digital multimeter, an
oscilloscope, a strip chart recorder, and a mini-computer
(Figure A. l) .
A.l. Triaxial Cell Assembly
A schematic diagram of the triaxial cell inside
the cold bath is shown in Figure A.2. The triaxial cell
was made of an 18 cm diameter and 35 cm.high aluminum
cylinder with steel top and bottom plates. The aluminum
cylinder was chosen for the following reasons: (1) the
cylinder permitted sample confinement at high cell
pressures, (2) light weight permitted easier handling,
(3) high thermal conductivity permitted temperature
changes in reasonable time period, and (4) the non-
circulating coolant inside the cell helped dampen the
179
180
temperature changes due to cycling of the external refrig-
erated coolant source (low temperature bath).
A load cell, attached to the steel bottom support,
permitted load measurements inside the cell. Confining
pressures acting on both top and bottom of the load cell
served to cancel its effect. The 7.1 cm diameter sample,
average length of 16.8 cm with its coupling cap and base
was connected to the load cell by a steel rod threaded
on both ends. The loading ram, passing through the steel
top of the triaxial cell, permits application of the cyclic
load from the MTS acturator. A gage head type LVDT (.125
in displacement range, 1.9 mV/.OOl in. sensitivity, and
0.21% linearity) was installed on the anti-tilt device
(Figure A.3) to monitor sample axial deformation. The
anti-tilt device consists of three basic components: (1)
a base clamp attached to the sample base with connecting
rods for the LVDT and the cap assembly, and (2) an anti-
tilt ring mounted on one end to the spring steel clamped
on the cap assembly connecting rod. On the other end a
screw with bearing plate contacts the LVDT probe shaft.
The anti-tilt ring was 6.3 mm larger in diameter than the
sample cap to allow free movement about the cap, (3) a
cap clamp attached to the anti-tilt ring with two spring
steel leaves which acted like pivot points for movement
of the anti-tilt ring. Thus the axial deformation was
181
doubled at the LVDT but the tilt of the sample cap, if
any, would not be transmitted through the spring steel
leaves. A picture of one sample with the anti—tilt
devices attached is shown in Figure A.4. Two thermistors,
attached to a steel bracket, were clamped loosely, but
very closely, to the sample to monitor the sample
temperature during the test. These two thermistors were
calibrated with a precision laboratory thermometer having
a scale devision of 0.1°C. The thermistors were capable
of reading to the nearest 0.1°C. The temperature of a
sample during testing was obtained by averaging the
readings from the two thermistors. The confining pressure
was applied by compressed nitrogen through a pressure
regulator.
A.2. MTS (Material Testing System)
The cyclic load was applied by an MTS electro-
hydraulic closed-loop test system which consisted of a
hydraulic pump (Figure A.5), an acturator (Figure A.6),
and a set of controllers (Figure A.7). Figure A.8 shows
a schematic diagram of the electro-hydraulic close-loop
test system. An LVDT in the triaxial cell provided a
signal proportional to the deformation of the sample. The
signal from the LVDT, called feedback, was fed into the
servo-valve controller which compares it with the signal
182
from the function generator, called "command." If
command and feedback are not equal, then the acturator
is not positioned as desired. The servo-valve controller
reacts to the relative difference between these signals
(both polarity and magnitude) and applies a control
signal to the servo-valve which changes the flow rate of
the fluid run into and out of the acturator to correct
the difference. Thus the acturator piston will apply a
continuous sinusoidal wave load under command of the
function generator.
A.3. Cooling and Circulation System
The components in the cooling and circulation
system are a cold bath, a refrigeration unit, a thermo-
switch, and a circulation pump. The cold bath (Figure
A.6) was 0.35 m.by 0.35 m.by 0.46 m and contained 0.048 m3
of a 50/50 mixture of ethylene glycol and water as the
coolant, excluding the volume of the triaxial cell. The
insulation around the cold bat was 2.5 cm thick styrofoam
placed next to the tank. The temperature inside the
cell was damped relative to cyclic variations in the
circulating coolant around the triaxial cell. The bath
permitted the coolant to enter at the bottom.and to return
to the refrigeration unit from an overflow at the top.
In addition, the coolant also passed across the top of
183
the triaxial cell through an auxiliary pipe to prevent
heat intrusion from above. The refrigeration unit
(Figure A.10) contained approximately 0.096 mg coolant.
The temperature of the coolant in the refrigeration unit
was usually somewhat lower than that of the cold bath and
was controlled by a thermoswitch, which turned the compressor
on and off, with a sensitivity close to 0.l°C.
A.4. Recording and Monitoring Devices
The dynamic Young's moduli were calculated from
the results recorded by a Sanborn strip chart recorder
(Figure A.11). The strip chart recorder, sometimes called
an oscillograph, is a multi-channel direct-writing instru-
ment which uses a bank of galvanometers to record a
number of variables simultaneously. Each galvanometer
drives a writing arm, which wipes with a hot wire ribbon
stylus across heat-sensitive paper while the paper is
moving over a knife-edge writing plateau. The frequency
response of the strip chart recorder was checked and it
was determined that there was no variation in the
amplitude when the frequency was varied from 0.05 Hz to
50 Hz. A typical strip-chart record is shown in Figure
3.4.
The damping ratio was computed from a photographic
record of the screen display of a Tektronics Storage
184
Oscilloscope (Figure A.7.). The oscilloscope has the
advantage of giving an immediate response to any electronic
deviation signal at very high frequencies so that the
possibility of introducing mechanical hysteresis while
evaluating the damping property of the sample was
minimized. A typical hysteresis loop picture was given
in Figure 2.5c. The area of the hysteresis loop was
measured with a planimeter from an enlarged trace of the
photographic record on the negative. The optical
distortion involved in the photographic process was
negligible.
The signals coming from the LVDT and load cell
were extremely "noisy" at low strain. To eliminate this
high frequency noise, several stages of multi-channel
filter electronics were used. The filtering electronics
were designed with extreme care to avoid the creation of
any "phase offset" for the signal going to the oscilloscope
and to avoid any "attenuation" for the signal going to
the strip chart recorder.
A digital multi-meter was used to monitor the
voltage output from the load cell and LVDT and thermistor
resistance during the tests.
During the latter stage of testing, a mini-
computer on-line data reducing system.became available.
185
The system (Figure A.12) was composed of a Computer
Automation "Naked Mini LSI-Z" mini-computer, a Datel
System 256 A/D - D/A converter and a teletype. The
system.was successful in evaluating damping ratios and
saved some labor and time for reducing the damping data.
186
Servoval
Actua
Hydraulic power
suvply
ler
Servo
Hydraulic
control
Triaxial cell
cell
Load frame
lsnt and
tion
unit
Output
recorders
Figure A.l Cyclic triaxial test system
187
To recorder
Loading ram
.1 ï¬â€”HL\ J
â€:32 -=- ) 7
Insulated cold bath
I 5
\
t ,s-anti-tilt
h ’2 device
t Thermistor 2%:
\ .° '.
t Aluminum ' 5:3;- { "m
\ “u ' Frozen soil
\ " " sample‘
A
\
Coolant \ ',pLoad cell
in
‘
Figure A.2 Triaxial cell inside the cold bath
188
anti-tilt ring
5 rin steel leaves .
p g screw adjustable
spring steel‘ \ 1 -/bearing plate
.5i—D probe shaft
cap clamp
spring actuated
cop gage head with
assembly N LVDT
connecting
rod gage head
connecting rod
base clamp
Figure A.3 Schematic of anti—tilt device
Figure A.4 Samp1e with anti-tilt device
installed
189
Figure A.5 Hydraulic pump
Figure A.6 Actuator and cold bath.
190
Figure A.7 Storage oscilloscope and
MTS controllers
hydraulic d9Ub'e sided
PM 1:: '"'°“
supply
actuator
amwï¬md
gflference loading rod
elween
shnms
hydrauhc .
t B'VUVUIVE
controller Konlroller LVDT frozen
ifunction command H3 sample
. enerotor . . m .
9 Signal 1.1.5.2.?
I
I
l
L ______ loadceH
Figure A.8 Electrohydraulic closed-
1oop test system
191
coolant
outflow
triaxial cell with
non-circulating
coolant
——-circulating
coolant
frozen sample
cold bath
coolant
'an
I OW Figure A.9 Schematic of cold bath
Figure A.10 Refrigeration and circulation
unit
192
Eoumzm umuDQEOUIwaï¬z NH.< wuswï¬m
umuuouwu uum30laï¬uum
HH.< muawï¬m
APPENDIX B
DYNAMIC YOUNG'S MODULUS FOR
SAND-ICE SAMPLES
193
E+05 PSI
E+05 P51
2 E NODULUS
3.
2: FIGURE 3.1
‘_ saanss SI-O,Sl-9,SI-IO,SI-12
;_ SAND CONTENT = 20 2
L 9 POINTS
2L.
2.
er
a:
r-
EL ‘3 %‘A
l. A A ‘3
‘3"-a a†N iu.h 5
L00 PERCNT 1 Rx STRRIN l
0.00 0.120 “o. "00 I... IMO "J 31.0 â€.0 turn
UST—lï¬OSCPO
2 E HODULUS
0.1
: FIGURE 3.3
_ SANPLES SI-O,SI-9,SI-tO,SI-12
. SAND CONTENT = 20 1
t 10 POINTS
::;;;g;;ém._£. ‘ “‘
- :----
A A
,
Jan ~21.“ 41.00 41.59 a...- "la- 0%
LOG PERCNT 1 ax STRRIN
DST—IFICPO
194+
E+05 PSI
E+05 P31
2 E flODULUS
ï¬d‘
gr
9: FIGURE 3.2
*t SANPLES SI-O,SI-9,ST-l0,Sl-12
g. SAND CONTENT s 20 z
9~ 10 POINTS
: p .
t
3.
3 :
i
. †A
3. l- ‘Am— A.
. T- : A —
AL
. 4%.“ :30 4..†41.09 if“ â€1300 0.:
LOG PERCNT 1 ex STRHIN
DST-IEBCPO
2 E MODULUS
,
at FIGURE 3.4
*t SAMPLES SI-8,SI-9,SI-10,SI-12
§+- SAND CONTENT = 20 z
.r 10 POINTS
6:
a?
~.
g r-
:b
3:
:C ‘ .
» A
.5E-——_ff_—2r_—""“““--—————.__
.l'll'J I L l J l 4
- .0- a.“ on... on... a... -.ou 0.7
LOB PERCNT 1 RX STRRIN
DST-IFSCPO
E+05 PSI
E+OS PSI
O-N I.†lie. “.0 I... 20.0 20-0 32-0 â€.0
195
2 E HODULUS
3C
3: FIGURE 3.5
. SANPLES SI-8.SI-9,SI-lO,SI-12
§~ SAND CONTENT = 20 z
9~ 13 POINTS
Eb
L.
y
or
8~
. " A
s-
.r“~1F‘ï¬r~§i‘1‘~‘\\“§“‘
5L
9 ~31'o00 it!) 44-00 41.†fill! - .100 0%
LOG PERCNT I RX STRRIN
DST—IFOSCPSO
2 E MODULUS
a.
: FIGURE I.7
E SANPLES SI-8,SI-9,SI-IO,SI-12
_ SAND CONTENT = 20 1
~ 12 POINTS
:_ .
N- A
A A
I A ‘,
‘ .5... J... .:... .3... .3. .3... .3
LOG PERCNT 1 RX STRRIN
OST-lFlCPSO
E+05 PSI
E+05 PSI
2 E HODULUS
}.
9, FIGURE I.S
‘. SANPLES SI-O,SI-9,SI-tO,SI-12
3F SAND CONTENT = 20 I
,P 12 POINTS
é"
j
3 :
:r
*C
8 A
a: A
5F “
l
o -3%.00 oil.†. :00 41.“ 0:.†c.4600 I}
LOG PERCNT l RX STRRIN
08T—1E3CP50
2 E HODULUS
9; FIGURE 9.8
;. SANPLES SI-G,SI-9,SI-IO,SI-12
~ SAND CONTENT s 20 z
z- 12 POINTS
g.
.F
e:
I l.
=1
; +- A ‘
l- A
3» an . e
O b A é
q-
.8"- l l L J J J .1
also a.“ a.» mu -I .u «no o.‘
LOG PERCNT 1 OX STRRIN
DST-IFSCPSO
E+OS PSI
E+05 PSI
196
2 E HOOULUS
[ FIGURE D.9
E SANPLES SI-G,SI-9,SI-10,SI-12
SAND CONTENT = 20 I
-
Q“
9
8
9_
8
__ 16 POINTS
i 1-
'.
g l'
l-
‘2
g P
1..
:r
a L m m
§~ .
I
O L..I_ L_ I I I I I
once -2.SG -z.oo -1.50 -1.00 -.ooo II.I
LOG PERCNT I RX STRRIN
SST—IPOSCPZOO
2 E MODULUS
FIGURE 3.11
SAMPLES SI-8,SI-9.SI-l0,SI-12
SAND CONTENT = 20 Z
15 POINTS
It-O It!) 20.! 24.0 20.6 32.0 30.! 40:0
Tï¬TTTTTTrTTrTTTTTTTTT
l l J l l l 1
«lo- 4 .Go a.†-| .u -T .oo - .m o.‘
LOG PERCNT I RX STRRIN
OST-lFlCPZOO
0.1
E+05 PSI
E+OS PSI
2 E HOOULUS
PL
,: FIGURE I.10
'_ SANPLES SI-O,SI-9,SI-10,SI-12
3E SAND CONTENT = 20 I
g» 16 POINTS
0 F .
8 l-
:F
P:
:F
‘L
g - o
;~ I
'3 ditto 41.“ 41.00 4..“ 41.“ â€[500 Go:
LOG PERCNT 1 OX STRRIN
OST-lEBCPZOO
2 E HODULUS
eh FIGURE 3.12
‘C SANPLES SI-G,SI-9,SI-10,SI—12
g» SAND CONTENT = 20 I
â€F 14 POINTS
: l-
5:
g;
e: A l A
2 1. AA A
8. r- P A4
S:
" l-
0:“- l I 1 l 4 l 4
QED a.» 4.00 mu am noon o.‘
LOG PERCNT 1
OX STRRIN
DST-IFSCPZOO
E+OS PSI
E+05 PSI
197
5 E HOOULUS
3F
'2: FIGURE I.13
'.. SANPLES SI-2,SI-3,SI-4
gl. SAND CONTENT = 20 I
.- 7 POINTS
:0 _
q F’
:F
S. L
;L
8 .
6 l’ \‘AA A
a- A A
J:
o 4:00 -2L.so -21.00 41.50 41.00 â€1:00 0.}—
LOG PERCNT 4 RX STRHIN 3
DST—4.05CPU
5 E ï¬ODULUS
3L.
er FIGURE I.15
‘I SANPLES SI-2,SI-3,SI-4
3F SAND CONTENT = 20 I
,: G POINTS
g.
.F
8 l.
3
i
8 .
' r-
5 4'... 4.50 4.00 T.S. -T.oo also. a}
LOG PERCNT 4 RX STRRIN
OST-4F1CPO
E+05 PSI
E+05 PSI
5 E HODULUS
‘1‘
;. FIGURE I.14
P SAHPtES 51-2'31-3,SI-4
:1 SAND CONTENT . 20 I
9* 7 POINTS
8 l. '
EU
I-
=1
ES . .
a: .
,l
0 ~91.†41.50 41.00 :50 ~31.†also: 0.:
L00 PERCNT 4 OX STRRIN a
OST-4E3CPO
5 E MODULUS
;: FIGURE 3.16
- SANPLES SI-2,SI-3,SI-4
z» SAND CONTENT = 20 I
,* 6 POINTS
é :
d
g
5' . .
4'.“ .1 .so -I .oo - | .u -I .oo . .300 0.1
L00 PERCNT 4 Rx STRAIN 3
UST44FSCPO
E+05 PSI
E+OS PSI
I.†.... I... I... I... I... I... 00.0 '0. “g.
IIIIIIIIIiII—IWITIrI
5 E MODULUS
I I
FIGURE 3.17
SANPLES SI-2,SI-3,SI-4
SAND CONTENT = 20 l
8 POINTS
D b
I... .... I... I... I... 8... 2... 3... 3... Oï¬
:01
L l J A J
- -†“:0‘0 01.00 '10“ 'N .00
LUG PERCNT 4
OST"4RUSCPSU
5 E flODULUS
FIGURE 3.19
SANPLES SI-2,SI-3,SI-4
SAND CONTENT = 20 X
7 POINTS
I I r I I I I I I
I I I I'I I I I I I I I
l I I l
_L
~$00
RX STRRIN
198
I
o I
1
I
.9... o: .50 o: .00 .140 -I .00
L00 PERCNT 4
OST—4F1CPSO
RX STRHIN
E+OS PSI
E+OS PSI
5 E HODULUS
Ir
;. FIGURE I.18
_ SANPLES SI-2,SI-3,SI-4
;. SAND CONTENT = 20 I
,P 7 POINTS
P:
E"
9%
fl
5
6
6 - Ml 4.00 4.00 I... 4.00 .100 0%
L06 PERCNT 4 9x STRAIN '
OST—4E3CPSU
5 E MODULUS
FIGURE 3.20
SANPLES SI-2,SI-3,SI-4
SAND CONTENT = 20 Z
7 POINTS
A... ...O I... I... 2... 2... I... 3... 3... 0:0
IIIIIIIIIIIITIIIIIII
" . '... 4‘... .i... 3... .3... -3... ï¬â€”
LOG PERCNT 4 RN STRAIN
OST—4F5CPSO
E+OS PSI
E+OS PSI
199
5 E HODULUS
3E
a? FIGURE 1.21
‘r SANPLES SI-2,SI-3,SI-4
;- SAND CONTENT = 20 z
.’ 10 POINTS
£1-
’1'
:r
:P
}
;:~\\‘jf
;b \
I #1 ._ _J_._.__L__..—1—————+_
aloe -: .c: -: .oo -1.So -1.oo - .500 0.
L05 PER NT 4 Ax STRAIN
USI—4EUSCP200
S L NODULUS
.[ FIGURE 3.23
3L SANPLES SI-2,SI-3,SI-4
:E SANI CONTENT = 20 z
"I 9 POINTS
:1-
;E
at
6
EC
‘A. A..a N. A..E A
LOG PERCNT 4 AN STRAIN
OST—4F1CP200
E+05 PSI
E+05 PSI
S E HOOULUS
I; -
._ FIGURE 3.22
'E SANPLES SI-2,SI-3,SI-4
;- SAND CONTENT . 20 I
F 10 POINTS
I F.
I-
: E
z.
8. .—
l.
2» .
'- .. A
g» .
8:
. l.
6 4%.†41.50 41.00 41.80 41.00 “1560 0.:
L06 PERCNT 4 RX STRRIN
OST—AEBCPZOO
S E HOUULUS
g.
9: FIGURE 3.24
‘E SANPLES SI-2,SI-3,SI-1
;. SAND CONTENT = 20 z
a» 9 POINTS
8- _
L
3E
fl
8. A
'L
8.
‘0’.- I 1 l l _l L 4
4500 4.00 4.00 -1.00 4.00 ..000 0.‘
L00 PERCNT 4 9x STRAIN
DST-4F5CP200
EROS PSI
E+OS PSI
200
8 E HOOULUS
A
0...
FIGURE 3.25
SANPLES SI-22,SI-23
SAND CONTENT = 20 Z
4 POINTS
\
’\
IITjIrIIIIIrIjIITlv‘I
A.3. .-00 I... I... .0.. I... â€I. â€0. â€I.
1
h
' _._l_.....__'__.__- _L EI I
- .OO .2.» -:.oo -I.So -1.OO -.SOO of
LOG PERENT 7 _Ax STRAIN
UST~IOPCSCPC
8 E
flCCULES
FIGURE 8.2?
SAMPLES SI-22,SI-23
SAND CONTENT = 20 Z
4 POINTS
I... 9.90 12.: ".0 212.: Ian 29.0 32.: 31.0 311.0
IfIrjijrrIï¬rrTj'T'Tijj—T
O
'0!
I I J l I .1
l o -.
~s’.00 4.50 4.00 . I .so -I .00 - .500 07
LOG PERCNT 7 RX'STRRIN
OST~10F1CPO
E+OS PSI
. E+OS PSI
I... L"
IIIITTIjITIIIWIIIIIII
I... .J. I... I... I... I... â€J 3... â€J 0.1.
IIITIIIrIrrrrIT'WIIITI
8 E flOOULUS
FIGURE B.26
SANPLES SI-22,SI-23
SAND CONTENT = 20 I
4 POINTS
" 'L
I... I... ..-. .Co. 2... .2.. 3... 0.1..
l J 1 I I J I
oa’.oo -I.so 4.00 -I.Ga -I.ao -.5'EI‘ 0.‘
LOB PERCNT 7 9X STRHIN
DST-IOEBCPO
O E MODULUS
FIGURE l.28
SAMPLES SI-22,SI-23
SAND CONTENT = 20 I
4 POINTS
'1
l I I J _l J J—
-s'.00 -: .u -I .00 .400 0.‘
L09 PERCNT 7 RX STRRIN
DST-IOFSCPO
E+OS PSI
E+05 PSI
201
8 E MODULUS
3'
l.
;. FIGURE I.29
. SANPLES SI-22,SI-23
;.. SAND CONTENT . 20 I
,~ 6 POINTS
:r
3;:
9
L00 PERCNT“ - 7 Tax STRAIN.
DST—ICPUECPSO
8 E MODULUS
3: FIGURE S.ST
". SAMPLES Sl-22,SI-23
§~ SAND CONTENT = 20 2
0L 6 _POINTS
"E
3E
:1: A
S:
SE
6 -a’.00 ~31.» 31.06 41.50 ï¬n i000 II.I
LOG PERCNT 7 RX STRRIN
OST-lOFlCPSO
E+OS PSI
E+05 PSI
8 E MODULUS
0*.
FIGURE 3.30
SANPLES SI-22,SI*23
SAND CONTENT = 20 Z
6 POINTS
I.†U.†I!-. I... "0. 1‘0. â€0' at. â€a.
I I I I I ï¬r I I I I T I I I j I T I . ‘—
0.1
i I 1 EL 1 I l
4.00 4.50 -z.oo -1.G0 -1.00 -.IOO 0}
LOG PERCNT 7 AN STRAIN
DST-IUEBCPSU
B E MODULUS
9: FIGURE 3.32
‘. SANPLES SI-22,SI-23
;. SAND CONTENT = 20 I
e» 6 POINTS
3 l.
3:
3: .
2 P
EF
6:
0â€] I l l J l I
«la «.30 4.00 4.00 4.00 -.000 0.‘
LOB PERCNT 7 FIX STRAIN
DST—IOFSCPSO
E+CS PSI
E+05 PSI
4.00 0.30 12.0 Io.o 20.0 24.0 t... 91.0 :sQo our.
'8 E MODULUS
mp
LOO 0.00 ".0 iOoO 20.9 IMO 28.3 32.9 30.0 ‘3,-'.‘
L
I FIGURE 3.33
L SANRLES SI-22,SI-23
- SAND CONTENT = 20 z
- 8 POINTS
L.
L—\
b ¥\\\b
E
3*}: -3... .47; "1‘... -1...
LOG PERCNT 7 RX STRHIN
DST—IOFUSCPZOO
8 E MODULUS
e.l
Z FIGURE n.35
. GANPLES SI-22,SI-23
L SAND cONTENT = 20 x
L 6 POINTS
'- A
E A
r
r
~31l.“ -:'.:.o oi†031.82 0|?†"1500
LOG PFRCNT 7 RX STRRIN 5
DST-IOFICPZOO
E+05 PSI
E+05 PSI
O E HOOULUS
FIGURE 3.34
SAMPLES SI-22,SI-23
SAND CONTENT = 20 Z
6 POINTS
Cu†.000 S200 S... "0. :‘0. â€0' 82-0 â€0. q.
lTTiTVlTTUTfTTII‘WTTI
A A
M
LOO PERCNT- ' 7 AX STRRIN s
OST—lOP3CP200
8 E MODULUS
9: FIGURE 8.36
“r SANPLES SI-22,SI-23
;. SANO CONTENT . 20 z
E 6 POINTS
3+
=C
;. .
p A
g2
"I
a of.†41.50 .31.†~31.“ a]... «In. 03'
L00 PERCNT 7 ax 51391"
UST-lOFSCPZOO
E+05 PSI
E+OS PSI
203
2 E HOOULUS
3'
3: FIGURE 3.37
. SANPLES SI-I1,SI-13,SI-16
g- SANO CONTENT = 45 z
.E II POINTS
=' :
é :
fl
T T-
; T- K \m
6+- J J_ 1\1\L I
~S’.OO -: .so 2 .Oo T.SO - I .oo - .soo IT.I
LOG PERCNT 1 RX STRAIN
UST~1FUSCPO
2 E HODULUS
9: FIGURE 3.39
’E SANPLES SI-11,SI-13,SI-16
;. SAND CONTENT = 45 z
.‘. 10 POINTS
3 L-
2 T-
. T-
Q
3
a. t
o b A Q
a- . S
6 «Inc 41.30 44.00 -II.EOL 41.00 ".500 071
L00 PERCNT I RX STRHIN
DST—IFICPO
E+05 PSI
E+05 PSI
2 E HOOULUS
FISURE 3.38
SANPLES SI-H,SI-13,SI-16
SAND CONTENT 8 45 X
9 POINTS
0.00 '.°° Etc. I... â€a. t... â€a. I... .0. q.
I r V r l U I F I r l r U I I I I I h
a
A
JO
0 l 1 I l I 1
ms: «.39 -:.oo 4.» moo .500 O.‘
LOG PERCNT I RX STRRIN '
1
DST-IEBCPO
2 E HODULUS
FIGURE LAO
SANPLES SI-TI,SI-13,SI-16
SAND CONTENT = 45 I
TO POINTS
.0†I.†".0 I... 10.9 I... 20.9 32.0 3... 0%.
l l l l l J_
or.“ 4.0 a.» a... 0.3“ O.‘
LOG PERCNT I RX STRRIN
OST-lFSCPO
..l
OTIITIUIrlrITIrljlji—Tl
:R...
8
E+OS PSI
E+OS PSI
204
2 E HODULUS
FIGURE 8.41
SAMPLES SI-lT,SI-13,SI-16
SAND CONTENT = 45 I
14 POINTS
LOO 6.00 we «.0 20.0 20.0 21.0 32.! am 00,.
IIITTIITTTiTTITYITWY
NM
0 I"_,4.E)° ‘iSI' -:1.O(‘ - [:50 - El-OO ' .1300 of
LOG PERCNT I RX SIRRIN
“ST-IFUSCPSO
2 E flODULUS
3L
at FIGURE 8.43
'. SANPLES SI-11,SI-13,SI-16
g— SAND CONTENT = 45 2
.' 12 POINTS
‘ F
SF
3 r
a: ..
.' A A.
P A
8.
4 A
I.
:P I J, I I I I
also or.“ a... o: .u own um 03
L00 PERLNT I Ax STRAIN
USTwlFlCPSO
E+05 PSI
E+OS PSI
2 E HODULUS
4*.
FIGURE 9.42
SANFLES SI-11,SI-13,SI-16
SAND CONTENT = 45 z
13 POINTS
0.00 .0†“.0 S... â€a. 1‘0. â€0. "0. â€0.
TTTIWTTTTTIUIYIrr'TII
oI
_ I—
L
p—
41.00 4.50 4.00 mm 03
L00 PERCNT 1 OX STRRIN
OST—lEBCPSO
2 E HODULUS
2: FIGURE p.44
‘» SANPLES SI-T1,SI-13,SI-16
3» SANO CONTENT . 45 z
.E 9 POINTS
'P
8
.t
3:
E» .
“_ A
E. .
g:
D'- l 1 l L l 1
.S'JO mu 4..- 4.30 .I... -4. .3
L00 PERCNT 1
OX STRRIN
DST-IFSCPSO
E+OS PSI
E+05 PSI
205
2 E MODULUS
3* _
..t FIGURE 8.45
‘.. SANPLES SI—IT,SI-I3,SI-IG
;- SANO CONTENT = 45 z
.* 15 POINTS
6:
g.
A".
S.
.b\ 3
8.- MH\
'b A
J-
LOG PERCNT . 1 .9X STRRIN.
DST—IEOSCPZOO
2 E NUDULUS
.: FIGURE I.47
*_ SAMPLES SI-11,SI-13,SI-16
g- SAND CONTENT = 45 Z
P 15 POINTS
é.-
31
fl
9. A
a A A
e~ A
OF ‘ A
8.?- A \
0:0" I I I I I I
3'.“ 4.50 4.00 a.†4.00 "no 0.7
LOG PERCNT I RX STRRIN
OST-lFlCPZOO
E+05 PSI
E+OS PSI
2 E HOOULUS
;.
3. FIGURE I.46
_- SANPIES SI-TI,SI-13,SI-16
g1 SAND CONTENT = 45 I
9: 15 POINTS
‘ L-
F
I.
.;
gL
{
g .. W
’_ A
a- .
6 dict! 41.50 41.00 41.50 41.00 ulna .71
L00 PERCNT l RX STRRIN
OST~1E3CPZOO
2 E NODULUS
9: FIGURE I.48
a. SAMPLES 51-11,SI-13,SI-16
;. SAND CONTENT = 45 2
“F, 11 POINTS
5:
g.
it a
z» “ ..
I:
.L
8,.
" i t. i... 3... :1... .1. .3... .S
LOG PERCNT 1 RX STRHIN
08T-1F5CP200
E+OS PSI
E+OS PST
'1_, 4.03 0.03 I:.O IO.O No.3 24.3 10.0 33.0
206
- s E MODULUS
L FIGURE 3.49
SANPLES 51-6,SI-18,SI-19
SAND CONTENT = 45 z
7 POINTS
12.0 I... a... «.0 a... :14 a... u,-
A
0.00 O...
lrIIIITVIr'TVU'I—TT
J J J l i I
.iO“ 02-†.!IN 0|.†.'l“ .0â€. 0..
L00 PERCNT 4 OX STRRIN 3
08T<4RUSCPU
s E MODULUS.
FIGURE 3.51
SANPLES SI—G,SI-1G,SI-19
SAND CONTENT . 45 z
7_ POINTS
3. o. .019;
rTIrITIIITIY'TrITTIjI
l
0. o“
LOO PERCNT 4
08T—4F1CPO
I I I I
.1.“ oh. â€no 0?
OX STRHIN
I
4'... 4..
E+OS PSI
E+OS PSI
S E NOOULUS
h
FIGURE 8.50
SAMPLES SI-6,SI-IG,SI-19
SAND CONTENT 8 45 Z
7 POINTS
.0†‘4'. ‘it. E... "o. t... â€a. ' "I. '0. *.
T T
IITrT—IITINITUIITU
0I
L.
L.
I I I
~14» -.m o.‘
RX STRRIN
LOG PERCNT 4
OST—4EBCPO
5 E MODULUS
FIGURE 3.52
GANPLES SI-G,GI-1G,SI-19
SANG CONTENT = 45 z
7 POINTS
4.00 0.00 11.0 ".0 20.0 20.0 20.0 31.0 39.0 0010
b
LITIFIjITITTIITII—jITTI
I I I
on.“ OJ. OJ
RX STRRIN
9'1
I I I
4*... .3.“ .1..- a.“
LOG PERCNT 4
OST-4F5CPO
E+OS PSI
E+OS PSI
207
'5 E MODULUS
FIGURE 3.53
SANPLES SI-6,SI-18,SI'19
SAND CONTENT = 45 Z
10 POINTS
c.oo O.oo 12.3 10.3 No.0 00.0 10.0 IO.0 II.I 0g,0
Iï¬TrrYTITjTTIIFTITEFY
6‘ _L .I I I I I I
also -: .5: 4.00 -I .sc 4 .00 um 07
L03 PERCNT 4 9X STRRIN
OST—4EOSCPSO
S E NOSULUS
2: FIGURE 3.55
‘. SANPLES 51-6,SI-18,SI-19
;. SAND CONTENT = 45 z
or 8 POINTS
F:
;R
ET
5:
E.
.L
S.
. F-
I
D .g.‘ ~81.“ oil.†“I... “I.†. .1.“ .j
LOG PERCNT 4 ï¬x SIRHIN
OST—4F1CPSO
E+05 PSI
E+OS PST
5 E MODULUS
FIGURE I.54
SANPLES SI-6,SI-lG,SI-I9
SAND CONTENT = 45 Z
8 POINTS
0.00 0.00 IIJ I... 10.0 “.0 I... 33.. Id Cr.
ITIIITTWTTITIUI‘TI‘ï¬I—TT
J I I I I I I
41.00 a.“ 4.110 -1.so 4.†~93 0.‘
LOG PERCNT 4 RX STRRIN 3
UST-4F3CPSO
5 E HODULUS
0.l
SI FIGURE 3.56
‘_. SAMPLES SI-G,SI-18,SI-19
;-. SAND CONTENT = 45 I
,~ 3 POINTS
5:
a»
E r
T- A
g- A
S:
g:
.:L I I I I I I I
-S'.00 4.50 4.00 a.» 440 -.000 0!
L00 PERCNT 4 OX STRHIN
OST-4FSCPSO
E+OS PSI
.000 '03, Ste. E... â€to .‘I. â€O. n‘. â€O. .‘r.
E+05 PSI
0‘1
:2.: 3-.3 43,3
I403 .40? 12.3 [0.0 23-0 N30 â€.9
208
'5 E NOOULUS
I FIGURE 3.57
. SAMPLES 51-6,SI-18,SI-19
. SAND CONTENT = 45 z
t 12 POINTS
L
I
I- A
.. \N A
T— A A
" A
1::J 410-- 721.53 “:00 41.53 "-7133— “74:37—04—
LOC PERCNT 4 RX STRAIN
- .. f‘ , - 3
OST—APOSEPEUU
5 E MODULUS
'1
L
. FIGURE 3.5T
. SANPLES SI-6,SI-1G,SI-19
~ SAND CONTENT = 45 z
5 11 POINTS
I.
L
b A .
:\\\>\f A
I. A A A
C .
-500— 41.03 41.00 ii... “I,†,3... 0%
COO PERCNT 4 AR STRAIN
DST—4F1CP200
E+05 PSI
E+05 PSI
S E HOOULUS
3..
.: FIGURE 3.51
'_ SANPLES SI-6,GI-13,SI-19
3L SANO CONTENT - 45 x
q- 12 POINTS
:L
g.
3:
9'. i
:h A A
:3“ A
I. A
3.
0 A
T-
3.
6 din 41.53 41.33 311.33 -1J.33 "1033 13.I
LOG PERCNT 4 RX STRRIN
OST—4E3CP200
5 E HODULUS
3F
.: FIGURE 3.60
33 SANPLES SI-6,GI-13,SI-19
2. SAND CONTENT = 45 z
2» 10 POINTS.
é_ 1
gr
:- ,. A
.
'. ,_ A
2 A
.*' . .8 ‘
3 L-
g '- A
g:
g:
. 0:... 41.“ 41.00 41.80 “Jo. â€lid 0.:
L00 PERCNT 4 RX STRAIN
OST-4FSCP200
E+OS PSI
E+05 PSI
8 E MODULUS
209
3L
9: FIGURE 3.61
‘. SANPLES SI-24,SI-25,ST-26
;. SAND CONTENT = 45 1
.~ 7 POINTS
:- .-
3:
g:
g:
'r
a: m ‘21:; 4103 -J'o -Joo - 1sun I
LOG PFRCKT 7 RX STRRIN
USI—IOPOSCPO
8 E MODULUS
3L
" L
3+ FIGURE 1.63
._ SANPLES SI-24,SI-25,SI-26
;. SAND CONTENT = 45 z
or 6 POINTS
fF
g.
. T-
:F
EC
'L
S, .
’L
9. 08%.!†41-50 81.00 II.“ 4‘... ’0i‘“ .3
L00 PERCNT 7 RX STRRIN
OST~10F1CPO
E+OS PSI
E+05 PSI
O E flOOULUS
OIL!
fir
FIGURE 3.62
SANPLEG SI—24,SI-25,SI-26
SAND CONTENT = 45 Z
6 POINTS
4.33 0.33 13.3 10.3 23.3 34.0 30.0 33.0 30.0
IIIWIEIWUfTTUU'UUï¬I
"'I
r
47.33 -0.53 4.33 -1.so o.soO 3.
L00 PERCNT 7
OST-IUFBCPO
8 E MODULUS
-E .00
RX STRRIN
.t FIGURE 3.64
=_ SAMPLES SI-24,SI-25,SI-26
g. SAND CONTENT = 45 I
A 6 POINTS
g.
or
3P
3:
' I
8. A
JE I I I I
. -3'.00 41.33 41.33 -1.00 o1.00 -.030 0.‘
L00 PERCNT 7 RX STRRIN
DST—IOFSCPO
E+05 PSI
E+OS P51
8 E MODULUS
FIGURE 3.65
SAMPLES SI-24,SI-25,SI-26
SAND CONTENT = 45 I
9 POINTS
13.3 13.3 33.3 24.3 30.0 33.0 30.0 0330
oTT—Yr'TT‘rTVIIï¬r'
210
:r
9L
_I
6 -3’.oa 4.53 4.30†-1.53 .1.CC €333 (LI—-
LOG PERCNT 7 RX STRRIN r
DST—IOPOSCPSO
8 E HODULUS
g.
9: FIGURE 3.67
3. SANPLES SI-24,SI—25,SI-26
g. SANO CONTENT = 45 z
4» 3 POINTS
2 I.
3L
3L
3.
d
I": I I
O ~3'l.00 41.80 ~21... I.“ 0|.†â€no O.I
LOG PERCNT 7 fix STRRIN
OST—lOFlCPSO
E+05 PSI
E+05 PSI
0.1*__73.03 0.30 13.0 10.0 30.0 34.0 00.0 02.3 20.3 43,0
u' I I I I I FT! ij rj I I T T I I r
B E HOOULUS
FIGURE 3.66
SAMPLES SI-24,SI-25,Sl-26
SAND CONTENT I IS I
9 POINTS
7TYITEITrTT'TEETI
I
I
0.00 0.90 [2.0 I... I... I... 2.... '0' â€a. Q.
I
6“ I I L J I I L
$.33 .0 .33 -3 .33 -1.03 -1 .33 - .333 0.'
L00 PERCNT 7 RX STRRIN 5
DST—10F3CPSO
8 E HOOULUS
FIGURE 3.68
SANPLES SI-24,SI-25,SI-26
SAND CONTENT = 45 X
9 POINTS
:30 :E‘RCNT... ““7 “Ax STERN“
OST—IOFSCPSO
E+05 PSI
E+OS PSI
00' A.†I.†".0 “.0 ".0 24.0 29.0 32.0 30.0 421.0
211
8 E MODULUS
FIGURE D.69
SANPLES SI-24,SI-25,SI-26
SAND CONTENT = 45 Z
10 POINTS
0.00 0.00 I24! ".0 20.0 20.0 20.0 82.0 30‘.“ 001..
TFTTTrfTTTTTTTTrTT
T
T I
o.
1
-3133 -3 .30 -3 .33 -: .53 -| .33 - .533 0.'
LOG PERCNT 7 RX STRHIN
DST—IOFOSCPZOO
8 E MODULUS
FIGURE D.71
SAHPLES SI-24,SI-25,SI-26
SAND CONTENT = 45 I
9._POINTS
IVTTTETITTTTTTT'ITTTTI
I .1 L _1 1 l 1
o0'.03 -3.53 4.03 4.00 4.00 -.000 0.'
LOG PERCNT 7 RX STRRIN
0
UST-lOFICPZOO
E+OS PSI
E+05 PSI
8 E HOOULUS
FIGURE l.70
SANPLES SI-24,SI-25,SI-26
SAND CONTENT = 45 I
10 POINTS
4.33 0.30 13.3 10.0 30.0 30.0 00.0. 03.0 00.0 00.0
TNTiTrNTï¬rTTNIIWjUrUN
a" J 1 _1 1 1 I J
4.30 .3.» -3.03 4.03 4.33 -.030 07
L00 PERCNT 7 RX STRRIN
DST-IOEBCPZOO
8 E HOOULUS
:u .
9: FIGURE 3.72
3, SAMPLES SI-24,SI-25,SI-26
;. SAND coNTENT = 45 z
.* 9 POINTS
i:
3 :
§L
g:
3:
1r
L.
. -0'.03 41.00 41.00 «1.00 «1.00 5000 0.:
L00 PERCNT 7 RX STRAIN
08T-10F5CP200
E+05 PSI
E+05 PSI
212
2 E MODULUS
FISUNE 3.73
SAMPLES SI-15,SI-l7
SAND CONTENT = 65 I
6 POINTS
.000 0.00 [2.0 ".0 "I. .‘0' â€0. "A. â€0: ‘cd
[T T T ï¬T T T T__T T T T Ti T T T T T TT
A A
I.- w
l | I J l l l
4.33 3.7—
).00 -2.30 -2-00 -|.SO --800
L00 PERCNT 1 ex STRREN
_ _ _ _ 1
USIWILOSCPU
2 E MODULUS
1
——
JT
i
FIGURE 3.75
SAMPLES SI-15,SI-17
SAND CONTENT = 65 Z
6 POINTS
TTTTT
.0 30.0 30.3 30.3 33.0 30.3 33,3
TTTTTTT
0.92 0.00 12.0 1!
FT T7 T T T
R
*‘“$ '
L. \
l l l l Q J
- .03 -3.03 -3.03 4.00» 4.03 -.003 03
L00 PEKCNT I RX STRRIN
OST~1F1CPO
’1
E+05 PSI
E+OS PSI
2 E MODULUS
“f.
iTTTTTTTTTTiTTTï¬TTTiT
FIGURE 3.74
SAMPLES SI-T5,SI-17
SAND CONTENT = 65 I
6 POINTS
0.00 0.†12-0 I... No. I... "0.. 32.. â€o.
° 0 3100 021. SO 0;: - 11.80 j.†0 .1.“ Dill
LOG PERCNT 1 ax STRAIN
UST—lEBCPO
2 E MODULUS
FIGURE 3.76
SAMPLES SI-15,SI-17
SAND CONTENT = 65 Z
6 POINTS
4.03 Doc. ".0 IO-O 20-0 86.0 23.0 32-0 33-0 COIO
TjTTTrTTTrTfTTjjjTriT
° 'Slrofl -:M in 41.“ . ti.†. .13. 0.:
LOG PERCNT 1 ax STRAIN
08T-1F5CPO
E+OS PSI
E+OS PSI
Q!
213
2 E MODULUS
3::
T Tï¬ï¬
.0" '0†O: a. N. 0. â€I. t. 0. P. 0’ â€.0 â€0° C
I
' FISURE 3.77
: SAHPLES SI-IS,SI-I7
_ SAND CONTENT = 65 z
. 8 POINTS
I.
I.
I-
I.
I.
I.
.- M N
-SI.OO ~81. so 4100 :1.80 . 31.00 -fl00 3 .I
LOG PERCNT 1 RX STRAIN
OST-IPOSCPSO
2 E MODULUS
P
[ FISURE 3.79
I SAMPLES SI-Ts,SI-T7
» SAND cONTENT = 65 I
7 POINTS
T I T T T '
TTTWTT
3" J J l ‘
. 4103 -3.03 -3.03 41.00 4.00 -.000 0.1
L00 PERCNT 1 RX STRRIN
OST—IFICPSO'
E+05 PSI
E+OS PSI
2 E MODULUS
q»
FIGURE 3.73
SAMPLES SI-IS,SI-l7
SAND CONTENT = 65 I
8 POINTS
0.33 0.03 13.0 I0.0 33.0 30.0 30.0 03.0 00.0
TTï¬ufTTTj—TTTTTTTTTTTIT
J l 41
4133 -3.33 -: .33 - I .53
LOG PERCNT I
DST—1F3CP50
2 E MODULUS
_l J -+_
“I.†'0bco o.
RX STRRIN
I
;[ FIGURE 1.33
~ SAMPLES SI-TS,SI-T7
§- SNNT cONTENT . as I
.f 6 POINTS
EL
0+
:r
a:
. .- N‘g\\
8. I-
6 -JIEN 41-“ o...†41-“ 41.†-.JIU 0.:
LOB PERCNT I RX STRRIN 1
OST-IFSCPSO
E+OS PSI
+05 PSI
A.†3.33 12.0 ".0 20.0 20.0 ".0 32.0 33-0 .01-0
' I T T T ,T T7 T 4T T T T T47 T T7 T T T T7 T 1’ T
“J I.
F
2 E MODULUS
2F!-
E+OS PSI
9, FIGURE 1.01
'. SANFLES SI-TS,SI-17
;. SAND CONTENT - Is I
.~ I POINTS
*2:
§r
St‘7“‘+%~
o +- \
6"} I I 1-. I
~3.00 -2.$O -£.CO -I.Su -l.00 .
LOG PERCNZ I RX STRRIN
I
UST—IEOSCPQUO
2 E NUDULUS
FIGURE 3.83
SAMPLES SI-15,SI-17
SAND CONTENT = 65 1
8 POINTS
‘0'. '0'. T20. E... '00. t... 1.0. ’2-0 ,.o° OOro
T T T T T T T 4T T T’ T7 T T T T TTT T TAT T ‘ri T
DDS PSI
0: I __J 4 i ,1 I
.00 -3.33 -3.00 -1.00 -1.03 -.003 31'
L00 PERCNT l RX STRRIN
OST~1F1CP200
2 E HODULUS
FICURE 3.82
SANPIES SI-TS,SI-17
SAND CONTENT . 65 z
9 POINTS
T77 T I I T T T T T T 7T T' T T T T
7
b
um mm um um ma «a «a a4 â€a qg
1* 4T T 4“T
41, l l l l 11 I
oaloo -3.33 -3.33 o1.03 ~1.00 -.033 03
LOG PERCNT I Rx STRRIN
UoT-IE3CP200
2 E HODULUS
"a
FIGURE 3.84
SAMPLES SI-15,SI-17
SAND CONTENT = 65 I
8 POINTS
. —-—
. '31. .21... -!‘-“ - ll.†3.. - .1“ O 5
L33 PERCNT 1 RN STRRIN
DST-IFSCPZOU
E+OS PSI
E+OS PSI
t J I J _l_. #1 l L
-313: ~2.So -3.3u -1.so -1.33 .033 3.r_
LUG PERCNI 4 RX STRRIN
USI~4PCSCPU
5 E MODULUS
31 FIGURE 0.37
"I SAMPLES SI-20,SI-3I
;.. SANI CONTENT . IS 3
.“ 4 POINTS
.3 F
"I
3
:3 L
L
8»
d
. b
édbL J I I J I _J
-i§i0 -3.03 o3.00 ~1.00 -1.00 -.003 0:7
L00 PERCNT 4 RX STRRIN
0.20 E-SO I2-O I.-° 20.0 2.0. "0. a0. 8.. “I.
T T T T T T T 1 T T T 1 T T 1' T T T T T T
.-l
5 E MODULUS
FIGURE 3.85
SAMPLES SI-20,SI-31
SAND CONTENT = 65 1
4 POINTS
215
08T—4F1CPO
E+OS PSI
E+05 PSI
«g_
T.†.000 T200 T's. â€a. 2.0. "a. â€I. â€0.
T T T I T T T j T j T T T T T F T j T T r
s E MODULUS
FIGURE 3.86
SAMPLES SI-20,SI-31
SAND CONTENT 8 65 Z
4 POINTS
9'1
J I_IJI I I 41 I +__
.0133 .3.53 -3.33 o1.so -1.33 -.033 3.
L00 PERCNT 4 3x STRAIN
CST-4E3CPU
5 E MODULUS
SI
.: FIOURE 3.33
‘. SANPLES SI-23,SI-TT
;» SAND CONTENT = 65 z
.[ 0 POINTS
:3
g.
L
:I
2T
3:
g:
6 oil-r00 -3..03 ~21.†- ll.“ 4‘.“ - .1.†0%
LOB PERCNT 4 RX STRRIN
OST-4FSCPO
E+OS PSI
E+OS PSI
5 E MODULUS
216
S E MODULUS
§+ :-
2: PIGURE 8-89 0: FIGURE 3.90
‘. SANPIES SI-2o.SI-31 '. SAMPLES Sl-20,SI-31
;_ SAND CONTENT = 65 I g. snug CONTENT = 65 z
.» 6 POINTS _- 6 POINTS
i†iâ€
'2 P 9r
St S: .
e _ -. __ A
g b 2 A
y- .- A
'2 A 0—0 .. __
2: A A A U3 :3, _ A
8- A Q'sâ€
-' U) 03
I O ’
g + 8...
- I- LIJ . r-
6 . .33 41.1.3 41.33 .11.33'— 41.33 ".333 117J 6 4%†41.50 in 41.33 41.00 c.1000 ï¬â€”
LOG PERCNT 4 RX STRRIN 3 LOB PERCNT 4 RX STRRIN 3
OST~IEOSCPSO UST-4P3CPSO
S E MODULUS S E MODULUS
E; $3
._ FIGURE 3.91 9: FIGURE 3.92
g. SAHPLES SI~20.SI-31 *. SANPLES SI-2o,SI-31
;. SAND CONTENT = 65 I g. SAND CONTENT = 65 z
.* 6 POINTS .' 6 POINTS
3: 3:
E: 3:
=2; 5...;
3_ “'E~
. I- [g g b
8 .. + 8. .
‘ b m .. .-
ALI -.
o . .00 .31.“ 41.03 41.33 41.33 "1303 ark a - .03 41.00 -3‘.00 .1100 41.00 «.300 0.IL
LOG I’IZRCNT 4 RX STRRIN 3 L00 PERCNT 4 RX STRRIN 3
OST—4F1CPSO
DST-4FSCP50
0—4
(0
I).
I!)
L)
LL!
0--0
(f)
If)
C)
DJ
5 E MODULUS
217.
5 E MODULUS
I: F
;. FIGURE [.93 0. FIGURE 3.94
. SANPIES SI-20,SI-3| '1. SANPLES SI-2O,SI—ST
§- SAND CONTENI . ‘5 z ;_- SAND CONTENT = 65 z
,- 3 POINTS .. 7 POINTS
:- I— :- p.
e? .I
II fr
é " 8' "
D '- ° +-
é’ A ‘6 5I
’ P
z _ A A 0—0 :L
"I A A g.) -— P
8: _ A 8 ..
a U) 0'
F O E
gp \\\\\\\\\\\\\\ + E»
O b “J . .-
élgt-OO—fzty - -3133 .13."-..‘153 “1533 3.1T— 5:01†~31.“ ~3J.oo ~11." 41.33 “1003 0}—
OG PEKCNT 4 RX STRRIN LOG PERCNT 4 RX STRRIN 3
OST~4POSCPQUU
‘5 E MODULUS
OST—4E3CP200
S E MODULUS
I-
3; FIGURE 3.9: .[ FIGURE 3.94
‘1 SANPLES SI-23,SI-IT "F SANPLES SI-2o,SI-31
2» SAND CONTENT = 65 I ;. SAND CONTENT = 65 I
Q†7 POINTS .I 6 POINTS
SE fl
2 r g _
_+ L
5†:3 g:
.I .. ._
03 w .
I- D -
$~ + a.
v .— “J b
rib fr: I l I l l l 1
" 3+3! 41.50 41.03 ~11.» $.00 .3000 0? O «£00 «.03 -3.03 .1.“ -I.00 -.000 0.‘
L00 PERCNT 4 RX STRHIN 3 L00 PERCNT 4 RX STRRIN 3
OST—4F1CP200
OST-4FSCP200
E+05 PSI
E+05 PSI.
LOO 1.00 ".0 ".0 20.0 24.. I... â€0. â€3 CO...
I AT Tg—Ti I IV I Vii T I I Y7 I 1 Y Y I 4T 1 T I
D
. 218
8 E HODULUS
FIGURE D.97
SANPLES SI-27,SI-28,SI-29,SI-30
SAND CONTENT = 65 2
6 POINTS
b
.° '1
".O ".0 10.0 20.0 19.0 32.0 30.0 00,0
_J_--_.L___.--J_.._ 1 I JI
2.02
-’.OO -l.$u °I.$O -|.13 0.503 0.
L08 PERCNT 7
DST—10FOSCPU
8 E MODULUS
RX STRRIN
5
FIGURE 3.99
SAMPLES SI-27,S
SAND CONTENT = 6
7 POINTS
I-28,SI-29,SI-30
5 z
â€r T471 I T V TEETV T T I 7’ I ’T I I I T I T V
8
E
3"
C' l I 4J l l l l
- .00 4.50 a 00 4.80. 4.00 «000 0.‘
L06 PEKCNT 7 RX STRRIN
DST-IOFICPO
E+05 PSI
0.L44470.00 0.00 11.0 II.0 20.0 24.0 10.0 32.0 00.0 oqtg
E+05 PSI
B E flOOULUS
FIGURE 3.98
SANPLES SI-27,SI-28,SI-29,SI-30
SAND CONTENT = 65 I
7 POINTS
T ET YAET I 4T7 I I IAETT I T I I I 4T I 1 I I Y
l l 1 I
-:T.00 4.00 4.00 4.30 4.00 -.soo o.’
LOG PERCNT 7 RX STRRIN S
OST—10E3CP0
8 E ï¬ODULUS
9: FIGURE T.Too
*. SANPLES SI-27,SI-28,SI-29,SI-30
g. SANO CONTENT = 65 I
“L 7 POINTS
g.
L.
2.
gr
=:
g:
g:
.; ~0.00 -:{00 T:;{00 -|tIO -1100 -::ii iii
LOG PERCNT 7 RX STRRIN
08T—10F5CPO
E+OS PSI
219
a E MODULUS
3L
;: FIGURE 3.101
- SAMPLES SI-27,SI-28,SI-29,SI-30
§~ SANO CONTENT = 65 z
.- 10 POINTS
:1:
“d;im.——-—1 _.___.L__. _.l_. . l J 1
' Q
-3.0( -2.:~: -.5(‘u 0.
L00 PERCLT 7
DST-103850
8 E HUUULUS
-2.01‘ -l.5' -14â€
9X STRHIN
T‘CSCJ
;: PICONE 3.103
S_ SANPLES SI-27,SI-28,SI-29,SI-30
A_ SANO CONTENT = 65 z
â€E O POINTS
2* .
o†A
3* .
9: 5:
:P
a L
“+-
g:
g:
“ .5... .1... ..'... .5... .3... .3... ..+
LOG PEHCNT 7 RX STRGIN
OST-lOFlCPSO
E+OS F’SI
E+05 PSI
8 E HODULUS
3L
9: PIOOPE 1.102
‘. SANPLES SI-27,SI-28,SI-29,SI-30
;- SANO CONTENT = as I
,- 10 POINTS
5:
3:
a:
a:
LOG PERCNT. . 7 ..nx STanN.
‘ _ 5
OST-lOEBCPbU
8 E MODULUS
1L
9L FIGURE 3.104
3. SANPLES SI-27,SI-28,SI-29,SI-30
" - SAND CONTENT = 65 Z
§~ 8 POINTS
_ A .
9t AA
:4». A
.E
a:
g:
a. ~8T.“ ~83 -!I.N - f.“ . t†, .1.“ :3—
L08 PERCNT 7 ax STRRIN
UST—lUFSCPSU
E+OS PSI
E+05 PSI
8 E HODULUS
FISURE 8.105
SANPLES SI-27,SI-28,SI-29,SI-30
SAND CONTENT = 65 1
12 POINTS
0.00 0.00 10.0 10.0 00.0 00.0 00.0 00.0 00.0 00,0
Tï¬'ITTTrTIrr'rjtTIT'TV
220
. ’,]0r:0 -!1.50 ~21.“ -~ [1:50—- -| .3: - .532 O . —
LOG PERCNT 7 RX STRRIN
s
UST~IOPUSCPZOO
8 E HODULUS
S
b A p
=\ â€â€œâ€œ::.:;'::;;:
n .- (A A use (mum-0'1.
q..
i; 5‘ .
a : A
:-' FIGURE 1.107
2* SANPLES SI-27,SI-2O,SI—2P,SI-30
8; SANO CONTENT = 65 z
4_ 11 POINTS \\\
6 3.x al.:fo .tl.00 41.1.; ~1L.00 J000 0.I
LOG PERCNT 7 OX STRRIN
OST-lOFlCPZOU
E+OS PSI
E+05 PSI
a E flODULUS.
FIGURE 8.106
SANPLES SI-Z?,S
SAND CONTENT = 6
POINTS
“11
l-28,SI-29,SI-30
5 Z
11
A.†0.00 11.0 “00 20-0 Ch. ".0 â€.0 3...
TIroITTITIUEVIVIYIj'
I l l l l L 1
-0‘.00 4.00 4.00 -1.00 4.00 -.000 0.‘
LOG PERCNT 7 ex STRAIN 5
OST"1033CP200
8 E HODULUS
i: A
9 1. A anus $1.27. 51.20
g 81—â€. SFâ€
"' A “ (CHM-0.".
2 _ 11 001010
9:: .
3 :
z“ FIEURE 8.108
2‘." SAMPLES SI-27,SI-28,SI-29,SI—30
g: SAND CONTENT = 65 Z
‘_ 11 POINTS
g.
6 _’I.†~31.“ ll.“ -IIJO -|l.' of.“ 0.:
L00 PERCNT 7 AN STRAIN
OST~1OF5CP200
APPENDIX C
DAMPING RATIO FOR SAND-ICE SAMPLES
221
DAMP RRTIO
DEMP RATIO
an an an an an an an Jâ€
I l
3 Dflf‘lPING
FISUNE C.T
SAHPLES SI'B,SI‘9,SI-10,SI-12
†SAND CONTENT = 20 I
9 POINTS
‘5
§.
§_
6 Tie: 4130 41.0: 41.00 ï¬n 3000 0%
L00 PERCNT I RX STRRIN 2
CST-IFUSCPU
3 DHT‘IPING
L FIGURE C.3
SANPLES SI-S,SI-9,SI-10,SI-12
SAND CONTENT = 20 I
10 POINTS
0!“ ol". .290 ~22. .2" .m JPO
T
E
‘3
S
I
§
05 I I I I I I I
4'.00 4.00 4.00 4.00 4.00 "000 T‘
LOG PERCNT I FIX STRRIN
OST-lFlCPO
222
ORHP RATIO
0.; 2 acct-0: 1.500900 .
OPNP RATIO
3 DHHPING
I
FIGURE C.2
SANPLES SI-O,SI-9,SI-10,SI-12
P SAND CONTENT = 20 1
10 POINTS
T
I ‘ 1
an an an an gâ€
PI" OIâ€
I"
T
b
D
b
L.
I A J_ I L I J
~0E00 4.00 4 .00 -I .00 -1.00 ..000 II.r
LOG PENCNT I 9x STRPIN 2
OST~1F3CPO
3 DRHPING
FIOURE C.4
SANPLES SI-O,SI—9,SI-10,ST-12
SANO CONTENT = 20 z
I 9 POINTS
.I00 .m .000 .020 .200 .270 .000
I I.
! Jon-02 7 .UM'“
j
9
l j l
4.00 -.000 0.’
AX STRAIN
O
LI
L
0 .fl .8.“ 4.00 0|.“
LOG PERCNT I
OST~1F5CPO
ORHP RRTIO
DAMP RRTIO
2223
3 DAHPTNG
NL
51.
g.
a h A
. ‘ .
m .
g. A AA
g.
5-
' FIGURE C.5
6' SANPLES SI—O,SI-9,SI-TO,SI—12
E- SANO CONTENT = 20 z
; 13 POINTS
5.
AL,
9 'O'JIO '21.“) SL-OO Tl-LSI" 41.00 ï¬ne 0}
LOB PERCNT ‘. RX STRRIN
OSTMIFDSCPSU
3 DRI‘TP I NC
é_ FIGURE c.7
; SAMPLES SI-B,SI-9,SI-10,SI-12
s- SAND CONTENT . 20 z
5. 12 POINTS
S.
.8- >-
g >—
' A
_ A
E . .
if A
:5 .s
E.
6 - n†~21.“ 08].“ #1.“ 41-“ O-ISN 0.1'
LOG PERCNT I RX STRRIN
OST-IFICPSO
ORHP RRTIO
DHHP RRTIO
a OANPING
0.
5» FIGURE C.A
£_ SANPLES SI-O,SI-9,SI-TO,SI-12
- SANO CONTENT = 20 z
5- 12 POINTS
g;
5.
0L 3 A
7 A
9L ‘
E.
:3...
E.
6 -§1-90 4'.†41.00 41.80 41.00 ~48†0.3
LOG PERCNT 1 AX STRAIN
DST—IFBCPSO
3 DHHPING
g_ TISONE C.O
- SANPLES SI-S,SI-9,SI-10,ST-12
§~ SANO CONTENT = 20 2
5. 10 POINTS
5.
g-
g-
.1
g» an ‘C
l- A A
A
?* . . .
§
'2?
FL- I I I I I L
. - 1.00 4.00 4.00 4.00 4.00 ~00- 07
LOG PERCNT 1 FIX STRAIN 2
OST-lFSCPSO
224
3 DRHPING
I:
5
5.
’ 3
5.
E
§L
0. FIGURE C.9
g. SANPLES SI-8,SI'9,SI-IO,SI-12
oi: SAND CONTENT = 20 I
;-_- 5.- 15 POINTS
a N
n: 9"
a?
)7 &'
(I
I: r_ .
0-1.W 4.LI.0 E00- -1 .0 1.00 41000 0}—
L03 PLRCNT I RX STRRIN 1
DST—IFDSCPZUO
3 DRHPINC
gr
5. FIGURE C.11
; SANPLES SI-8,SI-9,SI*IO,SI*12
5’ SAND CONTENT = 20 X
g. ,JA_.POINTS
E.—
g1—
5.’ A 5A
3. A A
c>§ "â€1E’AA
Z .-'
g $-
3: 4"
0'.
D :4.
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3 DAHPING
T‘ FIGURE C.10
5* SANPLES SI—O,SI-9,SI-TO,SI-12
g. SANO CONTENT = 20 z
15 POINTS
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5’ FIGURE C.12
a- SANPLES SI-O,SI-9,SI-TO,SI-12
; SANO CONTENT = 20 I
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SAMPLES SI'2,SI-3,SI-4
SAND CONTENT = 20 1
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5L FIGURE C.Ts
; SAMPLES SI‘2,SI-3,SI-4
ET SAND CONTENT = 20 I
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SANPLES SI-2,SI-3,SI-4
SANI CONTENT 8 20
7 POINTS
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OST-4F3CPO
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FIGURE C.16
2
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SANPLES SI-2,SI-3,SI-4
SAND CONTENT = 20 2
6 POINTS
A A
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4
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é FIGURE 0.19
. SAHPLES SI‘2,SI'3,SI—4
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OST—4F3CP50
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5.-
5- FIGURE 0.20
§_ SAHPLES SI-2,SI-3,SI-I
; SAND CONTENT = 20 2
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227
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FIGURE 6.22
SAMPLES SI-2,$I-3,SI-4
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5— SNNPLES SI-2,SI-3,SI-4
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5. FIGURE 0.25
§_ SAMPLES SI-22,SI-23
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50 FIGURE C.2?
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SAMPLES SI-22,SI-23
I SNNO CONTENT = 20 z
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9 DAHPING
FIGURE C.28
SAMPLES SI-22,SI-23
SAND CONTENT = 20 Z
4 POINTS
77
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9‘1 l-SOOE-SI T-SOOE-O!
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229
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FIGURE E.BT
SANPLES SI-22,SI-23
SAND CONTENT = 20 Z
6 POINTS
T
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b FIGURE C.3O
SANPLES SI-22,SI-23
_ SAND CONTENT 8 20 I
6 POINTS
I
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9 DAMPINU
FIGURE C.32
SANPLES SI-22,SI-23
’ SAND CONTENT = 20 I
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I’ FIGURE 0.33
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5 SAND CONTENT = 20 I
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IT
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FIGURE C.35
SAMPLES 81-22,
SAND CONTENT =
6 POINTS
SI-23
20 Z
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g F- M/
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DST-IDFICPZDD
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g.
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E SAMPLES SI-22,SI-23
° SAND CONTENT = 20 I
E- 6 POINTS
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FIGURE 6.36
SANPLES SI-22,SI-23
’ SAND CONTENT = 20 I
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231
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3' SANPLES SI-11,SI-I3,Sl-16
§~ SAND CONTENT . 45 2
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SI
;. FIGURE 0.39
; SAMPLES SI-II,SI-13,SI-16
3’ SAND CONTENT = 45 I
a. 10 POINTS
80
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FIGURE C.38
P SAMPLES SI-11,SI-13,SI-16
~ SAND CONTENT = 45 I
9 POINTS
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SAND CONTENT = 45 I
10 POINTS
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T
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232
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SAMPLES SI-II,SI-13,SI-16
SAND CONTENT = 45 I
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EL SAMPLES SI-11,SI-13,SI-16
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§* 12 POINTS
64. I I I I J L
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é- EISUNE c.44
£_ SANPLES 81-11,SI-13,SI-16
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233
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FIGURE 0.45
g _
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5’ SAND CONTENT = 45 I
g. 15 POINTS
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S SAMPLES SI-11,SI-13,SI-16
E» SAND CONTENT = 45 z
3_ 15 POINTS
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5 - ‘P A . 11â€Â»,-
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8. A
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3. SANPLES SI-11,SI-13,SI-16
g_ SAND CONTENI = 45 2
g 15 POINTS
6 3.00 .91.» 4).“ also 41.00 "1500 a}
LCD PERCNT I AX STRAIN 2
DST—1F3CPZOO
3 DAMPING
'83-"-
E» FIGURE c.48
' SAMPLES SI-11.SI—13,SI-16
E- SAND CONTENT = 45 z
5. 10 POINTS
3%
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DAMP RATIO
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234»
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!- .
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E I- A
5L ‘ A
5.
SP
§_ FIGURE c.49
° SAMPLES SI-b,SI-18,SI-19
EC SAND CONTENT = 45 2
Ir 7 POINTS
,L
. - .III 41.50 ’41.†44.50 41.00 â€1:09 0% -.
LOG PERCNT 4 FIX STRAIN
UST—4FDSCPO
6 DAMPING
g.
5r FISUNE c.51
' SAMPLES SI-I,SI-TO,SI-19
ï¬- SAND CONTENT . 45 z
5. 7 POINTS
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DAMP RATIO
6 DAMPIND
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5* TISURE C.So
£_ SAMPLES SI-6,SI-IG,SI'19
' SAND CONTENT = 45 1
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§+
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§_
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UST-4F3CPU
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5.
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§~ SANPLES SI-6,SI-18,SI-l9
§_ SAND CONTENT 8 45 Z
; 7 POINTS
8 I-
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II ‘ ‘
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1235
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3p
1 FIGURE 9.53
§- SAMPLES SI-6,SI-TG,SI-I9
g SANO CONTENT = 45 z
é‘ 10 POINTS
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§_ SAMPLES SI'6.SI-18,SI-I9
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s- A ‘
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A
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§_
5- FIGURE C.56
g. SAMPLES SI-6,SI-18,SI-19
' SANO CONTENT = 45 z
E- 8 POINTS
g-
g.
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g .-
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236
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PF FIGURE c.57
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~L SAND CONTENT = 45 I
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9.
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4
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. FIGURE c.59
SAMPLES 81-6,SI-18,SI-19
SANO CONTENT = 45 2
~ 10 POINTS
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ORMP RATIO
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§~ FIGURE c.5e
SAMPLES SI-6,SI-lB,SI-19
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SI 12 POINTS
g.
A
5.
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OST~4F3CPZOO
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5.
5. FIGURE c.60
; SAMPLES SI-6,SI-18,SI-19
S†SANO CONTENT . 45 z
a. 10 POINTS
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5,.
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8
FT
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OAHP RATIO
OAHP RATIO
237
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5F FIGURE C.GT
§_ SAMPLES SI-24,SI-25,SI-26
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5* 7 POINTS
§_ - .
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F
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9 DAHPING
5.
5 FIGURE [.63
' SAMPLES SI-24,SI-2S,SI-2G
ï¬- SANO CONTENT = 45 I
g. 6 POINTS
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FIGURE 0.62
SAHPLES SI-24,SI-25,SI-26
SAND CONTENT = 45 Z
6 POINTS
1 I I L J I I
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UST-lOFBCPO
9 DAHPING
FIGURE 6.64
SANPLES SI-24,SI-25,SI-26
SANO CONTENT = 45 z
6 POINTS
1 L l l J J
I
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DST—IOFSCPO
DAMP RATIO
OAMP RATIO
238
9 DAMPING
5‘ FIGURE 6.65
g- SANPLES 51-24,SI-25,SI-26
!_ SANO CONTENT = 45 2
° 9 POINTS
53
g b
g .
g .
§_ AA ‘A
A
g .-
i.
T r
3..
9. - .00 -i$0 450 41.80 dJ-N "1‘00 LIL
LOG PERCNT 7 AX STRAIN
OST—lUFDSCPSO
9 OAHPINO
5.
5. FIGURE C.67
5* SAMPLES SI-24,SI-25,SI-26
- SAND CONTENT = 45 I
E- 8 POINTS
g.
E N-
g.
E
S
E.
N
5. .
:3 J l l l l J
. .00 a.“ 4.†out! omo «no o.‘
LOO PERCNT 7 AX STRAIN
OST-lOFlCPSO
OAMP RATIO
DAMP RATIO
9 OAMPING
T“ FIGURE C.GI
§~ SAMPLES SI-24,SI-25,SI-26
§_ SANO CONTENT = 45 I
9 POINTS
g.
g.
El-
g.
E!-
gh-
E-
U... J.†.3.†.A
LOG PERCNT 7 AX STRAIN 5
DST-IOFBCPSO
9 OAMPING
g...
§~ FIGURE C.GG
§_ SAMPLES SI-24,SI-25,SI-26
; SANO CONTENT = 45 z
g†9 POINTS
g.
g.
5».
5T
gy-
E. a .
’ “*—zï¬r———-;3——
S- a “‘
E.
9. -O:.00 ~31.“ 41.†- NJ.“ 4].†- .1.†0.:
L00 PERCNT 7 AX STRAIN
OST—IOFSCPSO
DAMP RATIO
DAMP RATIO
1239
9 DAMPING
Q.
5_ FIGURE C.69
' SAMPLES 81-24.SI~25,SI-26
3’ SANO CONTENT = 45 2
g- 10 POINTS
3
E
i
E
ï¬r
E-
g ..
5.
:PI I 4 J I _L I
â€.00 -!.59 -!-OO -|-SC -|.OO -.500 0.
L00 PERCNT 7 AX STRAIN
I
DST~IOFDSLVZUO
9 DAMPING
g.
A FIGURE C.71
E SAMPLES ST—24,SI-25,51-26
5* SANO CONTENT = 45 Z
a. 9 POINTS
5.
E I-
§ ..
' A
g T.
° A
S " A ‘—
g __ T
u: ‘- A ‘A '
. A
g L.
:I'l L g 1 l J J
- .oo 4.50 4.00 a.“ a.†«‘50 o.‘
LOG PERCNT 7 AX STRAIN
DST-IDFlCPZDD
DAMP RATIO
DAMP RATIO
0.1 scoot-o: 1.83924!
b
b
9 OAMT’ING
g.
5* FIGURE C.7o
g. SAMPLES SI-24,SI-25,SI-26
' SANO CONTENT = 45 z
5' 9 POINTS
QT
E ..
5_
NE
'2 A
a. ,,jL,——*""â€"’—fl'flflfl
g -——'z"“ “
'z A
$.-
A
,L
0 ion 31.“ 41.0; 41.50 -I].OO .ioo 9.47:
LOG PERCNT 7 AX STRAIN 6
DST—IDFBCPZDO
9 DAMPING
I
FIGURE C.72
SANPLES SI-Z4,SI-25,SI-26
†SANO CONTENT = 45 I
9 POINTS
.323 JSO .m .3"
T
T T
T
J" 0Ԡa!" a!â€
I
I I I I I L
. .oo .1.“ 4.00 -I .so a... â€In o.‘
LOG PERCNT 7 AX STRAIN
DST-10FSCP200
DAMP RATIO
DAMP RATIO
3 DAMPING
FIGURE c.73
’ SAMPLES SI-TS,SI-T7
L SANO CONTENT = 65 2
dz. O'.° A". .209 .m a!“ I" .m
I
240
§
5 G POINTS
614'.†32.50 jinn—7135" - 11.00 . .Soo OI—
LOG PERCNT I AX STRAIN
2
UST-IFODCPU
3 DAMPING
EN»
‘ FIGURE C.75
iF SAMPLES SI“IS,SI-I7
§_ SANO CONTENT = 65 z
4 6 POINTS
g h
I-
I L
U-
†Tab-o :30 .2130 -IJ.SO in "Jun LT:
LOG PERCNT I AX STRAIN
DST-IFICPO
DAMP RATIO
DAMP RATIO
3 DAMPING
0". 0". 0‘†.M' 0’†0.“ cm 0*
I
p
FIOURE 6.74
_ SANPLEG SI-IS,SI-l7
8
EL SANO CONTENT = 65 z
s ' 6 POINTS
If
:JL.
° ~ï¬00 -tl.GO -81.00 41.50 of.†“0.80. 0.:
L00 PERCNT I AX STRAIN .
DST-IFBCPD
3 DAMP I NO
%- FIGURE C.7G
g. SAMPLES SI-IS,SI~17
§ SANO CONTENT = 65 z
.“ 6 POINTS
5P ‘
§- ‘ A
g .
g ..
E.
g h—
gr
9 ~II~N -lloIO '8'“ 41.“ oil.†â€â€˜3“ LT—
LOG PERCNT I AX STRAIN 2
DST-IFSCPD
DAMP RATIO
DAMP RATIO
241
3 DAMPING
gâ€
g.
SP I .
i_ G t
E b
!_ FIGURE C.77
° SAMPLES SI-TS,SI—17
E- SANO CONTENT = 65 z
3. G POINTS
IL
g .-
E.
:‘L I I J I l J I
a .,[,o a.» 4.00 4.50 am -.soo o}—
LOG PERCNT I AX STRAIN 2
UST—IFDSCPSO
3 DAMPING
5’ FIGURE c.79
5L SAMPLES SI-TS,SI-T7
é SANO CONTENT s 65 z
-’ 7 POINTS
5.’ \
E ‘ ‘
5P
5_ A
g_
Q I-
S.
g .-
E.
.l“' L l l 1 l l J
4'..- -N.Go an 4.39 a... -.m o.‘
LOO PERCNT 1 AX STRAIN
OST-lFlCPSD
DAMP RATIO
DAMP RATIO
3 DAMPING
5T.
gL
g-
5, - A
SP A
g .
TL FIGURE C.7S
5» SAMPLES SI-TS,SI-17
g_ SANO CONTENT = 65 I
g 8 POINTS
g. .-
E,
0;. L l I l I J l_
4'.†4.50 -: .oo - I .so -I .oo - .uo o.T
LOG PERCNT I AX STRAIN ?
DST-IFBCPSD
3 DAMPINO
5' FIGURE C.Go
§~ SAMPLES SI-TS,SI-17
g. SANI CONTENT . 65 z
' G POINTS
g.
55
g .
g .
g _
g:
S-
g .-
3.
r“- l l l 1 L
. 4150 4‘.“ 1.x 4.» «.00 "an o.‘
LOO PERCNT I AX STRAIN 2
DST-IFSCPSD
DAMP RATIO
DAMP RATIO
242
3 DAMPING
FIGURE C.GT
~ SAMPLES SI-TS.SI"7
SANO CONTENT . 65 2
an an an an an an an.qp
T I
8 POINTS
:3 ..
g
I? F
6+- J J I I I I I
47.59 -2 .TO -2.oc 'I .So oI .ao -.soo II.I
LUG PLRLNT I AX STRAIN 2
DST~1F§UCPZUU
3 CAMPING
fl" FIGURE C.83
Q’ ' SAMPLES SI-15,SI-I7
§_ SAND CONTENT = 65 I
5 8 POINTS
§_
' A
§â€â€œ*‘nr— A
8 ZTTTYT“‘_--—————___.
J
g .
E.
g I.
é-
‘ «In ~21.» 4‘40 41.5; an.» â€In 03—
L00 PERCNT I AX STRAIN
OST~1F1CPZDD
DAMP RATIO
DAMP RATIO
3 OAMPING
g.
g.
g;
g" A- 5 ' ‘ A
.£_ 1 A ‘_7_3
E» _
8 FIGURE c.82
TI SAMPLES SI-IS,SI-17
5P SANO CONTENT = 65 I
§_ 8 POINTS
E. -
g .—
§_
a -:00 ~11. 80 -!l-OO - Il-SO - ll.†- $00 0 .IL
LOG PERCNT I AX STRAIN 2
OST—lFBCPZDD
3 DAMPING
g_
E- FIGURE c.84
- SAMPLES SI-TS,SI-T7
ï¬- SANO CONTENT = 65 2
g, 7. POINTS
5.
E D-
S
E
2‘
3.
S
E.
.- .gI.†41.30 ~11.†“J.“ 4: 0 .1.“ #
LOG PERCNT I AX STRAIN
DST—1FSCPZDD
6 DAMPING
’ FIGURE c.85
. SAMPLES SI-20,SI-SI
SANO CONTENT = 65 Z
4 POINTS
an an an an au,au aann
I I
2 JOCK-02 7 .SOOE-O!
I
I.
I I I I I
-310: 4.5: -z.oa -I.sc 4m
LOG PERCNT 4
DAMP RATIO
+
(.221
FIGURE C.G7
" SAMPLES SI-20,SI-31
~27.
ï¬n SANG CONTENT 8 65 z
4 POINTS
5.
g»
E-
g.
E" A
h
C
DAMP RATIO
Oi nan-u HOSE-OE
I I I I I
oaloo oI.Go -:.oo -I.GO -|-lfl
LOG PERCNT 4
OST-4F1CPD
1
° 0:00
AX STRAIN
DST-4FDSCPD
6 DAMPINO
I
AX STRAIN
2453
I
o.‘
_I
m'
DAMP RATIO
DAMP RATIO
6 DAMPING
I’ FIGURE c.86
Er SAMPLES SI-20,SI-3|
,_ SANO CONTENT = 65 z
' 4 POINTS
5,
5x
g_
E~__'_j;_ï¬L———————"â€â€"—T——T
Q" A A
qr-
L
g»—
A
.Jb—
°.iw .;S .:A .tu -tA .IA 33
LOG PERCNT 4 AX STRAIN A
OST~4F3CPO
6 DAHPING
S.
gr FIGURE C.OG
: SAMPLES SI-20,SI-ST
G- SANO CONTENT = 65 z
5, 4 POINTS
§-
5.
5.
El-
? . A
;- ~
A
orb-I I I I I I I
osioo -:.Go -I.oo -I.Go -I.No -.NNN o.‘
LOG PERCNT 4 AX STRAIN
OST—4FSCPO
DAMP RATIO
DAMP RATIO
244
6 DAMPING
I" FIGURE C.SP
5* SAMPLES SI-20,SI-31
g- SANO CONTENT = 65 I
6 POINTS
g.
A A
g.
E» A 6 A
g_
E F-
g I-
E. T-
? .-
E-
,L
° Di†ORLJO 081.30 «to 41.00 “1590 0.1];
LOG PERCNT 4 AX STRAIN
DST—4FDSCPSD
6 DAMPING
g-
5_ FIGURE c.91
; SAMPLES SI-20,SI-31
G- SANO CONTENT = 65 z
5. 6 POINTS
5.
E.
g _
z; _ A
g _ .
5. -
G F
3. .
FL- I I I L
. . l..- 41.“ «i.» 4.0 -I.oo -.m o.‘
LOG PERCNT 4 AX STRAIN
OST-4F1CPSD
DAMP RATIO
DAMP RATIO
6 DAMPING
g.
5- FIGURE C.9O
§_ SAMPLES SI-2O,SI-IT
° SANO CONTENT = 65 I
5- 6 POINTS
g.
E- A
g _
. A A
E». P
g ..
E»
E
:P
‘.;A .5“ .am .5†.5“ .IA .3
LOB PERCNT 4 AX STRAIN I
DST-4F3CPSD
6 DAMPING
g.
5» FIGURE c.92
§_ SAMPLES SI-20,SI-31
; SANO CONTENT = 65 z
S~ 6 POINTS
EL
5 .
g .
g _
g P-
E. .
P A
g†I
O. . I.†021-“ ~81.†“I.“ 4..†"I.“ 0.:
LOG PERCNT 4 AX STRAIN 4
DST-4FSCPSD
DAMP RATIO
DAMP RATIO
LSOOE-CZ 7 .SOOE-M
.m .1» an no .m an .m .390
,j, 1
S
I.
F
.-
0.1
.IIO .130 .178 .200 .228 .250 .27S
.ZPO
T
I
- 37.00
[I
6
h
P.
-
DAMPING
FIGURE C.93
SAMPLES SI-20,SI-31
SANO CONTENT = 65 2
8 POINTS
I I
I I
-:‘-53 -2-00 °I-$O -I.09
DAMPINI;
FIGURE c.95
SAMPLES SI-20,SI-31
SANO CONTENT = 65 I
7 POINTS
I
-SOO
LOG PERCNT 4 AX STRAIN
I
8'~4FDSCPZDD
245
I
O.|
DST-4F1CPZDD
E
E
E
A-
D I I J I I ‘1 I
4170 an -N.oo 4.9 4.00 -.m o.‘
LOG PERCNT 4 AX STRAIN 2
DAMP RATIO
ORMP RATIO
6 OANPING
N' FIGURE c.94
ï¬- SAMPLES SI-20,SI-31
gr SANI CONTENT = 65 z
' 7 POINTS
5 .
‘g»
5 .
g _ A
g '_——T2"3‘-—1»—_________________
a. L.
E
.z I-
3. ..
§_
J‘QOO 44.50 41.00 i.» - II.†it†o I
LOG PERCNT 4 AX STRAIN 1
OST-4F3CP200
6 DAHPING
g“
- FIGURE c.96
5- SANPLES SI-20,SI-TT
§_ SANO CONTENT = 65 I
4 6 POINTS
g ,.
g L
g .—
S- I
c2 A A
g p
g A
A; .
6 4'..- 4‘.“ «in ~11.“ 4L..- -.lun 01L
LOG PERCNT 4 AX STRAIN
DST—4F5CPZDD
DAMP RATIO
DAMP RATIO
246
9 OAMPING
" FIGURE C.97
. SAMPLES SI-27,SI-28,SI-29,SI-30
SAND CONTENT = 65 I
_ 6 POINTS
an an an an an an
.123 .IOO
T
5"
293m.†7036"."
I
b-
I—
II.l
I I _L I I I I _
4'.» 4.39 4.0: 4.50 4.03 -.soa II.1
LOG PERCNT 7 AX STRAIN 6
DST—IDFDSLPO
9 DAMPINO
-Nâ€
_ FIGURE C.99
P SAMPLES SI-27,SI-28,SI-29,SI*30
SAND CONTENT = 65 Z
7 POINTS
.100 0", o'SO .273
1
JD. Jâ€
fl
-III
I
O .tzot-a 7 .Icot-u
7— N
DI
p-
4 J I I 1 ___1 l___
-a.oo -:.so -¢.oo oI.so on... -.uoo 04'
L00 PEKCNT 7 AX STRAIN 6
DST-IOFICPD
DAMP RATIO
DAMP RATIO
w†auIau an anAgp
9 DAMPINO
I
L FIGURE c.98
SANPLES SI-27,SI-28,SI-29,SI-30
_ SAND CONTENT = 65 z
7 POINTS
,
g.
g.
$- A
E A e—
; r- 6 A
A
Sr
§_
5+- 1 l l I l l 1
os'.oo 4 .so 4 .00 -I .so -I .u -.m 0.‘
L00 PERCNI 7 AX STRAIN A
DST—IDFBCPD
9 OAMPING
gr
FIGURE C.IOo
§~ SANPLES SI-27,SI-28,SI-29,SI-30
EL SAND CONTENT = 65 z
' 7 POINTS
§_ .
g.
5.
g.
g_
I? p
5.
E" . ,.
:3 - 45
9. . .00 '21.“ -!‘.fl 4‘.“ Th. out. O.I
LOG PERCNT 7 AX STRAIN
DST-IOFSCPO
DAMP RATIO
DAMP RATIO
247'
9 DAMPING
FIGURE C.101
SAMPLES SI-Z?,SI-28,SI-29,SI-30
'Tâ€
g SAND CONTENT = 65 I
§~ 10 POINTS
§_
5.
g-
¥r ‘ A
S» .a
E 5
:- l J 1..-..- L I g I
am» 4.50 4.03 4.30 4.03 -.soo 0.
L00 PERCNT 7 AX STRAIN
DST-IDPUSCPSU
9 09:1? I NU
%»
:_ EISUNE c.103
†SAMPLES SI-27,SI-28,SI-29,SI-30
5- SAND CONTENT = 65 I
g 8 POINTS
g.
g L-
g I
i: b H
g. A
g. A
Er
:4 L I J I_ _L I
who «.80 4.00 44.50 on... also 0.1
LOG PERCNT 7 AX STRAIN
OST-lOFlCPSD
DAMP RATIO
DAMP RATIO
9 DAMPING
II FIGURE C.Ioz
§~ SANPLES 51-27 51-20 51-29 51-30
E SAND CONTENT a'Is z ' '
- 10 POINTS
g.
ig»
ES
§_
5.
g- A
9 ————Ar—it—"2"â€â€œ_—_——————_—_—.
%r A
P A
g I-
a
LOG PERCNT. . 7 .nx STRAIN-
DST-IOEBCPSO
9 DAMPING
5_ FIGURE 6.104
: SAMPLES SI-27,SI-28,SI-29,SI-3o
g- SAND CONTENT = 65 2
§_ 7 POINTS
5.
5.
gr
5.
g .-
E.
g _ A
A
.g‘ h \
OIL-L l l J l l J
3.00 4.30 4... a.“ a... -.uo o.‘
LOG PERCNT 7 OX STRAIN
DST—IOFSCPSO
CAMP RATIO
DAMP RATIO
24¢!
9 DAMPING 9 DAMPING .
T:- I»
;_. FIGURE 6.105 é FIGURE 6.106
. SAHPLES SI-27.SI-28.SI-29.SI-30 -' SNNPLES SI-27,SI-28,SI-29,SI-30
g. SAND CONTENT = 65 2 g. SAND comm = 45 1
gr '2 POINTS §_ 11 POINTS
2: I»
§- Sp
5r 5»
E- S- ‘
I a; ‘
.: Z I†2
S- 3? E~
3*. E g
S gg;â€
DIE} I..- I J... I I _I_ D 5b1 I _L I 4 I _.L
-:.oa -:.::I -I-.on -I.s:- -I.oo -.300 07— 4'.†or.†4.00 4.30 -I.oo â€son TNT
LOG PEACH? 7 AX STRAIN 6 LOG PERCNT '7 AX STRAIN
USI-lOF—IOSCPZOO DST—10F. CPZOO
9 UHHPING 9 UAMPING
EL FIGURE c.107 £_ FIGURE c.109
; SANPLES SI-27,SI-28,SI-29,SI-30 ; SAMPLES SI-27,SI-28,SI-29,SI-30
N~ SAND CONTENT = 65 1 Sr SAND CONTENT = 65 1
g. 11 POINTS 5E 11 POINTS
5L §_
$~ 5*
2~
£-
9 F-
5 cag A
1'3 Z AI- ‘ #_
a a: In a: A
'.’ m TI- A ‘6
§ A.5 .
:r z :-
.L 8
9 -i? 4..“ «in -IJ.SO 4..“ - .15“ 0% . 08%.†'81.“ ~81.“ all... oil.“ of.“ 0.:
LOG PLRCNT 7 AX STRAIN LOG PERCNT 7 AX STRAIN
OST-lOFlCPZOO 6 UST—lOFSCPZOO
APPENDIX D
DYNAMIC YOUNG'S MODULUS FOR
GRAVEL-ICE SAMPLES
249
PSI E+OS
0.00
“TWV'
PSI E+OS
40.0
.0 36.0
_r I _
32
.0 78.0
’I' ‘T'“l‘ï¬â€˜"T"T' I
24
I"
70.0
l6.0
F—T T'-T
[7.0
I’_T ‘
4.00
‘Pï¬
0.
P0
I
I
I
I
I
I
(
SAMPLES 6°18: G’I9o
GEAVEL CONTENT I 243
8 POINTS
FIGURE 0.1
G-ZO
L. if I I J I
-3.:. -2 s: -: aO -I.so -I.co - $33 o_r__
LCD FEECNT I AX STRAIN
_ 1
z __ 1 [EPA
Y I i F: E] LJLJ F) E]
2 E K3:S_JS
qI
9"?- SMPLES G’IBO 5'19: 6‘20
I— GFAVEL CONTENT - 24:
9;_ 7 POINTS
‘0
L FIGURE 0.3
e; T-
9%
g
9%
NT—
9
g b
2: N—
o. P'-
N I"
D
9..
D
N—
D
9— A
él-l L I I I I I
-3too -2.Sa -z.oo -I.so -I.oo -.soo OJT
LOG PERCNT I AX STRAIN
GT—l F1
CP
0
250
E+OS
PSI
PSI E+OS
No.0
24 20.0 32.0 36.0
?0.0
0.00 12.0 16.0
“T“T‘T'jï¬â€˜I “T—T
4.00
2 E MCDOLUS
SAMPLES Gone.
I GRAVE. CONTENT - 24:
8 POINTS
†FIGURE D.2
T
I_T
E
-3300 ~2.$0 -2.33
LOG PERCNT
GT—l F3
2 E MODULUS
G'l9o
6'20
CPD
GT-I F5 CPD
0
§“‘ SAMPLES s-Is. O-I9. O-2a
~ BAAVEL CONTENT ' 248
9__ 7 POINTS
8
OP ETSORE O.4
O'N—
NP
9..
NP-
O
5?
L
9..
0.!—
NP-
5
6 ‘\\w£
i °
.f“. I I I .4L I
-3:OO -2.SO -2.oo ~I.SO ~I.Oo -.saO a}
LOG PERCNT 1 AX STRAIN
PSI E+OS
PSI E+OS
251
2 E MODULUS
53ҠsANPLEs c-Ie. 6-19. 640
r nmvu. CONTENT - 2N:
:__ ll POINTS
.ï¬ FIGURE I.5
"L
:P
' T-
: L
â€L
'- P}: A ..
J: T I I I I I I
-3.CJ v2.50 -:.OO -I.sa -I.OO -.soo O:F'T
LDC: FEAST-ST I AX STRAIN
2 E MODULUS
2}» sAI-IPLES c-Ie. O-IO. c-2O
,_ GRAVE]. CONTENT O 241
9__ 5 POINTS
.: EICURE 9.7
"r-
:r
" L-
“ r
8- A
o - A
g _ A
6- I I I I I I I
45: 4.30 -: .00 -I .so -I .oo - .300 O.1
LOO PERCNT l AX STRAIN
GT-l F1 CPSD
PSI E+DS
PSI E+05
2 E MODULUS
3"? smut-.3 c-Ia. (MS. 6-20
F BAAVEL CONTENT I 2‘3
9 p 8 POINTS
OF PISURE I.S
s; L-
Er
o I- \
a A
3 - A
6"- I . I I I I I_
one: -2.so -2.OO -I.sa -I.OO -.530 o.‘
LOG PERCNT 1 AX STRAIN
2 E MODULUS
3“ SANPLEs G-Ia. 6-l9a c-za
b GPAVEL CONTENT I 24!
9 __ 0 POINTS
.’ FIGURE 0.8
g.
of
9 T'
2 L-
: L—
8. a
O h- A
6“ I I I L I I I
-:'.OO -2 .so -2 .00 -I .so -I .oo -.soo O.‘
LOG PERCNT I AX STRAIN 1
GT-l F5 CF50
PSI E+05
252
2 E MCWLUS
Z}- SANPLES e-Is. G-I9. G-aa
GPAVEL CONTENT - an
IL ll PGINTS
9’ FIGURE 0.9
"F
“L
$__ v I . I I I I
-3.33 -2.50 -Z.00 -I.SO -1-00 -.520 DJ
LOG PETCNT 1 AX STRAIN
(w
uT—I FOSCPZOO
2 E MODULUS
O
53"" SAMPLES 03-18. 049: G-2G
I— GRAVE. couTaIT - 24:
:_ II PaINTS
9L FIGURE 0.11
at
:F
— P
:H- I I l 1 l I
~Jloo -z.so -z.oo -I.So -I.oo -.soo 0.?
L00 PERCNT 1 AX STRAIN
GT-l F1 CPZOO
EIOS
PSI
PSI E+05
2 E MODULUS
3ԠSANPLES G-IG. G-Io. G-aa
~ GPAVEL CONTENT - 24:
9_ II PoINTs
9:4 FISURE n.10
"F
N P
2* . A A.
o"\\
r—
é—_ I I I I I I .
-3200 -2.sc ~2.20 -I.SO -I.OO --SCO 0-
L00 PERCNT 1 RX STRAIN
2 E MODULUS
2““ SAMPLES G-Ia. (#19: 0-20
GPAVEL. GGNTENT - 24:
9 ll PoINTs
:~ FIGURE n.12
gr
3: A
F
éflb I I I I I I 144
-3Ioo -2.So -z.oo -I.So -I.oo -.soo 03
L00 PERCNT 1 AX STRAIN
l
GT-l
F5 CPZOO
PSI E+OS
PSI E+05
253
S E NOCULUS
gm. SAHPLES G-zI. 6-22. 6-23
_ vaEI. OONTnIT - 24:
9_. 0 POINTS
"L
9 FIGURE 9.13
2 L
‘3 L
A-
O I I l
-3233 -2.SO ~2.00 -I.so -I.oo -.soo air——
LOG PERCNT 4 AX STRAIN
GT 4 FOSCPO 3
S E MODULUS
3* SAHPLES G-zI. G-zz. 6-23
I GRAVEI. cONTENT - 24:
9__ 3 POINTS
9†FIGURE 9.15
: F
53
.J
O l l
-:lOO -z.IO -z.oo -I.SO -I.OO -.SOO O.I
LOG PERCNT 4 AX STRAIN
GT-4 F1 CPO
PSI E+05
PSI E+05
0.00 12-0 16-0 20-0 24-0 20.0 32.0 38.0 001.0
.00
00'
401-0
T—
S E MODULUS
' SAHPLIS 6'21: 0'22: 3'23
P RIAVIL CONTENT O 208
8 POINTS
". FIGURE D.14
' I ' I l I L
-3ï¬oa -2.SO -z.oo -I.so -I.Oa -.SOO O.
LCG PERCNT 4 AX STRAIN
GT—4 F3 CPD
5 E MODULUS
SAHPLES 8'21: 0°22: 6-23
h GRAVEL CONTENT C 243
=2 _ 7 POINTS
OF FIGURE 0.16
2 A
v A
8 A
é_' A 3
«ET. I I I I I I
-3T3O -I.SO -z.oo -I.so -I.OO -.SOO O.I
LOG PERCNT 4 AX STRAIN 3
GT-4 F5 CPO
E+05
G-OO
'T'TT—"T'—7_'W
PSI
70.0 24.0 20.0 32.0 35.0
15.0
12.0
4.00
38.0 QOrO
32.0
10.0 20.0 21.0
0.00 12.0
¢.00
‘OrO
5 E MODULUS
†SANPLES 6-21.
3 POINTS
I
S E MODULUS
’ SAHPLIS 0‘21;
L. GRAVE. CONTDJ
8 POINTS
l TET
-J'.OO -2 .SO -2 .00
L00 PERCNT
GT-4 F1
254
8'22: 8'23
I- BRAVE. CONTDJT I 243
†FIGURE 0.17
8.22: 6-23
1' 0 248
I FIGURE 0.19
l 1 l
"‘ ~50 ‘E .00 -0300 O.
.L__
4 AX STRAIN
CP5O
E+05
PSI
PSI E+OS
S E NCCULUS
0
€*‘ SANPLES a-en. O-ea. Goa:
. vaEI. cONTnIT - an
9_ 3 POINTS
05 FIGURE 0.18
'a L
°.
9:
O. I 1 I I L .
'3.33 ‘ '2.53 -2.33 -I.53 -1.00 --533 O.
1
L03 FERCRT 4 AX STRAIN
GT—4 F3 CPSO 3
5 E NODULUS
O
3‘“ SANPLES O-zI. G-22. G-23
.- GMVEL CONTENT I 24!
9 ,_ 8 POINTS
0
— FIGURE 9.20
O
3‘†F—
a -
‘é h-
e:
«'3
D
2: I—
“r
2- . .
~ I- A
E?“ 1:15 ‘3
" A
g __ A
c',-E I I I I I I I
~3’.OO -2 .53 -2 .00 -I .SO -I .00 -.SOO o.‘
LOG PERCNT 4 AX STRAIN
GT-4 F5 CF50
PSI E+05
PSI E+05
255
S E MODULUS 5 E MODULUS
2'" SMPLES O-Eh 6-22o 6’23 2“"- mgs 3-2;, 3.22, 3.33
GaavEL CONTENT - 2‘! _ GRAVEL CONTENT - ea:
9 9 POINTS 9__ 9 POINTS
"~ FIGURE n.21 "- FIGURE p.22
' m
D
4.
LL]
3
CL.
I I :3 . I A I I I L
3'-OO -2-50 -2-00 4.50 -1.30 -.SCO 0.1 -3‘.00 -2-SD ~2.00 -I.SJ -1.33 -.500 O.'
L33 PERCM 4 AX STRAIN LOG PERCNT 4 AX STRAIN
— r-\ — I
I—4 FO5EP200 Gl—4 F3 CPZOO
S E MODULUS S E MODULUS
31- smPLES G-zI. O-aa. 6-23 2}— SAIIPLES G-2I. G-22. 6-23
- GRAVEL CONTENT - 24: - GRAVEL CONTENT - 24:
9 9 POINTS 9__ 9 POINTS
" FIGURE '-23 "- FIGURE 3.24
IL" . . .
. é A
2 ID -
9 r- A A
8 uIE'
" .... ,- A
8. a: 3—
c 0.. ' _
6‘ I' I L I I I :LI I L I I I +
-§30 -2.SO -2 .00 -I .SO -I .00 -.SOO o.‘ -SI.OO -1 .so -2 .00 -I .50 -l .00 -.S00 O.
LOG PERCNT 4 AX STRAIN 3 L00 PERCNT 4 AX STRAIN 3
GT-4 Fl CPZOO
GT-4 F5 CPZOO
PSI E+05
PSI E+US
256
8 E MODULUS
g3" SAHPLES O-ao. O-TI. 6-32
~ BBAVEL CONTENT . 2g;
:__ 9 POINTS
9* FIGURE n.2s
" I—
N r-
J
8:†M
<5 9. ' I I I I l
-a.:a .2.53 -:.C: -I.SO -I.oo .sao :
L3G FERCNT 7 AX STRA
T F‘ .
I—IOFOSpPO
8 E KCUULUS
:4 SAMPLES G-SO. G-OI. 6°32
'_ GEAVEL CONTENT - ea:
9 8 POINTS
0. FIGURE 0.2?
o. b
v I-
:F
-. A A
8-
S-
:b I I I I I J
43100 ~2.So -z.OO ~1.SO -I.OO -.SOO
LOG PERCNT 7 AX STRAIN
GT—IOFI CPO
E+OS
PSI
PSI E+05
8 E MODULUS
3.- SMPLES C-ao. can 642
' _ GRAVE. CONTENT - 2a:
9 9 POINTS
"F FIGURE 11.26
" I-
r
0'?-
N L
9.
9
.A
-00
G
T’_T'"TT
D
ob
6 J_ I I L I I I
-3130 -2.50 -2.C3 -1.50 -I.CO -.S33 0.
LOG PERCNT 7 AX STRAIN
5
8 E MODULUS
3* SAMPLES O-ao. G-SI. 642
F CRAVE. CONTDIT - 2‘!
9L . HINTS
°~ FIGURE 3.28
â€F
2, I'
or
N r-
3 — A
- A
3 '- A
:-l I I I I I I
-JIOO -z.so -z.oo -I.EO -I.OO -.SOO OJ
LOG PERCNT 7 AX STRAIN
GT-10F5 CPO
PSI E+05
PSI E+US
8 E MODULUS
3“" SAMPLES 3-300 3-310 8'32
GRAVE. CONTDJT O 203
:_ 9 POINTS
:~ FIGURE I.2I
2T
“ L
g.
r-
8: A A
6 .0
I A
3r
0. I I ' I I 1
-3'.OO -2.SO -2.OO -I.SO -1.JO -.sca 07—
L00 FERCNT 7 AX STRAIN
8 E MODULUS
g" SMPLES G-SO: 6'31: 6-32
I- OPAVEL CONTBJT - 24!
c3_ 9 POINTS
"L FIGURE I.31
fl
T I-
9-
S: (I ‘5
- A
g. - \
â€I I I I I L I
-s'.OO -:.SO -2 .00 -1.50 -I .00 - .500 o.'
LOG FERCNT 7 AX STRAIN 5
257
0T-10F1 CF50
E+05
PSI
PSI E+05
8 E MODULUS
3.. SANPLES G-SO. GoaI. 6-32
' .. Guava. CONTENT - 24:
o___ 9 POINTS
3F FIGURE 0.30
2L
"F
3L
N F
3P
PT A
I— A A
3~ ‘3 A A
I:— I I I I I I I
-3-00 -2.50 -2.00 -I.SO -I.OO --SCJ O-
LOG FERCNT 7 AX STRAIN
8 E MODULUS
3"" SMPLES G-OO. 8-310 6'32
BRAVE... CONTENT O 2‘!
9 9 POINTS
"- FIGURE |.32
a I- A
e- A A
or I L I I l I l
-T‘.Oo -2 .SO -2 .00 --I .SO -I .oo - .300 O.‘
LOG FERCNT 7 AX STRAIN 5
GT—10F5 CF50
E+OS
PSI
PSI E+05
258
8 E MODULUS
31L smzs e-ao. 0-31. 8-32
I' Guava. comm? - an
.3_ 9 mun:
"I- FIBURE 0.33
"I-
:r
NI-
}
cf".I I I I I I I
-3.:a -2.so -z.33 -I.sa 4.30 -.saa o.‘
LOG PERCNT 7 AX STRAIN
GT—IUIOSCPZOO
8 E KGDULUS
3“ smpus 6-30. 6-31. 6-32
" _ Guava. comm? - 24:
9b 9 Pom-rs
:» FIGURE 3.35
8
«II-PI I l I 4 I I I
-:loo -z.so -2.oo -I.so -I.oo -.sao o.‘
LOG PERCNT 7 AX STRAIN
GT-IOFI CPZOO
E+05
PSI
PSI E+05
8 E MODULUS
I}- smnzs 6-30. 6-31. 6-32
03mm. coumn - an
9 9 rows
of FIGURE 11.34
of
}
EI A A A
I-
8.“ A A
F
v:- I I I I I I
-3I.'}3 —2-50 -2-00 4.50 -I.OO --553 Oj
LOG PERCNT 7 AX STRAIN
GI—IOFB CPZOO
8 E MODULUS
2‘" swans 8-30. 6-31. 8-32
» cmva. comm? - 2n
:_ 9 POINTS
9* FIGURE 0.36
gr-
cr-
2’ ob A
P\&\‘
2: A A A
8-
rb! l l l L L 1
33100 -z.so -z.oo -I.so -I.oo -.soo n.‘
LOG PERCNT '7 RX STRRIN
GT-IOFS CPZUO
E+OS
PSI
PSI E+05
259
2 E MODULUS
ol—
9†SAMPLES 6-14. 6-15. 6-16. a-I1
I— emvn. comm? - 42: ‘
:__ 10 POINTS
D- FIBURE n.37
"L
a: a
'I A A
c' g I I I I I I
-3-.:a -2.sc -z.ao -I .53 -I .oo -.Eco 0.7—
LOG PERCNT 1 AX STRAIN
Gi—I FOSLPO
2 E KCCULUS
é“ SAMPLES c-Ia. G-Is. aoIG. G-I1
- GRAVEL CONTENT - 42: '
:_ II POINTS
"— FIGURE I.39
i
9
Er a
s h A
'. __ A
.JL.
1 J l l l J
-J'.oo -2 .50 -2 .00 -I .so -I .00 «.800 o .'
LOG PERCNT 1 AX STRAIN
GT—I F1 CPO
PSI E+05
PSI E+OS
2 E MODULUS
§‘ sanPLEs c-II. c-Is. G-IG. G-I1
CRAVE. CONT“? O ‘2‘ °
3_ II onurs
:~ FIGURE n.3G
n +-
6 I. A AA
3— 8
. A
I. A
:- I I I I I I
-3‘.ca -2.so -2.co -I.so -I.oo -.soo 0d
LOG PERCNT 1 AX STRAIN
2 E MODULUS
3“. snanEs c-Ia. e-Is. G-IG. a-I1
'I. GRAVEL CONTENT - a2: '
=3 _ II POINTS
"_ FIGURE 0.40
" I-
9T
3 L
J I A
8[ A A
6.“ I I I I I I
-3‘.oo -2 .so -2 .00 -I .so -I .oo -.soo o.I
LOG PERCNT 1 AX STRAIN
GT-l F5 CPO
PSI E+OS
PSI E+OS
260
2 E MODULUS
9““ SMPLES s-Ia. c-Is. G-IG. G-IT
BAAVEL CONTENT - 421 '
2 11 POINTS
3_ FIGURE p.41
2?
:F
J
—P-
TI.
g__ A
J M
C A:
I: I I I I I I I
-3'.oo -z.so -2.oo I.so -I.oo -.sao U.I
LOG PERCNT I AX STRAIN
2 E MODULUS
3ҠSAMPLES G-Mo G-IS: 8-16. 6-I7
_ GRAVE]. CONTENT - ‘28 '
9_ II POINTS
â€_ FIGURE I.43
NI-
:F
-r- A
8 _ AA
5 A ‘
Ob A &
°. '- A
"_ A
-_ I I I I I L7
-Jloo -z.so -z.oo -I.so -I.oo -.500 0}
L00 PERCNT
1 AX STRAIN 1
GT—I F1 CPSO
'PSI E+OS_—_
PSIIE+05
0.00 12.0 IG.O 20.0 24.0 28.0 32.0 36.0 40rd
Coo
II'Tï¬fI
2 E MODULUS
SAMPLES O-l‘: 6°15:
GRAVE. CONTDIT - .2;
I2 POINTS
6'16: G-I'I
FIGURE v.42
I
L l I
-3‘.oo -2.so -2.00 4.50 -I.ao -.soo o.I
LOG PERCNT 1 AX STRAIN
2 E MODULUS
Ew- SAMPLES G-Ia. G-Is. G-IG. 6-17
,_ BRAVE!- CONTDIT I ‘2‘ '
9__ In POINTS
:~ FIGURE v.44
OF
:r
.F
- I-
2'_ 4 ‘ï¬
8..
0 IA
D ’- A
6“ I I I I I l L_
-:.oo -2.50 -z.oo -I.sa -I.oo -.sou as'
LOG PERCNT l AX STRAIN l
GT—l F5 CPSO
PSI E+OS
PSI E+05
261
2 E MODULUS 2 E MODULUS
é“ saunas a-Ia a-IS e-IS. (MI 3* “up; - - . -
" “WW“- °°"T’3"T ' 4;; ' ' P cmvéscgu'IgI'ra-‘i'uc “9 a. n
3.. IA POINTS 9__ 14 roxurs
0- FIGURE 0.45 "F FIGURE L“
_F 2C
5_ uaé’
_ O b
8 I. +
a LIJ
o L A H
2- A " ‘0
I A A “-
ï¬ll-OJ -21.50 -21.00 41.50 41.00 NISOO 0} o -JI.00 -21.50 -21.00 41.50 41.00 «1500 O-I
LCG PERCNT l AX STRAIN LOG PERCNT 1 AX STRAIN
1
_
GT—l FOSCPZOO GT—l F3 CPZOO
l
2 E MODULUS 2 E MODULUS
§-.- SAMPLES c-Ia. e-IS. a-Ie. G-I'r 3Ҡsaunas 6"“ “"5' 3"" 6'â€
L. Suva, con-ran- . 42; - _ GMVEL comm? I 42! '
q__ Ia poxurs 9__ 14 POINTS
"_ FIGURE |.47 :_ FIGURE D.48
S '- 2 L.
2* 2*
EF
O I. .-
§- In
c:
+
E- uJ
8. 5
. m
5"- I I I I I I 6 I I I I 1 l I
4.00 -2.So -2.00 -| .50 -I .oo -.soo II.I -S‘.oa -z.so -2 .00 -I .so -I .oo -.Soo o.‘
LOG PERCNT 1 AX STRAIN LOG PERCNT 1 AX STRAIN
GT-l F1 CPZOO 1 GT—l F5 CPZOO
E+05
I
S
PSI E+05
262
5 E NCDULUS
gL- SAHPLES S-ea. 6-25. 0-26
_ BRAVEL CONTENT - 42:
q .— 7 POINTS
6 FIGURE v.49
9:
l2
_ “\\\\\\\\:E\\\\
5’. AA A
DI. \b\\<AD\\\\\\\\\\\
:3 h I I I I I I
~2tco ~:.sa -z.oa -I.Sa -I.oo -.sco OJ
L33 FERCNT 4 AX STRAIN
C)
IT— FOSCIO
5 E NCDULUS
§~~ saunas a-za. a-zs. 6-26
_ GRAVEL CONTENT I 42:
9 7 POINTS
6‘ FIGURE v.51
"L
N I—
o'— A
2_ m.
S_ A
JEN 44 I I I I 4_
-31ca -z.so -z.aa -I.SO -I.oo -.500 03
LOG PERCNT 4 AX STRAIN
GT—4 F1 CPO
PSI E+05
PSI E+05
S E MODULUS
3* SANPLES 6-24. 6-25. 6-26
_ BRAVEL CONTENT ' ‘21
9__ 1 POINTS
"— FIGURE 1.50
«P
é“ A
OT A
Jw' I I I I I I
-3-OO ~2-50 -2-03 -I.SO -l.03 0.500 DJ
LOG PERCNT 4 AX STRAIN
S E MODULUS
3“ SAHPLES 6-24. 6-25. 6-26
, canvzn CONTENT - 42:
9 7 POINTS‘
:— FIGURE n.52
-L
gwI I I I I I I
~3Loo -z.so -z.oo -I.so -l.00 -.soo oJ
LOG PERCNT 4 AX STRAIN 3
GT-4 F5 CPO
EIOS
PSI
PSI E+05
2%
5 E MOCULUS
é“ SAHPLES 6-24. 6-25. 8-26
I- GMVE. CONTDJT O ‘23
:__ O POINTS
9†FIGURE 9.53 .
n I-
o' _
OF
T
.. I- A
3— A
'F
c:— I I I I I
-3 c: -2 so -z.co -I.so ...:3 - G-: :L'
C3 SERCNT 4 AX S-RF’N
3
__ ,_ A
- _. ‘ (I
CI 4 FODLPEQ
5 E HCSULLS
0|
é“ SANPLES 6-24. 6-25. 6-26
'— GRAVH. CONTWT D 42%
9__ 8 POINTS
OF FIGURE 1.55
"L
y
L
g.
o _
5 r—
L
9-
"L
8-
6
g. b
r-
u 4 I I J I L.
-r.co -2 .So -2 .00 -I .So -I M - .530 T
LOG PERCNT 4 AX STRAIN
GT—4 F1 CP5O
SI E+05
P
PSI E+OS
5 E NCDULUS
3“" SAMPLES 6-24. 0-25. .
I- CMVEL CONTDJT - ‘2'0 26
:L_ 8 POINTS
OF FIGURE |.54
"L
~ I-
-3'.:J -2 so -z.c3 -I.so -I.co - 5:: O.‘
L23 FERCNT 4 AX STRAIN
3
T" (—
GI—4 F3 CPOO
S E MODULUS
oI
§* SAHPLES O-aa. O-2S. 6-26
I" GRAVE. CONTENT - 423
9__ 8 POINTS
OF FIGURE 0.56
e:
3
c.5- I I I I . I I g
-3223 -z.so -:.Oo -I.so -I.oo -.SOO OJ
LCG PERCNT 4 AX STRAIN
GT-4 F5 CP5O
F+05
SI
P
E+05
PSI
5 E MODULUS
9L
g“ SAHPLES 6-24. 6-25. 6-26
- GRAVEL CONTENT - 42:
9__ 9 POINTS
9- FIBURE 0.57
HI—
-0
‘TTIT‘T_'I
20.0 24
l6.0
1'T"F""T~‘T"'F_"T'_T"'1_'"F_“T
264
9 w
C3
3 +
6 DJ
3. w
6] I I I I I I I
-3‘.?o -z.s: -z.:: -I.so -I.c3 - 530 0.7—
L33 PERCEIT 4 AX STRAIN
3
(A .F. 4 ‘FW C: (“ 7‘ â€W 1“
L7 "H- F-LJLJer/23LJLJ
5 E KCCCL'S
ql
§_ SAMPLES 6'24: 8'25: 6'26
L ORAUIEI. cONTEIIIT - 42:
O, _ 9 POINTS
†FIGURE I.59
C
RI
L—
O
S
c: _
3'.
9L
2
L
D
6 L
u-I L- A
o %
b; l_ A A A LO
’— A O
8 _ +
a; “J
a If:
v 0.
6 I I I I I I I
-3'.'JO -2 .So -2 .00 -I .so -I .00 -.SOO O.I
LOG PERCNT 4 AX STRAIN
GT—4 F1 CPZOO
5 E MODULUS
°-.J
9" SMPLES 0°24: 0-2So 0-26
- GRAVE. CONTEJT - 428
9__ 9 POINTS
2
9* FIGURE 3.58
g_
9 _
N L—
R _
K.
40r0
36.0
32.0
20.0
16.0 20.0 24
12.0
0.00
.00
S E HOSULUS
P SAMPLES O-2a. O-zs. 6-26
L GRAVEL OONTaIT - 42:
_ 9 POINTS
L FIGURE 0.60
L
IA
7 IA
'- A
L—
P
d-L l 1 l I I '
-s'.oa ~z.so -z.oa -I.so -I.oo -.Sco O.‘
LOG PERCNT 4 AX STRAIN
GT-4 F5 CPZOO
E+0
PSI
PSI EIOS
265
8 E NCCULQS
°.
S—‘P SAMPLES 6‘27: 6’28: 5'29
I— GRAVEL CONTENT U 421
‘E’_ 6 POINTS
ID
9 FIGURE 0.61
L.
D
2:»—
9E
.
37
d
97'
I
:f\ a
2;— 8K
I!
of
D's—
‘L.
J.
:31 ' 1 I I I 1
-3‘.sa -2.sa -2.:c -I.ss 4.33 -.s:': O.‘
LOG PERCKT 7 RX STRSIN
"7‘ C m "" r“
C’ l — 1 0| U D L P O
8 E MCCJ ;S
O
gL SAHPLES 6-27. 6-28. 6-29
_- GRAVE]. CONTDIT I 428
q 6 POINTS
3
0— FIGURE 3.63
2".»—
O
.: I—
N
I—
9
I:
at
6
N
O
in—
.. A
9
3 A
L-
8_
6
I"
O
C? .—
6“ I 1 L l I I J'—
-3£OO -2.sa ~2.ca -I.so -I.OJ -.5:O O.
LOG PERCNT 7 ï¬x ST RIN
GT—lOFl
CPO
E+OS
PSI
E+05
PSI
8 E MODULUS
é“ SANPLSS 6-21. 6-28. 6-29
~ ORAVEL CONTENT - 42:
9__ 6 POINTS
3
9: FIGURE 0.62
9E
‘?
NI—
O
8;.-
ï¬T
[6.0
0
T
4/
N I- A
r \\%A
8 L.
o I—
0
SI-
6T I I . I 1 I .
-3.:o -2.so -2.:: -I .so -I.cO -.5:c c.'
LOG FEFCNT 7 RX STRQIN P
C)
~T—10r3 CPD
8 E HUCULUS
‘1L
3 SAMPLES 6'27: 6'28: 6'29
.. GPAVEL CON‘I‘EII‘!‘ I 423
q 6 POINTS
"- FIGURE 0.64
O
o i—
=3 .-
i
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2" u—
‘3 : A
'- I-
O. _ ‘z
4
c3- 1 1 I 1 l 1 1_
-:‘.aa -2 .so -2 .00 -I .30 -I .00 - .530 O.’
LOG PERCNT 7 RX STRRIN
GT—IOFS CPO
E+OS
PSI
PSI E+OS
20.0
266
8 E MODULUS
O
2....- SMPLZS 0'27: G-20: 0-29
_ GRAVEL cONTSNT - 42:
9+ 0 POINTS
2,
9I FIGURE 0.65
â€L
O'D—
CI’ I.
‘0
C: A
~ _ .A
P 135
o IA
9 ._
O
.. A
O
‘3
‘
:5 I I ! I I I
-2'.OJ -z.SO -z.OO -I.SO -I.OO -.5OO O.'
LOG PERCNT 7 RX STRRIN
GT—IOFOSCPSO
8 E MODULUS
EL' SAHPLES 6-27. 6-28. O-29
I- GRAVE. CONTENT I 423
:__ 8 POINTS
9†FIGURE 0.67
g I.
3
2'. I-
; L
- I-
. I-
6- I I I I I I I_
-3‘.OO -z.so 4.00 -I .SO -I .00 - .500 O.‘
LOG PERCNT 7 RX STRRIN
GT-IOFI CPSO
PSI E+OS
PSI E+05
32.0 30.0
20.0
24
20.0
8 E MSDELUS
" SAMPLES 0'27: 6'20: 0'29
.. GRAVE. CONTDJT ' ‘2:
__ 0 POINTS
P FIGURE 0.66
r
-:I'.Oa -z.so -z.OO -l.50 -;.aa -.saa O.'
LOG PERCNT 7 RX STRRIN
GT—IOFB CPSU
8 E MODULUS
g" SAMPLES @4270 0-20: 6.29
_. BRAVEL CONTDIT I ‘2!
=2_ 6 POINTS
â€- FIGURE 0.68
o. F'-
z’ .—
O
Si
.. A
35* 4A A
a, ' a
i r-
. I-
:r- l I I I I I I
-s‘.oo -I.so -z.oa -I .so -I .o: -.530 O.‘
LOG PERCNT 7 RX STRRIN
GT-IOFS CPSO
E+OS
PSI
PSI E+05
8 E MODULUS
267
§‘ SAMPLES 0.21: 0-20: 0'29
CRAVEL CONTENT - ‘2:
c: 9 POIN‘I'S
Z- FIGURE 0.69
c;7_ I I I I I I
-3133 .2.50 -z.oa -I so -I.Oo -.sca 0!
L83 PERCNT 7 RX STRRIN
Gl-IOFUSCPZUO
8 E MODULUS
éT‘ SAMPLES 0-27: 0-28: 0-29
.- GMVEL CONTDIT I 423
9__ 9 POINTS
9L FIGURE I.7I
“L
s:
:._ I I I I I If
-IEOO -I.SO -z.OO -I.so -I.OO -.soo O.‘
LOG PERCNT 7 RX STRRIN
GT-lOFl
CPZOO
PSI E+US
PSI E+05
32.0 38.0 COIO
20.0
-3Laa
LOG PERCNT 7
8
J
E MODULUS
SANPLES 0-27, ¢.g., 5-2,
Oansz CONTENT . .23
9 POINTS
FIGURE p.56
I I I I I I
:.SO -z.OO -I.sa -I.OO -.SOO OJ
RX STRRII
GT—IOFS CPZOO
8 E MODULUS
3w SANPLES G-zT. G-ea. O-29
_ GRAVEL cONTzNT - 42:
9__ 9 POINTS
â€L FIGURE 0.72
:I
‘u r
:I
e[
"L
2"}-
"L
,L
O L I l 1 L J l
-3290 -2.SO -z.OO -I.SO -I.OO -.SOO O.“
LOG PERCNT 7 RX STRRIN
GT-IOFS CPZOO
E+OS
PSI
PSI E+US
268
2 E MODULUS
§“' SAMPLES G-II. G-Ia. O-Sa. 6-35
I GRAVEL CONTENT I 598
9__ I0 POINTS
"I-
._ FIGURE n.73
2L
3L
NL
OF
CE
.I-
9 (3A
9- A
v A
37 I I I I 444 I I
-3IJO -z.so -2.OO I so -I on -.500 OJ
LCD PERCNT 1 RX STRRIN
20-0 32.0 30.0 40r0
24
-3IOO
GT—I FUSCP
2 E MODULUS
SANPLES 0'11: 0°13:
BEAVEL CONTENT I 59!
I0 POINTS
FIGURE 0.75
L I l l
'0o50 -2-00 -l.50
LOG PERCNT l
C}T'-1 F'l
E]
5'340
l
0.35
l
' I300
I
l
of
RX STRRIN
EiF’EJ
PSI E+OS
PSI E+05
0.00 1210 I0.0 20.0 2‘ 20.0 32.0 30.0
C.00
2 E MODULUS
' SAMPLES O-II. G-IS. G-aa. G-Ss
- ORAUEL cONTENT - 59:
IO POINTS
' FIGURE 0.74
I
DD
6 I I I I I I 4L—
-3£cO -2.so -2.OO -I.so -I.OO -.soo OF
LOG PERCNT I RX STRRIN
GT—I F3 CPU
2 E MODULUS
§“' SAHPLES G-II. O-Ia. G-aa. G-Ss
_ GRAVEL CONTENT I 598
:__ O POINTS
9* FIGURE 0.76
"I
2L
2— A
.-I—
g A
6; A
,L
a I I IE I I I I
-3.OO -z.so -z.OO -I.SO -I.Oo -.800 O.'
LOG PERCNT l RX STRRIN 1
GT—l F5 CPO
F+OS
PSI
PSI EIOS
.0 20.0 2¢.0 20.0 32.0
I6
02.0
24.0 20.0
T7 I
20.0
269
2 E MODULUS
SAMPLES G'III G'ISO
GRAVEI. CONTWT I 593
I. POINTS
6'34: 6-35
FIGURE 0.77
I I I I I I
- -$O -I.00 -.SOI‘.‘ 0.|
L33 PERCNT I RX STRRIN
FOSCPSO
2 E HSSULUS
1L
9 SAMPLES G-II: 0°13. 6-34: 0-35
__ OPAVEL CONTENT I 598
9 IO POINTS
0- FIGURE 0.79
I I
I
I L I _L I I
-F.co -I.SO -z.oo -I .so 4 .OO -.SOO O.'
LOG PERCNT 1 RX STRRIN
GT-I F1 CPSU
PSI E+05
PSI E+OS
2 E MODULUS
3“. SANPLES O-II. O-IO. 9-34. 3-35
SWIVEL CONTDIT I 593
9[ IO POINTS
"~ FIGURE n.78
2L
NP
.. I-
†F-
I-
o 42.3: -z.sa -2z.ca I.Sa -I.:: -.s:c 0.7
L33 PERCNT I RX STRRIN
2 E MODULUS
3“. SAHPLES O-II. G-Ia. 6-34. 6-35
L ORAVEL OONTENT - so:
9__ IO POINTS
.F FIGURE 0.80
cF
«It
- I-
‘h
_
-3I.OO 41.50 -2l.ao -ll.50 41.30 - .1500 Off
LOG PERCNI I RX STRRIN
GT-I F5 CPSO
PSI E+05
4.00
I I I r I I 7T" I 7T
PSI E+05
6.00
l2.0 I6.0 20.0 24.0 20.0 32.0 30.0
0.00
C%O
I
_o.
I—II—
l2o0 10-0 20-0 24.0 20-0 32-0 30-0 ‘0
2 E HODULUS
SAMPLES G-Ilo 0'13:
BRAVEL CONTDIT I 593
I2 POINTS
FIGURE 0.81
-LW
PERCNT 1
2 E MODULUS
SANPLES 0-11: 0-13:
GRAVEL CONTENT I 59!
12 POINTS
FIGURE 0.83
5-34:
I l I I I
-:ï¬::
'2-00 -2-00 -I-50
LOG PERCNT I
0'300 6'33
I
-.500
RX STRRIN
FOSCPZOO
0-35
I
. .500
GT—l F1 CPZDO
270
4&47
0 I
1
Of
RX STRRIN
E+OS
PSI
PSI E+OS
2 E MODULUS
c:
gL SANPLES O-II. O-Ia. G-Sa. G-Ss
_ GRAVEL CONTENT I SO!
9 I! POINTS
:3 7
q“ FIGURE I.82
.I
2r—
{
c:
g _
oh
é—
F
O'H-
i
I:
.E
6II I I I I I I
-3.CO -Z.$0 -2.00 -I.53 -I.33 -.533 0:
CG PERCNT 1 RX STRRIN
20.0 32.0 36.0 40IO
2‘ Do
GT-l F3 CPZOO
2 E MODULUS
~ SAHPLES O-II. G-Ia. G-aa. 6-35
_ GRAVEL CONTENT - 59:
I2 POINTS
~ FIGURE 0.84
I I I l I I
-:2oa -z.SO -2.00 -I.sO -I.OO -.SOO O.I
LOG PERCNT 1 RX STRRIN 1
GT—l FS CPZOO
PSI E+OS
PSI E+OS
2F7].
5 E HOCULUS
gi’ SAMPLES 0‘90 O'IOO 0'33
OHAVEL CONTENT I SOS
9 O POINTS
n— FIGURE 0.85
3» A
OF- A
? . °
I.
c:‘ . I I IIIL I I I
-3;OO -2.so -2.OO -I.sa -I.Oo -.soc o.r__
L03 PERCNI 4 RX STRRIN
T
GI—4 FOSCPO
5 E MODULUS
éU' SAHPLES 6'90 OIIOO 5-33
GRAVEL CONTENT I 59‘
9 8 POINTS
"L FIGURE 0.87
O
u-I
o
O
I I I I I
-SIOO -2.SO -z.OO -I-SO -I.OO
LOG PERCNT 4
GT-4 F1 CPO
_L
OJ
RX STRRIN
PSI E+OS
PSI E+05
S E MODULUS
é“ SANPLES G-O. a-IO. O-Oa
~ GRAVIL CONTENT - SOS
:__ 0 POINTS
"_ FIGURE 0.86
"r
OF
S: g A
S‘- I I I I I I I
-3zca -z.so -z.OO -I.so -I.OO -.SOO ofl
LOG PERCNT 4 RX STRRIN
S E HODULUS
g“. SANPLES G-O. O-IO. 6-33
_ GRAVEL CONTENT I 59!
q__ 0 POINTS
â€_ FIGURE 0.88
9% A
8__ A
8L. A
g.
I.
nr
0 I L I I I I I
-SIOO -:.So -z.OO -|.SO -I.OO -.800 O.‘
LOG PERCNT 4 RX STRRIN
GT-4 F5 CPO
PSI E+OS
PSI E+OS
272
5 E MODULUS
3*- was 5-9. a-Io. cos:
CMVEL CONTBJT 0 59!
C: I POINTS
6* FIGURE 3.89
g L-
g r
I.
N I—
gr
L.
o A 4A
; — A
I
o ' I l ' I 1 I
3.00 2 50 -2.30 -l.SC -l.OO -.530 O.‘
LOG PERCNT 4 RX STRRIN
5 E MO ULUS
ol
é" SAMPLES 6-9. 6-10. 6-33
I. cmva. com-arr - so:
9__ O POINTS
OF FIGURE v.91
"r
:E
“I
I; r-
6L
r
:hI I I I I I _L
-I'.oo -: .so -2.ao -I .so -I .oo - .soo II.r
LOG PERCNT 4 RX STRRIN
GT-4 F1 CPSO
PSI E+05
PSI E+US
5 E MODULUS
3* anus 6-9. c-Io. 6-33
I- OMVEL CONTDIT I 893
9_ 8 POINTS
9* . FIGURE I.9o
N I"
or
o"— I I I I I I
-3'.oc -:.so -2.:a -I.so -I.co -.soo o.-
LCG PERCNT 4 RX STRRIN
GT—4 F3 CPSO
S E MODULUS
:9— SAHPLES 0'90 @100 8-33
I- BPAVEL CONTB‘T O 59!
9_ 8 POINTS
9* FIGURE v.92
3L
c5.+ L I I l I I
-3‘.ao -2 .so -2 .03 -I .so -I .oo -.soa o.’
LOG PERCNT 4 RX STRRIN 1
GT—4 F5 CPSO
273
E+OS
PSI
PSI E+05
5 E HCDULUS 5 E HODULUS
3"" SAMPLES S-Oo O-IIo O-OO 2“ SAMPLES 0'90 Boll: O-OO
I- mm GONTDIT I 59‘ CRAVE. comm I 593
9__ II POINTS q__ 9 POINTS
"L FIGURE I.93 ". VIBURE 3.94
2L
:‘L
J
6}-
é†m
*- O
o +
z†w
a 5
" Q.
r.
Jb I I I P 6 I I I I I I -
-3'~JO -2-50 -2.00 -I-SO -I.OO -.533 O? -3'.OO -2-50 -2-00 -l-SO -I.30 --$00 0—'
L33 PERCNT 4 RX STRRIN LOG PERCNT 4 RX STRRIN
5 E MODULUS 5 E MODULUS
§*- SAHPLES O-9. O-IO. 0-33 3â€. SAHPLES 6-9. O-llo O-Oa
I. GRAVE. CONTDIT I 593 _. BPAVEL CONT“? I 59!
9.- 9 POINTS c:__ 9 POINTS
"I FIGURE 0.95 "- FIGURE I.96
‘2 I.
“ I-
m I."
(3 .-
m §~
._. I‘
m 8,
0.. " _
6 I g I I I I I 6- I L I I I l #L
- .oo 4.30 am 4450 4.00 -.sao NF -a'.oo 4.30 -2.oo -I.sO -I.Oo -.soo O-‘
L00 PERCNT 4 PX STRRIN 1 L00 PERCNT 4 RX STRRIN 3
GT-4 F1 CPZOO
GT-4 F5 CPZOO
E+OS
PSI
PSI E+OS
38.0 40{0
32.0
8
E MODULUS
MES G'Io
‘ POINTS
3°20
CRIVZL CONTENT I 593
FIGURE 3.97
7
6'3
1
-I.OO
RX STRRIN
T—IOFOSCPO
I
' 050°
274-
I
OJ
a E MODULUS
2.3—— was (M. 6-2. O-a
- BRAVE. CONTDIT I‘ 598
9__ 5 POINTS
:- FIGURE p.99
3
“L
;F
; h
cf—I I I I I I I
-:Iaa -z.so -2.oo -I.so -I.oo -.soo O.'
LOG PERCNT 7 9x STRRIN
GT—IOFI
CIF’E]
PSI E+US
PSI E+05
8 E NODULUS
3" smnzs O-I. 5-2. 6-3
I emva. CONTENT -' :9:
q 5 POINTS
:2:
a- . FIIUIE n.98
n I-
IS-O 20.0 2‘
I2-O
0-00
.00
o -3330 -2'.SO “21.03 -I.-SO -Il.05 -.'533 O.:
LOG PERCH 7 RX STRRIN
8 E MODULUS
3w» SANPLSS O-I. One. so:
CBAVEL CONTENT I 59:
q _ 3 POINTS
o- FIGURE H.100
or A
3L A A
N- A
s:
8_
r-l I I I I I I
-IIOO -z.so -2.Oo -I.su -I.oo -.soo OJ
LOG PERCNT 7
RX STRRIN
S
GT—IOFS CPO
E+OS
PSI
PSI E+05
8 E MODULUS
1275
8 E MODULUS
3L SANPLES (III: 602: 0'3 3'“ WLES C-Io O-Zo O-S
I" BRAVE. CONTBIT I‘ 598 .- BMVEL CONTENT I' 59!
Z __ 6 POINTS 9 __ 6 POINTS
"L FIGURE 3.101 "_ FIGURE l.I02
c, _ 2F
2†2†A
I. I. A A
y f A
I- ..
3 2- A
N h N r—
3 m
E" ID iâ€
I— O I—
o + o
I- .._. P-
8 .. (f) 8 _
Q (L .
I'
o'— I I I I I I I 6". I I I I I I
-I'.:: -z.so -z.oo -:.sa -I.oa -.s:o o.I 4.30 -2.so -2.ao -I.sc -I.oo -.soo II.T
LOG FERCNT 7 FIX STRRIN LOG FERCNT 7 RX STRRIN
S S
Gl—IOFOSCPSO GT-IOFB CPSO
8 E HODULUS 8 E MODULUS
3“†SMPLES O-Io 8'2: 6'3 3"“ SANPLES B-Io 0'2: G-O
.. CRAVE]. CONTDIT I 598 _ CRAVE]. CONTDIT I 59!
‘2 6 POINTS 0, __ 6 POINTS
"- FIGURE H.103 " FIGURE D-104
I3 " A Z _
? AA g
I A F
a A 3
N *- N ’-
O I— O '-
é†In 5
I— O r-
o + o
2- IA :-
8, _ "a? 3 _.
v Q. ‘ r
5 I 4 I I I 1__ 0'". I I I I I I I
-:‘.OO 4.30 -2 .OO -I .so -I .OO -.soo II.I -I‘.oo 4.50 -2 .OO 4 .so -I .00 -.soo O.‘
LOG PERCNT 7 RX STRRIN 5 LOG PERCNT 7 RX STRRIN 5
GT—IOFI CPSO
GT-IOFS CPSO
PSI E+05
PSI E+05
276
8 E MODULUS
§“' SANPLES C-Io O-Zo 6-3
I. CMVEL CONTENT I SO:
:__ O POINTS
:» FIIURF p.105
2L
I-
6â€. I I I I I I I
4.30 -2 .so -2 .00 -I .so -I .oo - .500 07—
L00 PERCNT 7 RX STRRIN
8 E MODULUS
Em' SAHPLES O-I. O-z. O-a
_ CRAVE CONTMT I 59!
9_ 8 POINTS
â€Zr FIGURE I.Io7
†I
“P
,I-
O I I I I I I
oIEOO -:.so -z.oo -I.so -I.Oo -.sOO o;‘
LOG PERCNT 7 RX STRRIN
GT—IOFl CPZUO
PSI E+05
PSI E+05
8 E MODULUS
OrO
I
.. ML†O'Io 3'2: 5'3
~ ONAVEL CONTENT I 598
z __ C POINTS
9“ FIGURE l.106
{
3
OF
u I—
. I-
r—
6 I. I I I I I I I
-3.ao -z.so -2.00 -I .so -I.OO -.sco o.‘
LOG PERCNT 7 RX STRRIN
GT—IOFB CPZOO
8 E MODULUS
SN‘IPLES 6.]: 6°20 8'3
CRAVE). CONTDUT I 59!
O POINTS
FIGURE H.108
[2.0 18.0 20.0 2C.O 20.0 324) 38.0 401.0
llIï¬llIIIIITIrITIiTIII
o -3'.oo 41.50 41.00 - 11.50 -Il.Oo - .lsoo [LI
LOG PERCNT 7 RX STRRIN
GT-IOFS CPZOO
APPENDIX E
DAMPING RATIO FOR GRAVEL-ICE SAMPLES
277
DRMP RRTIO
DRHP RRTIO
JGO .220 -260 .300 .340
.140
ITIII
.300 II
3 DRHPING
SAHPLES GI I Co 6‘ I 90 OIPO
_ GRAVEL CONTENT I 241
O POINTS
- FIGURE EJ
L
j
I
I
b
I
A
A
\K:\\
8 CI)
7 ’- .—
8: CI:
é _, 0:
a I
v P E
C]:
r- C)
o . I I I I I L
~3'.oo -z.so -2 .00 -I .so -I .oo - .500 of
LOG FERCNT I RX STRRIN
3 DRMPING
;‘ SAMPLES 6‘18. 6'19: 6.20
g-- CRAVZL CONTENT I 248
' P 7 POINTS
:2 †FIGURE E .3
F
' L
i
O '- o
N (I
3_ a:
'33- a.
v Z
" CI:
__ D
' I I I I I 4 L
-Ilc:, -z.so -2.oo -I.so -I.oo -.soo o.I
LOG PERCNT 1 RX STRRIN
GT-l F1 CPU
278
3 DRMPING
JI' SANPLES O-IO. O-I9. O-2O
g - GRAVE. coumt - an
“I- O POINTS
3- FIGURE £.2
, F
t— A
3- A A
rL
O l I I | I I I
-3:cc -z.so -z.cc -I.so -I.co -.sco o.I
LOG PERCNT I RX STRRIN
2?
3 DRHPING
I smzs s-Is. eon. O-aa
g- CPAVE. CONTENT I 2‘3
IL 1 POINTS
3- FIGURE E.4
g _ A
3 '- A
‘5._ I I I I IIIIII I IIII
-IEOO -:.so -2.oo AI.so -I.oo -.soo o.‘
LOG PERCNT l RX STRRIN 2
GT—I F5 CPO
DRMP RRT IO
DRMP RRTIO
279
3 DRYIPING 3 DRMF’ING
;“' SAMPLES G-IOo G-IO; 8-20 J†SANPLZS G-IB: G-IO: 6.2.
a — GRAVE. comm: - 2a: §~ vau. comm: - an
.L IO POINTS -+ 3 pgxu15
S__ o
â€I FIGURE E.5 a- FIGURE [.6
8 th
7_' 3..
J J
“I’— 2&—
I— A .—
2 A o
. L .A L
8 o
." g.—
"’ .h— A A
8_ o ___——1r~jr'—Fâ€â€˜â€”——————————_fl———
g- 9.. 8-
.h .— '7
8. CE «'-
5. a: ï¬_
8: 8
c."- 0. c;
v Z I.
(I
i D .-
o ' I I I I . I o I I I I I I I
-3. -2.50 -2.3: -I.sa -I.oo -.533 J.‘ -atoo -2.so -2.oa -I.so -I.oa —.soo on
LEG PERCNT l RX STRRIK LOG PERCNT l . RX STRRIN
GT—l FOSCPSO 2 GT—l F3 CPSO
3 URXPING 3 URHPING
J -I9 0°20
h SAMPLES G'IBo G-I9o 6.2! F SAHPLES G-IB: G o
E- vau. comm? - 24: Ei vaa. CONTENT - 24S
'_ a nuns 'r 5 nuts
2— FIGURE 5.7 3- FIGURE [.8
. P P
E * § L
T L T _
on A , W O 8-
2 - -—--—-— 4i if " C: 1 _
3* CI: 3â€
“I“. m I...â€- ï¬
3 § aa. :9
3- % .- A
I- a II-
.JL 0 -
O ‘ I l 1 l l l I J l I l l I
-:.co -2.so -z.ao -I.so -I.oo -.soo o.‘ -s.oo -z.so -2.ao -I.so -I.oo -.soo o.
LOG PERCNT I RX STRRIN LOG PERCNT l RX STRRIN 2
GT—l F1 CPSO 1 GT—l FS CPSO
DRMP RRTIO
DRHP RRTIU
.300 j
I
.260 .300 .340
I47 I I
I
4T7
I
.220
I
0'80
.140
3 DRMPING
SAMPLES G-Is. G-IG. G-ao
BRAVEL CONTENT - 24:
II POINTS
FIGURE E.9
280
a?
gr
I
JTI I; . . I I I
-:.:o -2 so -2.co -I.so -I.ca -.soc o.’
LOG FERCNI 1 RX STRRIN
7‘ (K "\
GI-l FOSpUZOO
3 DRMFING
‘†SAMPLES 6°18. G-I9a 6-20
§.. GRAVEL CONTENT - 24:
' _ II POINTS
3- FIGURE E.II
' I-
3:
Orâ€- : I I I I I 4_
3.00 -:.sa -2.oo -I .50 -I .oo - .soo o.I
LOG PERCNT 1 RX STRRIN
GT-l F1 CPZOO
DRMP RRTIO
DRMP RRTIU
.300 .3‘0
T’ I
.260
I I I TgiI
.380 :
DRHPING
SAMPLES G-IO: G'Iï¬o 8.20
BMVEL CONTDJT I 2!!
II POINTS
I
FIGURE E.IO
8F
.2 I
gr
9_
O I 1 1 ‘ l 1 J;
4.3:: -2.sa ~ :3 - .sa -I.oa -.sao o.‘
LOG ERIN? 1 RX STRRIN
T r“ A.
GI—l F3 CPauO
3 DRMPING
'{" SAMPLES G-IB: 0-I9o 6'20
§.. GRAVEL CONTENT - 24:
.r- 9 POINTS
2 FIGURE E.12
Q" A
g: —‘ :‘A :33 7‘; A
aid-I I I I I I I
-s‘.oo -z.so -z .00 -I .so -I .oo -.soo o.‘
LOG PERCNT 1 RX STRRIN 2
GT-l F5 CPZOO
DRMP RRTIO
ORMP RRTIO
281
6 ORHPING
;“' SAMPLES 6-21: 0-22: 0-23
g-— BRAVEL CONTENT I 248
'_ O POINTS
3." FIGURE [.13
'IL
§- A A
.~ A A
2— A A
AL
0 ' l 1 I L l I
~3200 -2.50 -2.00 -I.SO vl.03 -.503 DJ
LOG PERCNT 4 RX STRRIN
6 DRNPING
‘E SAMPLES G-2lo 6-22o 0-23
8 .. GRAVE CONTBIT I 248
â€L 8 POINTS
§~ FIGURE E.15
'L
J“. I I I I I I
-3loo -2.so -2.oo .I.so -I.OO -.soa O.I
LOG PERCNT 4 RX STRRIN
GT-4 F1 CPO
DRMP RRTIO
ORMP RRTIO
6 DRHPING
‘L SAMPLES 6'21: 6'22: 6°23
2.. Guam OONTaIT - a:
.I 8 POINTS
3- FIGURE [.14
OF
°L
'L
I’M
g- A
I:_Y I I I I I I
-3\00 -2.50 02.00 -1.50 -I.OO -.503 O.‘
LOG PERCNT 4 RX STRRIN
6 DRMPING
IL SAMPLES G-2lo 6-22o 6-23
§— vaa. CONTDIT . 24:
'_ 1 POINTS
$~ FIGURE (.16
.I-
gh-
é-
o _' ‘5 1‘
is H 73
--.l l I l IIL AJ, 1
-a.oo -2.so -2.oo -I.so -I.oo -.Goo o.'
LOG PERCNT 4 RX STRRIN
GT—4 F5 CPD
4
DRMP RRTIO
ORMP RRTIO
282
6 DRRPING 6 DRMPING
O'T SAMPLES O-2Io G-22: 0°23 1" SAMPLES O-Olo 6-2& 0-23
3,. OMVEL couran . 24g 8 GRAVE. CONTDJT - 243
_ 8 POINTS â€F a poms
9. FIGURE [.17 OF
F:_ :3" FIGURE E.18
. L 9::
. I- “I
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E on
J ~‘
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g 0‘ ‘5
3 o. 8 ..
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D .1—
1. I 1 1 1 1 1 6 l l l ' l ' l
-:..a -2.50 -2.03 -I.so -I.oo -.scO o.‘ -3‘.ao -z.so -2.00 4.59 -I.oo -.s:3 Oj—
E...) PLAONI 4 RX STRRIN LOG PERCNT 4 RX STRRIN
_. F‘
GT 4 FOSOPSO GT—4 F3 CPSO
6 DRNPING 5 DRMPING
j" SAMPLES O-alo 6'22: 6-23 3'- SAMPLES O-Elo 6.22; 0-23
3 _ GRAVE]. CONTmT - a“ g - OBAVEL CONTEJT I 24!
° __ 8 POINTS ' P 8 POINTS
3,. FIGURE E.†° FIGURE mo
0 '- ° F
k e ;*
éL A A Egg
I- °‘ :2
8 ~ 0- 3.
0 Z '
" CI:
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6 . L 1 1 1 1 1 :5 L L 1 1 1 1 1
ans: -: .so -2 .OO -I .so -I .oo - .500 o.' -3'-00 '1 $0 '1'00 'I '50 " ~°° ' -‘°° ‘3
LOG PERCNT 4 RX STRRIN LOG PERCNT 4 RX STRRIN
GT—4 F1
CPSO
GT-4 F5 CPSU
DRMP RRTIO
ORMP RRTIO
.140 .100 .220 .260
.100
4.000E-0?
——F' T“ V"_F"'T—_I
I
.100 .220 .200 .300 .3‘0 .300
l I
.IIO
283
6 CCF‘IPI-‘IG
OT saunas G-zn. G-zz. 6-23
3L OPAVEL CONTDJT - an
r 9 POINTS
I." FIGURE [.21
I FT IFFTF I I I
I
6 DQMPENG
1' saunas G-zn. G-22. G-aa
— GRAVE. CONTENT - 24:
1 8 POINTS
- FIGURE E.23
F.
IFFT—FI
.m- “A
Z _ A?‘
:5“. I I I I, I I I
-aaoo -z.so -z.ao -I.so -I.OO -.soo o.I
LOG PERCNT 4 RX STRRIN
GT-4 F1 CPZOO
DRMP RRTIO
DRNP RRTIO
6 DRHPING
JG saanzs G-RI. 0-22. 643
g _ GRAVE. couTsNT - an
F 9 POINTS
2— FIGURE E.22
L .
'L
’ r
7 F .A ‘
§r A
g P
g'L
'L
r?-
°l__L I I I l I 1
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LJG PERCNT 4 RX STRRIN
6 DRHPING
:F saunas O-2lo G-ea. was
:3 F GPAVEL CONTENT - 24x
'1. 0 POINTS
3. FIGURE E.24
r.
. r
'L
a
.100
40
I l I If I I I
4.000E-02
-:Loo -z.so -:.OO -I.so -I.oo -.soo OJ
LOG PERCNT 4 RX STRRIN 3
GT—4 F5 CPZOO
DRMP RRIIO
ORHP RRTIO
284
9 DRHPING
;+' SAMPLES 6'30: 0-3Io 0'32
: ,.. GRAVEL CONTBIT I 2“
'_ 9 POINTS
E: FIGURE E.25
. h (3 (3
8L A A
L— A A A
33 I I I I I I I
-3£:3 -2.so -2.aa -I.so -I.oo -.soc O.T
LOG PERCHI 7 RX STRRIN
[—- r"
GT-IOFOOCPO
9 URMPING
“L SAMPLES 0-300 G‘JI; 5'32
g- GRAVE. CONTDJT I 2‘:
' 0 POINTS
3_ FIGURE E.27
g.
'L
a:
5
§"__I AA
3 ‘5‘&~—4L——
r- I I I I I I
oaioo -2.so -z.oo ~1.SO -I.oo -.soo OII
LOG PERCNT 7 RX STRRIN
GT-lOFl CPO
DRMP RRIIO
DRMP RRTIO
9 DRMPING
4+" SAMPLES G-ao. G-OI. 6-32
8 T GRAVEL CONTENT I 24!
'1 0 POINTS
2— FIGURE E.26
g h
'L
.»
E- 2‘: %
.-0- ' I 1 ~ - I -
-J:OO -z.sa -z.OO -I so -I.aa -.523 O.'
LOG PERCNT 7 RX STRRIN
F-
GT—lOrB CPD
9 DRMPING
" SAMPLES G-an. O-Olo 8-32
E cansz CONTENT - ca:
.300 .340
.200
5 POINTS
FIGURE E.28
GT—10F5 CPO
1L
§_
;L
E:
:1 ï¬i-Aï¬I: I A I J
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LOG PERCNT 7 RX STRRIN 6
DRMP RRTIO
DRMP RRTIU
285
9 DQMPING
0+ smut: 6-30. 6-31. 03-32
:2 - SWIVEL CONTDJT ' 24$
'L 9 POINTS
§— FIGURE [.29
'I-
. r
'7 2
% EA A S
. A F_
8 CE
% m
a m
"t 2
C]:
D
6L' I I I I I
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LOG PERCNT 7 FIX S’T’QIN
1 f—
GT—IOrOSCPSO
9 CRMPING
JT' SAMPLES G-JO: G-SIo 6-32
gI. GEM/EL comm? - 24:
'P 9 POINTS
2- FIGURE [.31
J
'L
0‘ c:
v:— I—
s- g
2'," An 3 A
3m- A ‘1 0—
. , z:
* CE
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6 I I I I I I I
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LOG PERCNT 7 RX STRRIN
GT—lOFl CPSO
9 ' DRHPING
J’- SMPLES 5'30: 3'31: 0'32
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° L 9 POINTS 3
O
:3 ~ FIGURE E .30
L .
§ _
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O
a I.
i
I.
9..
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8-
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2 f3 a
§
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LOG PERCNT 7 RX STRRIN
GT—IOFB CPSO
S DRHPING
T SAMPLES O-SO. G-Olo 6-32
§_ 6mm com-m1- - 24:
'b 9 POINTS
3— FIGURE [.32
§
g I—
r-l_ :I 4 l : 1 1 l l
oshoa -:.so -z.oo -I.so -I.oo -.soa o.‘
LOG PERCNT 7 RX STRRIN
GT-lOFS CPSO
DRMP RRTIO
DRMP RRTIO
.100 .220 .260 .300 .300
‘0
9 DQNPING
;"' saanzs a-ao. a-3I. 6-32
.9, _ 3mm comm: - 24:
° 9 POINTS
— FIGURE 5.33
286
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§._
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-3x:3 -2.sa -2.oa -I.sa -I.ao -.soa oiT
L3G PERQNT 7 RX STRRIN
"* 1
UI_IOFOSCPZOO
9 DRMPING
“L SAMPLES 6'30: 0°31: 0.32
g- GRAVE. CONTBJT - 24!
'r 9 POINTS
g_ FIGURE 5.35
J
3i—
gh-
::
L.
9_
s:
8 A
O..—
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LOG PERCNT 7 RX STRRIN
GT-IOFI CPZOO
DRMP RRTIO
DRNP RRTIO
9 DRHPING
;+' SAHPLES G-OO: O-JIo 0°32
3" ORAVZL CONTENT 0 2A!
'_ 9 POINTS
5 FIGURE E.34
§-/
NP- A
? A
Iai- A
'I
é¢.l I I ' I I I
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LOG PERCNT 7 RX STRRIN
9 DRMPINO
+p SAHPLES G-OO: 0°31: 6-32
§_ GRAVE. comm-r - 2‘4:
'_ 9 POINTS
5 FIGURE [.36
J
gI.
$..
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-—‘—_—m—ï¬r——ag-
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-3.oo -z.so -:.oo -I.so -I.oo -.soo U.‘
LOG PERCNT 7 RX STRRIN
GT—lOFS CPZOO
DRMP RRTIO
URHP RRTIO
287
3 DFIrtF’ZNG
éT‘ SAMPLES G-IA: O-ISo G-Iéo G-I?
g—- BRAVEL CONTENT I 42! '
' 0 POINTS
§_ FIGURE 5.37
. b ‘3
o A
gr-
L A A
EC A
o r
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8__
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LCG PERCNT 1 RX S.SSIN
1
'r' r-
GI—l FOOCPO
3 DFMPING
“F SAMPLES c-Ia. G-IS: G-IOo O-I7
§_ Guava. comm? - 42: '
‘L 8 POINTS
SF FIGURE E.39
O r
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3
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2, IA
_. 13
O
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r I I I I I I l
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LOG PERCNT 1 RX STRRIN
GT—l F1 CPO
DRMP RRTIU
DRHP RRTIO
.300
3 DRMPING
SAMPLES 6' I 40 0' I So
ORAVEL CONTENT C 423
O POINTS
FIGURE E.38
U-IG. O-IT
If!
I
OF
QL A
E- .
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gi:
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L00 PERCNT 1 FIX STRRIN
‘“' "' ’1
C} |- 1 F :3 [:F’[]
3 DRHPING
" SAMPLES G-IA: G-IS: G-l6: 0'11
§— 6mm comm? - 42x '
'F 3 POINTS
C)
5‘ FIGURE [.40
. P
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i
3.
P
g _ .A
§:..
5 _
6-_I I L I I I I
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L00 PERCNT 1 RX STRRIN
GT—l F5 CPO
RRTIU
DRMP
DRMP RRTIO
.2£38
3 DPï¬PING
JL SAMPLES G'Iflo G'ISo G'IOo G'I'I
§_ GPAVEL CONTENT - 42:
'_ 9 POINTS
9_ FIGURE E.41
P 43
o .A
2 ~ A A
u ’- A H
8 A
.I
.I
Ii
r-
c.
I?“
a: I I I I I
-3.:o -z.sa -. :3 -I.sa -I.OJ -.sco O.‘
LCG FERCNT 1 RX STRRIN
. “,- 1 f I—
GI—I IOSCPDO
3 CRRPING
I
"' ISI\F‘F"LILS ‘3"I‘lo (5"I25; ‘3"II6 (3..1 1
gL Oanan CONTENT - 42: I
-L 0 POINTS
5? FIGURE [.43
J
R
g.
. I-
2 _
8b
th‘T“*ï¬iA~A
I a
9’- \
5
8L.
gh-
a.
5-4 I I 4 I I I
-y.oa -z.so ~2.OO -I.so -I.:a -.s:o O.r“
LOG PERCNT 1 RX STRRIN
GT-l F1 CPSO
DRMP RRTIO
DRNP RRTIO
3 DRMPING
I.—
SAMPLES O-Ia. 6-15. 6-16. O-I1
§.. OFAVEL CONTENT - 42:
' +- 9 POINTS
3. FIGURE E.42
gt '
E
§_
2:: A A A
a: A
F 3 %
EI—
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g '-
gi—
§_
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-3'.:: -Z.SO 4.30 4.53 -l .00 - 500 O.’
ECG PERCNT l RX STRRIN
3 DRMPING
J— SAMPLES O-Ia. O-Is. O-Ie. O-I1
§.. GRAVEL CONTENT - 42: '
_ 8 POINTS
3— FIGURE E.A4
8 _
Q
g
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O
2. .—
8 >-
2..
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8 _ IA
3‘ u -
§"
C? —
«IT-I I I I I I I
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LOG PERCNT l RX STRRIN
GT—l F5 CPSO
DRMP RRTIO
DRMP RRTIO
2139
SAMPLES (3'le 6-15: G-IO: 6-17
FIGURE E.45
A.
(3
3 DRMPIHG
5.. GRAVEL CONTBIIT - 42!
. II POINTS
L
3
u L 8
g A
7" A A
OF" A A A
.I80 .220
I ’FrF'l FFI‘
I
.l40
L
;L
c3—_I I I I I I I
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LC3 PERC\T 1 RX STRRIN
l
7‘ E— r‘
I—l FODCFéOO
3 DRMPING
‘* SAMPLES G'IO: O'ISo 6.16: 8-17
§.. GRAVEL CONTENT - 428 °
-_ II POINTS
3. FIGURE E.I7
s:
at
.L
2F
1" A A
b Ix; {3 £3
2 _. A ‘19
g.
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r I I I I I I
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LOG PERCNT I RX STRRIN
C}1'-1 F'l
CFZOO
URMP RRTIO
DRHP RRTIO
3 DRNPIN
+P SAHPLES O'I‘a O'ISO G‘IO, O'IT
g. Omwm. comm: - 42:
'_ II POINTS
5. FIGURE 5.46
F'
8..
a:
._ A A
O
a " u
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8
s:
g:
3C
8
SF:
DTT- 1 I I I I I
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L33 PEECNT 1 RX SEFRIN
1
l-l F3 C9200
3 DRKPING
"l" SAMPLES G-le G'ISo 6-16: G-IT
§._ GRAVE. CONTDJT U 423 '
-_ II POINTS
0
9‘ FIGURE [.48
3..
s:
g F-
a:
9..
. b
§- .5 A
8' A '$ g3 A
g ._
8. I—
rbi I I I I I L_
-3Fao -z.so -z.oo -I.so -I.OO -.500 03
LOG PERCNT l RX STRRIN
GT-l F5 CPZOO
RRTIU
DRMP
DRMP RRTIO
290
8 ORESING
47‘ SAMPLES 6-24. 6-25. 5-26
:I- GEAVEL CONTENT ' 42$
'_ 1 POINTS
3. FIGURE E.49
'L
8
8
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2
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I- A" A
at
8
gh-
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8..
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J“. I I I I I L
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LOG FERCN_ 4 RX STRRIN
r—
GT—4 FOOCPO
5 D3UTPIPUG
;“ SAMPLES 6-240 8'25: 6-26
5.. GRAVEL CONTENT - 42!
-_ 1 POINTS
3. FIGURE [.51
OP
8—
L
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3;»-
8
.r
8..
r
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8-““‘4¥—1r—*é4
éL
§..
D..—
Jm I I I I I Ii
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LOG PERCNT 4 RX STRRIN
GT—4 F1 CPO
ORMP RRTIO
ORMP RRTIO
5 URNPING
:— WPI-ES 8-24. 6-25. O-26
g- CRAVEL CONTENT I ‘2!
'L 1 POINTS
3» FIGURE E.$0
F.
g .
4F
8 h-
. I-
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Z'- “ J“ 5
F-
5.
Or"- I l I I I I
-3 c: -z.so -2.00 -I.so -I.oc - 5:: on
LOO PERCNT 4 RX STRRIN
4
6 ORMPINO
4“ SAMPLES 6-240 5-250 3'26
8.. CRAVEL CONTENT - 42%
9 7 POINTS
3- FIGURE E.52
g:
g ..
OF‘
at
§:'_‘—;;——tr—— A
gï¬-l I I I III I I
-3LOS ~2.so -2.OO -I.so -I.OO ..500 O.‘
LCG FERCNT 4 RX STRRIN
GT—4 F5 CFO
DRMP RRT IO
DRMP RRTIO
291
6 DRI‘YPING 6 DRMPIIIG
cf- smnzs 6-24, 3-25, 5.2, 0+ smus o-ea. 5-25. c-zo
3 _ BMW-:1. comm: . .2, g _ amva. comer: - 42:
. r- . â€1‘75 ' _ 8 â€RNTS
:32“ FIGURE 6.53 2- FIGURE £3.54
r- I—
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v E v
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4‘33 -2 .SO -2 .00 -l .53 -| .00 -.500 07 -J‘-83 -2 .53 -2.C3 -I .53 -1 .JJ - .503 0-'
LOG PERCNT 4 Rx STRRIN LOG PERCNT 4 ex STRRIN
4
D E
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§_ 6mm. comm? - .2: g — GRAVE. con-mn- - 42:
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LOG PERCNT 4 RX STRRIN LOG PERCNT 4 RX STRRIN 4
GT—4 F1 CPSO 4 GT—4 F5 CPSO
URNP RRTIU
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292
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SHIN—£5 0'24: 6.250 3.26
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FIGURE F.SB
5 DRNPING
:— SAHPLES 6'24: 6'25: 3'26
3 _ cmva. con-ran - 42:
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3. FIGURE E.S7
' I.
g_ o
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a A
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8 O
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3 CI:
3 - o:
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V CE
r—- C3
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4
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I — 4 F C L, I Z O O
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E- GRAVE. CONTDJT ' 423
- 9 POINTS
9_ FIGURE E.59
,gï¬
%
D
g r—
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53 _
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8 _
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2 _. t—l
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GT-4 F1 CPZOU
53
9 h A
g_
gh-
§_
â€3333 -Z.S° '2100 -Io$C -I.33 -.$OC O.T
LOG FERCNT 4 RX STRRIN
I
GT-4 F3 CPZUU
5 URMPING
0+ SAMPLES 3-24. 6-25. 6-26
3 I- “MVEL CONTWT C 42!
° _ 8 POINTS
3— FIGURE E .60
g:
g F—
8%
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g —
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§ ___.__——Jv—4S3""‘—1gk——————fl——.——————————-——"‘—————.
O p— A
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O.- I l I l l l I
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LOG PERCNT 4 RX STRRIN 4
GT-4 F5 CPZOO
RRTIO
URMP
DRMP RRTIU
9 DRHPING
SMPLES 6°27: 6’28:
6 POINTS
FIGURE 5.6!
O .3UO
4~r—+—
~34
I
I
.300
I
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I00
F‘I’T I "T" luI—‘W ‘T’I T
URMP RRTIO
.220
.I4U
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O-OOOF-OI
I-
I“?
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6'29
BRAVE. CONTDJT - A23
293
l
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GI—IUFOSCP
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- 6 POINTS
5_ FIGURE 5.63
.220 ~2OO
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40
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FIGURE 5.62
-JOO I
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F‘ ...
Ul-10F3 CPU
9 DRKPING
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§.. GRAVEL CONTENT - a2:
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3_ FIGURE 5.64
:I
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DRMP RRIIO
DRMP RRTIO
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.300
B4
9 SRï¬PING
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P a poxNTs
— FIGURE [.65
.IRO .?20 .260
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“I“TflI—TgW" '_1_, Ingl' " "I'M!
E A
6 L. I ' I
-J'-CC -: 33 -z.:3 -l s: -I ~. - ':: :.
LCG FERCK‘T 7 3% S'ri'N
UI—IOFOSCFCJ
9 DSHPINS
'1'" SAMPLES G-2'h G-28: 6-29
I: _ OPAVEI. CONTB‘JT I 428
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3— FIGURE E.67
L.
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6 P I I I I 4 I
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T' F‘CD
GI—10F1 p.50
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9 DRHPING
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3 " OMVfl. CONTENT I 428
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2_ FIGURE E.66
;
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.. : q _
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9 DRMPING
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3- FIGURE E.68
I.
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DRHP RRIIU
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5_ FIGURE E.69
SF A
§ .. A
6L I I I I I
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9 URKPING
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3 " GRAVE. CONTENT . A23
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3- FIGURE 5.71
i
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DRMP RRTIU
DRHP RRTIU
I
.100 .220 .260 .300 .340 .300
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.I40
9 DRHPING
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9 POINTS
FIGURE [.70
a -s:.za 41.5: -z'.c: -I.so -I'.::o -.s:::: II.j
LOG PERCNT 7 RX STRRIN ..
D
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2. FIGURE E.72
°: L.
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GT-lOFS CPZOO
DRMP RRIIO
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29+
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296
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2. A .
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SI- FIGURE E.73 CL 3_
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3_ FIGURE 5.75 2- FIGURE E.76
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297
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3 OPAVSI. cONTSNT - 59:
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3_ FIGURE E.77
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3 URflPING
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3_ FIGURE E.33
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6'35
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2— FIGURE 5.06
g P-
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2— FIGURE [.88
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6 IL I I I I I ’I‘“
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DRMP RRTIU
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300
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6 DRMPING
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4
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R†FIGURE E.92
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GT—4 F5 CPSO
DRMP RRIIU
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301
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3. FIGURE E.93
g;
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URMP RRTIO
DRMP RRTIO
6 DRMPING
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3» FIGURE [.94
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A
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4
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6 DRflPING
‘L SAHPLES 6'90 G‘Ilo 3°33
8.. ORAVEL CONTENT 3 S98
q 9 POINTS
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4
GT-4 FS CPZOO
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302
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3» FIGURE E.97
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9 DRMPING
1†SAMPLES 6']: 6’2: 6'3
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3- FIGURE E.99
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GT—lOFl CPO
DRMP RRTIO
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4L
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3» FIGURE [.98
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FIGURE E. 103
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GT—lOFS CPSO
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2- FIGURE E.102
I r-
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a:
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FIGURE 5.105
9
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.. '— ._ '
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9 DRflPIN
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3_ FIGURE E.Io7
P
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P
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s: 53
7 F-
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SAHPLES G-Io 0’2: 0'3
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FIGURE E.106
' 1 I I
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CC PE CHI 7 RX STRRIN
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Gi—10F3 CPzOO
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3 FIGURE E.108
:L
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LOG PERCNT 7 RX STRRIN
GT-lOFS CPZOO
APPENDIX F
DATA FOR UNDER-SATURATED SAMPLES
TEST TEMPERATURE = -4°C
305
Table F.1 Experimental Results for Under-Saturated Samp1e US-l
3:232:28 a. . ““2333: ‘ â€
(P81) (cps) (1) (psi) Strain - 10’22
200 0.05 .00388 288793 .165 253576
.00685 263153 .171 .171
.01801 234427 .173
0.3 .00393 372092 .177 332078
.00709 340163 .172 .176
.01801 311067 .178
1.0 .00378 450593 .174 409487
'.00695 420846 .167 .168
.01734 388653 .167
5.0 .00321 640085 .166 546086
.00604 579827 .153 .147
.01485 517275 .141
50 0.05 .00388 207177 .193 185787
.00719 192110 .199 .199
.01811 173096 .201
0.3 .00402 288568 .198 261343
.00719 270084 .202 .200
.01792 245652 .200
1.0 .00398 367609 .189 273157
.00719 340148 .184 .184
.01740 195587 .183
5.0 .00340 537176 .178 451257
.00608 479162 .165 .158
.01485 425412 .151
0 0.05 .00393 124031 .303 105681
.00695 113395 .337 .299
.01801 93771 .274
0.3 .00398 194016 .275 145194
.00709 162637 .255 .239
.01801 114509 .219
1.0 .00398 238946 .253 161537
.00709 193561 .215 .193
.01782 131233 .155
5.0 .00335 348704 .205 218262
.00575 274039 .173 .144
.01552 170555 .121
306
307
Table F.2 Experimental Results for Under-Saturated Samp1e US-2
Confining Interpolated E 6 D
Pressure Fr:2u:;cy Stigin (2:1) D Values std
(psi) 9 p Strain - 10722
200 0.05 .00404 303131 .163 280714
.00652 301539 .166 .175
.01636 263069 .183
0. 3 .00404 395475 .177 373831
.00665 390646 .167 .174
.01627 358353 .176
1.0 .00391 479721 .172 449159
.00656 465297 .153 .161
.01636 431831 .163
5.0 .00328 692996 .151 586617
.00508 647548 .142 .137
.01438 553314 .134
50 0.05 .00391 240899 .220 215381
.00665 231946 .197 .211
.01699 197881 .215
0.3 .00404 341273 .209 304017
.00661 322018 .192 .200
.01681 282122 . 202
1.0 .00396 439366 .184 . 375269
.00643 408096 . 174 .178
.01645 339628 .179
5.0 .00360 589449 .168 493154
.00548 562755 .157 .151
.01420 455115 .147
0 0.05 .00409 158834 .342 124299
.00674 155380 .275 .281
.01762 93102 .262
0.3 .00404 212794 .256 183445
.00674 204764 .225 .210
.01267 171704 .200
1.0 .00400 259846 .230 192056
.00665 235609 .187 .169
.01699 145304 .138
5.0 .00324 363857 .185 233228
.00584 305756 .142 .117
.01510 180654 .096
Tab1e F.3 Experimental Results
308
for Under-Saturated Samp1e US-3
Confining
Interpolated E 8 D
Frequency Strain Ed
P D V 1 t
“2321'? “I†m (981) s...2.“§s.3-2z
200 0.05 .00287 708243 .198 541543
.00667 574294 .202 .213
.01600 491271 .223
0.3 .00299 824314 .188 730417
.00667 778704 .179 .183
.01600 684125 .185
1.0 .00282 989308 .170 887293
.00650 949046 .150 .149
.01514 838592 .145
5.0 .00214 1355238 .145 1112341
.00548 1189273 .114 .101
.01292 1081032 .096
50 0.05 .00368 399482 .241 356174
.00693 386648 .240 .267
.01609 327118 .289
0.3 .00321 609920 .219 544886
.00689 577680 .202 .212
.01609 510869 .217
1.0 .00312 738436 .193 665042
.00684 711784 .163 .163
.01574 623069 .157
5.0 .00261 1051730 .169 844764
.00556 963647 .131 .116
.01369 782963 .107
0 0.05 .00334 438021 .282 336543
.00719 363801 .288 .285
.01643 292622 .284
’0.3 .00317 633552 .241 439550
.00706 517661 .217 .208
.01626 345652 .195
1.0 .00304 916965 .223 540494
.00659 648309 .174 .164
.01609 493849 .147
5.0 .00278 972404 .183 679578
.00573 844226 .129 .105
.01301 601895 .094
309
Table F.4 Experimental Results for Under-Saturated Sample US-4
Confining
Interpolated B 6 D
Frequency Strain Ed
Pressure D Values at
(P81) (cps) (1) (psi) Strains - 10' I
200 0.05 .00372 645960 .224 502132
.00740 516065 .222 .223
.01674 446159 .223
0.3 .00381 804789 .200 694927
.00712 730285 .198 .195
.01637 640802 .191
1.0 .00372 964576 .184 853506
.00702 887950 .170 .164
.01581 805140 .155
5.0 .00270 1255198 .161 1100132
.00549 1198415 .156 .120
.01321 1054880 .103
50 0.05 .00409 396781 .252 348886
.00753 359944 .246 .254
.01674 323950 .259
0.3 .00405 537798 .235 479812
.00749 520498 .208 .207
.01674 432580 .197
1.0 .00367 727064 .222 593755
.00712 666385 .171 .169
.01656 510020 .152
5.0 .00326 955223 .183 663376
.00516 691304 .135 .120
.01414 627124 .109
0 0.05 .00405 371242 .296 277650
.00753 321148 .255 .267
.01740 210994 .262
0.3 .00395 517590 .242 371908
.00735 453034 .228 .211
.01693 268591 .190
1.0 .00372 641596 .211 443581
.00712 549996 .190 .170
.01693 314635 .145
5.0 .00293 928343 .160 527719
.00581 675989 .144 .125
.01498 409892 .111
.310
Table F.5 Experimental Results for Under-Saturated Samp1e US-S
Confining Interpolated E 6 D
Pressure Fr:gu:;cy Stt;;n (2:1) D Values at
(psi) p p Strains - 10'21
200 0.05 .00338 806531 .207 722561
.00667 798113 .164 .181
.01664 657813 .185
0.3 .00343 1004195 .157 941558
.00686 1018406 .135 .145
.01646 880250 .147
1.0 .00302 1297229 .131 1108369
.00686 1155772 .117 .125
.016 1041413 .120
5.0 .00265 1491470 .111 1284739
.00521 1346240 .087 .080
.01381 1251637 .076
50 0.05 .00343 691569 .194 578563
.00731 617260 .182 .189
.01719 517769 .191
0.3 .00366 861500 .157 762387
.00709 848035 .138 .138
.01682 679624 .132
1.0 .00357 1006564 .144 877825
.00704 971192 .112 .112
.01655 785100 .103
5.0 .00206 1381558 .106 988203
.00571 1153877 .087 .0782
.01463 879263 .072
0 0.05 .00366 566192 .203 453507
.00741 524115 .162 .171
.01755 366360 .165
0.3 .00366 719397 .164 570356
.00727 670298 .123
.01755 453324 R.A.
1.0 .00338 907348 .132
.00731 737160 .101
5.0 .00261 1047076 .119
.00562 941578 .075
311
Table F.6 Experimental Results for Under-Saturated Samp1e US-6
Exist? a. . “Max:218 ‘ â€
(psi) (cps) (z) (9") Strain - 10’21
200 0.05 .00360 426842 .179 355144
.00719 352314 .200 .191
.0169 334439 .189
0.3 .00373 563790 .154 493038
.00697 495396 .162 .162
.01672 470141 .165
1.0 .00360 693336 .138 606459
.00674 626336 .145 .145
.01654 571480 .146
5.0 .00328 846445 .125 760431
.00616 799186 .130 .119
.01438 731730 .113
50 0.05 .00382 344343 .206 295695
.00674 313168 .228 .225
.01708 270060 .229
0.3 .00337 529977 .184 429529
.00683 456440 .178 .190
.01681 386468 .198
1.0 .00369 583885 .153 514114
.00683 553908 .149 .155
.01654 471323 .159
5.0 .00324 790449 .135 642661
.00562 740041 .120 .118
.01465 583034 .115
0 0.05 .00382 221060 .263
.00719 248427 .260
0.3 .00369 321688 .213
.00719 338764 .221
1.0 .00369 376771 .165
.00706 388967 .164
5.0 .00315 462009 .122
.00598 494476 .110
APPENDIX G
DATA FOR SALINE SAMPLES
TEST TEMPERATURE = -10°C
312
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