Montreal GeoHydro Technical Simulation Research Institute
Montreal- LaSalle
Canada
LABORATORY TESTING AND DATA PROCESSING OF FROZEN SOILS
Hamdy Youssef, Ph.D.
© 2006 Hamdy Youssef, Ph.D.
drhamdyyoussef@yahoo.com
ABSTRACT
The objective of the book is to present detailed description of samples
preparations of frozen soils for triaxial and compressibility tests. In addition, the
testing procedures and data processing are presented for the following types of
tests:
1.Triaxial and uniaxial compression; strain-rate controlled test with volume
change
measurements,
2.Triaxial and uniaxial stress-relaxation tests [volume-constant tests]
3. Compressibility tests.
Experimental results with analysis are presented for each type of test. Utilization
of the systematic methods, for testing procedures and data processing, by
means of the computer program with graphics output [FROZENSOIL.1] will
facilitate Laboratory Testing of Frozen Soils by Cold Regions and Ground
Freezing Civil Engineers and Academics. In addition to providing comparable
experimental results, as output from several frozen soils laboratories, for more
understanding of the low temperature material mechanical behavior. This will
contribute to establishment of the frozen soil mechanics science, by obtaining
the experimental short and long-term parameters for mathematical models,
utilized for design of constructions on frozen grounds, as well as in civil and
mining ground freezing projects.
ACKNOWLEDGEMENTS
The author appreciate the support of The US Army Corps of Engineers, Cold
Regions Research And Engineering Laboratory-USA CRREL, Experimental
Engineering Division, Geotechnical Research Branch, through the research
contract Award: DACA89-83-M-0202.
The support of The University of Montreal, The Government of Quebec and The
National Research Council-Canada are appreciated.
The method utilized for frozen sample preparation for triaxial testing is mainly
that utilized at USA CRREL and modified at The University of Montreal. The
author prepared the samples, performed the tests and analyzed the results. In
addition, the author developed the logistics for data processing and the
computer program FROZENSOIL.1 with assistance from P. Tan and M. Favre in
the graphics part. Thanks are due to the technical staff of the Geotechnical,
Mining and Structural Laboratories of The University of Montreal for their
assistance during the experimental research.
Dr. A. Assur, Chief Scientist and Mr. W. Quinn, Chief Geotechnical Research
Branch made the USA CRREL publications including the Draft Russian
Translations available to the author. Their encouragements are very much
appreciated.
The research and teaching experience achieved at The University of
Alexandria- Egypt and Concordia University as well as The University of Calgary-
Canada are acknowledged. The author appreciates the design experience at
Ruhr University Bochum-Germany, and the consultant offices of Prof. A. Shukry-
F. ASCE, Alexandria-Egypt and Firma Stämpfli-Switzerland.
TABLE OF CONTENTS
ABSTRACT i
ACKNOWLEDGEMENTS i
TABLE OF CONTENTS ii
LIST OF TABLES iv
LIST OF FIGURES v
CHAPTER 1 INTRODUCTION 1
1.1 Permafrost Engineering- Frozen Ice and Soils 1
1.2 Frozen Soils and Ground Freezing Techniques 2
1.3 Sample Preparation-Testing Procedures and Data Processing 2
CHAPTER 2 SAMPLE PREPARATION 3
2.1 Frozen Samples for Triaxial and Stress-Relaxation Tests 3
2.1.1 Saturation of the Samples under Vacuum 3
2.1.2 Freezing Process 5
2.1.3 Disassembly of the Samples from the Mold 5
2.1.4 Treatment of the Samples 8
2.1.5 Final Stage and Storage of the Frozen Samples 8
2.2 Frozen Samples for Compressibility Tests 11
CHAPTER 3 TESTING PROCEDURES 13
3.1 Experimentation 13
3.2 Laboratory Simultaneous Testing of Ice and Frozen Soils 15
3.3 Triaxial Compression Testing of Frozen Sand with
Volume Change Measurement 20
3.3.1 Testing Procedures 20
3.3.2 Experimental Results and Analysis 25
3.3.3 Discovery of the Volume Change Behavior Mechanisms 34
3.4 Triaxial-Stress Relaxation of Frozen Soils (Constant Volume Tests)
42
3.4.1 Testing Procedures 43
3.4.2 Experimental Results and Analysis 43
3.5 Compressibility of Frozen Soils 56
3.5.1 Testing Procedures 56
3.5.2 Experimental Results and Analysis 59
CHAPTER 4 COMPRESSIBILITY OF FROZEN GROUNDS-
DATA PROCESSING AND DOCUMENTATION 63
4.1 Introduction 63
4.2 Data Processing During Testing 63
4.3 Calculations of the Compressibility Coefficients 66
CHAPTER 5 YOUSSEF’S FROZENSOIL.1 DATA PROCESSING
AND DOCUMENTATION OF TRIAXIAL RESULTS
OF FROZEN SOILS 69
5.1 Data Recording and Decoding 69
5.2 Program FROZENSOIL.1 IDENTIFICATION 69
5.3 FROZENSOIL.1 Flow Chart 71
5.4 Listing of the Computer Program FROZENSOIL.1 71
5.5 FROZENSOIL.1 Input and Output Results 83
5.5.1 Triaxial Constant-Strain Rate Compression Test-
Typical FROZENSOIL.1 Output [Test FS2] 85
5.5.2 Triaxial Stress-Relaxation Test-
Typical FROZENSOIL.1 Output [Test FS29R] 95
5.6 Recommendations 114
CHAPTER 6 CONCLUSIONS 115
REFERENCES 117
AUTHOR INDEX 129
SUBJECT INDEX 135
LIST OF TABLES
Table Page
1. Physical Properties of Frozen Sand Samples 26
2. Test Conditions and Maximum Stresses of Frozen Sand Samples
28
3. Physical Properties of Frozen Sand Samples Tested
for Triaxial Stress-Relaxation 44
4. Unrelaxed Deviatoric Stresses as a Function of Time
during the Triaxial Stress-Relaxation Process 48
5. Compressibility of Frozen Ground, Brodskaya [USSR] 57
6. Compressibility Testing of Frozen Soils-
Test and Frozen Sample Identification 64
7. Compressibility of Sand- Ice System-Example of Data Recording 65
8. Compressibility of Sand- Ice System-
Calculations of the Compressibility Coefficients 67
9. Triaxial Compression Tests-FROZENSOIL.1 Input
Data 85
10. Triaxial Compression Tests-FROZENSOIL.1 Output
Results 86
11. Triaxial Stress-Relaxation Tests-FROZENSOIL.1 Input
Data 95
12. Triaxial Stress-Relaxation Tests-FROZENSOIL.1 Output
Results 111
LIST OF FIGURES
Figure Page
1. Saturation of Sand Samples 4
2. Freezing Process of The Water Saturated Sand 6
3. Disassembly of The Frozen Samples From The Mold 7
3.1 Removing The Frozen Sand Samples from The Mold 7
3.2 The Freezing Mold and Some Extracted Frozen Samples 7
4.1 Trimming of The Frozen Sand Sample Ends using Electric Saw 8
4.2 Surfacing The Samples Ends using Lathe Machine 9
4. Treatment of The Frozen Sand Samples 9
5.1 Final Treatment of The Frozen Soil Samples 9
5.2 Final Treatment of The Frozen Sand
Samples 10
5. Final treatment of The Frozen
Samples 10
6. Laboratory Simultaneous Testing of Ice and Frozen Soils 17
7. Triaxial Cell with Self-Cooling System [TCWSCS] and
Automatic Measurement of Volume Change of Frozen Soils [AMVC-
FS] 18
8. Prototype of Youssef’s Triaxial Cell with Self Cooling System
[TCWSCS] 19
9. Schematic Drawing of The Experimental Set-up 21
10.1 Experimental Set- up of The Triaxial Compression and
Stress-Relaxation Testing of Frozen
Soils 22
10.2 Experimental Set-Up for Triaxial Testing of Frozen Soils
utilizing Kerosene as a trandparent, coolant, and confining liquid 23
11. Typical Results of Triaxial Compression Test of Frozen Sand with
Volume Change Measurements 27
12. Triaxial Stress-Strain- Volume Change Behavior of Frozen Ottawa Sands
[ơ = 276.64 kPa] 30
13. Triaxial Behavior of Frozen Sand Samples with Volume Change
Measurements
[σ = 138.32 kPa] 31
14. Triaxial Behavior of Frozen Sand Samples with Volume Change
Measurements
[σ = 448.32 kPa] 32
15. Triaxial Behavior of Frozen Sand Samples with Volume Change
Measurements
Tested at Different Strain Rates 33
16. Triaxial Behavior of Frozen Sand Samples with Volume Change
Measurements utilizing Kerosene as a Coolant and Confining Medium
[Samples Tested without rubber Membrane] 36
17. Comparison Between The Results of Samples Tested with
and without Rubber Membrane [ Vcr = Volume of Cracks] 38
18. Comparison between The Results of Several Samples Tested
with and without Rubber Membrane 39
19. Comparison between The Results of Samples FS45, FS14, FS44,
FS47, FS25, FS43 Tested with Rubber Membranes and
The Results of Sample FS48IK 40
20. Frozen Sand Sample FS48IK Tested for Triaxial Compression
with Volume Change Measurements 41
21. Typical Experimental Results for Triaxial Stress-Relaxation
of Frozen Soils 45
22. Triaxial Stress-Relaxation Test Results on Frozen Sand
[constant volume test] 47
23. Shear Stress Ratio of Frozen Ottawa Sand as a Function of
Time and Relaxation- Strain 51
24. Stress-Strain Behavior after Stress-Relaxation Cycles for
two Frozen Sand Samples 51
25. Stress-Strain Behavior of three Frozen Sand Samples with Stress
Relaxation Cycle near the Peak Stress 52
26. Relationship between the Deviatoric Stresses and Relaxation
Time in Logarithmic Scales 54
27. Experimental Results of Triaxial Stress-Relaxation of Frozen Sand
with Several Relaxation Cycles at different Relaxation Strains 55
28. Compression Curves of Frozen Sands and Ice 58
29. Compressibility of Sand-Ice System [Frozen Ottawa Sand]
typical Deformations and Strains vs. Time Curves 60
30. Compression Curve of Frozen Ottawa Sand 60
31. Data Acquisition System utilized for recording the results of
Triaxial Testing of Frozen Soils 70
32. Desk Top Computer utilized for data decoding 70
33. Flow Chart of The Computer Program FROZENSOIL.1
for Laboratory Testing of Frozen Soils under Triaxial Conditions
72
34. FROZENSOIL.1: Triaxial Compression Results
Deviatoric Stresses as a function of Strain 89
35. FROZENSOIL.1: Triaxial Compression Results
Major to Minor Stress Ratio as a function of Strain 90
36. FROZENSOIL.1: Triaxial Compression Results
Octahedral Stresses Ratio as a function of Strain 91
37. FROZENSOIL.1 : Triaxial Compression Results
Octahedral Normal Stresses as a function of Strain 92
38. FROZENSOIL.1: Triaxial Compression Results
Octahedral Shear Stresses as a function of Strain 93
39. FROZENSOIL.1: Triaxial Compression Results
Volume Change as a function of Strain 94
40. FROZENSOIL.1: Triaxial Stress- Relaxation Results
Major to Minor Stress Ratio as a function of Strain 109
41. FROZENSOIL.1: Triaxial Stress-Relaxation Results
Deviatoric Stresses as a function of Log Time 110
42. FROZENSOIL.1: Triaxial Stress-Relaxation Results
Deviatoric Stresses as a function of Inverse of Time 111
43. FROZENSOIL.1: Triaxial Stress-Relaxation Results
Deviatoric Stresses as a function of Square Root of Time 112
44. FROZENSOIL.1: Triaxial Stress-Relaxation Results
Inverse of Deviatoric Stresses as a function of Log of Time 113
45. FROZENSOIL.1: Triaxial Stress-Relaxation Results
Inverse of Deviatoric Stresses as a function of Inverse of Time 114
Chapter 1
Introduction
The Arctic, Sub arctic and Antarctic are generally referred to as Cold Regions.
The Grounds in the Cold Regions exist partially or totally in its crystalline state:
Ice. The grounds are referred to as frozen grounds or frozen soils. Due to the
natural existence of frozen grounds, their textures are result of the geological
formation. Frozen soils are multi-phase natural composite materials. The
quantity and quality of ice and water phases in frozen soils change with
temperature and stresses. The demands for constructions on Cold Regions
have created a relatively new engineering science, namely: Geotechnical
Engineering for Cold Regions or Permafrost Engineering.
Outside the Cold Regions, water generally exists in soil pores in its unfrozen
state and the ground is referred to as unfrozen soils. Constructions on unfrozen
soils started with the Egyptian Civilization more than 5,000 years. Since 1862, it
was realized that it is advantageous in some cases to freeze the unfrozen soils
for construction purposes. A new construction technique was created, namely:
Artificial Ground Freezing.
1.1 Permafrost Engineering-Ice and Frozen Soil
Frozen grounds exist in nature in large geographical areas of the World (22
million square kilometers in Canada, USA-Alaska, Russia and Northern Europe).
When the soil remains frozen for several years, the ground is called Permafrost )
usually in the Arctic regions above the latitude 66º 32' North of the Equator and
in the Antarctic). In the Sub arctic (regions adjacent to the Arctic circle) the
permafrost is discontinuous. In Cold Regions the ground temperature normally
range from zero to –15 ºC (Andersland and Anderson 1978 [7]). In addition, the
depth of freezing changes from hundreds to few meters. The ground
temperature profile is not uniform but varies from its coolest temperature at the
earth surface to zero at the lower depth of permafrost.
Furthermore, the temperature is not constant with time, it fluctuates during the
four seasons of the year, and accordingly there is a change in the frozen soil
physical and mechanical properties. In regions where the temperature during
the year fluctuates around 0ºC, the ground is seasonally frozen; this is a
seasonal extension of the Cold Regions.
During freezing, the ground water partially or totally crystallizes and transforms
to its solid state: Ice. The formation of ground ice depends on many factors, its
uniformity and the geological features of soil deposits (Tsytovich 1975 [133] and
Vyalov et al. 1980 [153]). Thus, the ground ice exists in nature in several forms.
It ranges from intergranular ice in the soil voids to several meters of vertical or
horizontal ice mass.
Frozen soils are complex multi-phase composite material (soil mineral particles,
unfrozen water, ice and gasses). The quality and quantity of the ice-water
phases vary with temperature and applied stresses. The freezing of the ground
is associated with a volume increase (frost heave) and its thawing is associated
with a volume decrease (thaw settlement). Frost heave and thaw settlement are
causes for unacceptable deformations for construction in the Cold Regions, if
their influences are not taken into account during the design. The response of
the composite material to external thermal and mechanical stresses, as well as
its behavior and deformation mechanisms has to be taken into account for each
engineering project in the cold climate, thus Laboratory Testing of Frozen Soils
is of primary importance. Due to the high viscosity of the intergranular ice, the
designer must depend on the total stress concept for developing and utilization
of constitutive and rheological mathematical models.
1.2 Frozen Soils and Ground Freezing Techniques
It is technically possible to freeze the unfrozen ground in the temperature range
of -15ºC to -196ºC utilizing liquid nitrogen (Stoss et al. 1979 [123]). Artificially
freezing the ground increases its strength and decreases its compressibility and
permeability due to freezing of its water content. These controlled soil behavior
provide construction advantages for underground mining, open excavations and
deep underground subway stations. In addition, artificially frozen ground protect
hydraulic engineering trenches from the influx of ground water, and for urban
districts, in case of emergency, control the influx of water from sewage as well
as water pipes (Jessberger 1979 [63], Braun et al. 1982 [29], Tsytovich 1975
[123], and Careaga et al. 1972 [32]).
Utilization of the ground freezing technique for construction under difficult
soil conditions requires knowledge of the physical properties of the ground, the
geometrical design of the location of the freezing probes, the selection of a
suitable freezing temperature and thermal calculations to evaluate the time and
volume of the soils to be frozen around the probes. Then a stress analysis of
the frozen soil wall is carried out taking into accounts the stress-strain and time
characteristics. This necessitates adequate Laboratory Testing of Frozen Soil
samples to obtain experimental knowledge of the mechanical behavior and
properties, which is essential for design.
1.3 Sample Preparation-Testing Procedures and Data Processing
As it can be concluded from the two previous sections, it is important to prepare
and test different frozen soil samples in the laboratory with different physical
properties and ice contents subjected to different thermal and mechanical
stresses. The experimental results on frozen soils up to now were reported from
several laboratories utilizing different methods for sample preparations, testing
equipment and procedures as well as data processing. This made it difficult to
exchange knowledge and develop adequate mathematical models thus there is
a need for standardization of Laboratory testing of frozen soils.
The present book provides mild stone step in this direction. The frozen samples
prepared, are two- phases ice-sand samples, the testing temperature is -5ºC.
The types of tests are:
1. Triaxial Compression, strain-rate controlled tests
2. Triaxial Stress-Relaxation tests, and
3. Compressibility tests.
Typical results of the Author’s research for each type of test are reported with
analysis. This, in addition to documentation of the computer Program
FROZENSOIL.1 for data analysis and graphics of the experimental results.
Chapter 2
Sample Preparation
Sample preparations for triaxial, stress-relaxation and compressibility tests of
frozen Ottawa sand (20-30 mesh) are presented in this Chapter, at the testing
temperature of -5ºC.Strain-rate controlled triaxial tests, as well as triaxial stress-
relaxation tests, have been conducted on cylindrical samples: 3.81 cm (1.5”) in
diameter and 7.62 cm (3”) long. Compressibility tests have been performed on
frozen cylindrical samples having the following dimensions: 6.40 cm (2.52”) in
diameter and 2.025 cm (0.8”) in length.
2.1 Frozen Samples for Triaxial and Stress- Relaxation Tests
The steps followed for sample preparation for these types of tests are
essentially the same as used at USA CRREL (Sayles 1974 [111]) and modified
at The University of Montreal (Arteau 1977 [9] and Youssef 1984 [173]) and are:
2.1.1 Saturation of the Samples under Vacuum
A vacuum-sealed Plexiglas Mold was manufactured to contain twelve samples.
Porous stones were placed in the Mold at the bottom of each sample to allow
uniform and undisturbed flow of water to the sand samples during saturation. A
greased split plastic Mold was placed around each sample to permit extraction
of the frozen samples from the tubes without disturbance. The top and bottom
plates of the Mold had a rubber ring to insure air sealing during saturation.
Dry sand was poured in the Mold and then the Mold was placed on vibration
table for five minutes to achieve the desired density. The Mold was firmly closed
and subjected to vacuum through the top plate, while the samples were
saturated from the bottom plate, as shown in Figure 1. A slow flow rate of water
was permitted in order to prevent any disturbance of the sand structural
skeleton. Circulations of at least three times the samples volume of water inside
the Mold during saturation was found necessary for removing the air bubbles
from the voids.
2.1.2 Freezing Process
After saturation, the freezing Mold was placed in a temperature controlled cold
room at the testing temperature of –5 ºC. The top plate was then removed and
a three dimensional insulators were placed around the Mold to allow one-
dimensional freezing from the top to the bottom of the samples, as shown in
Figure 2.1. The water level inside the plastic tube connected to the bottom of
the Mold, was set at the same level as that of the top of the samples to prevent
flow of water [initial hydraulic equilibrium]. An electric heating wire was placed
inside the tube to permit free movement of unfrozen water during the freezing
process. Vertical initial stress of 13.88 kPa was applied on each sample, before
freezing, through a loading pad, as shown in Figure 2.2 to produce more
uniform samples and keep the sand particles in contact. The freezing process
lasted 76 hours, in order to insure total freezing of the intergranular water.
Fig. 1 Saturation of sand samples
(© Courtesy of Dr. Hamdy Youssef, The University of Montreal-Canada)
2.1.3 Disassembly of the Samples from the Mold
At the end of the freezing process, the bottom of the Mold was removed, and
thereafter the Mold was placed inside a steel frame. A vertical piston, driven by
a manual hydraulic press, was used to remove the samples contained in a
plastic tubes as shown in Figure 3.1. Overall view of the Mold and the extracted
frozen sand samples contained in the plastic split tubes are shown in Figure 3.2.
2.1.4 Treatment of the Samples
Each sample was carefully removed from the split Mold, and then trimmed to the
desired length using an electrical saw located in the cold room, Figure 4.1.
Thereafter, each frozen sample was placed in a split wooden Mold and placed in
a Lathe machine, Figure 4.2, for fine surfacing of the sample ends.
Fig. 2.1 The samples Mold surrounded by three-dimensional insulation
2.1.5 Final stage and storage of the frozen samples
Five measurements of the length and diameter of each sample were taken. The
sample weight was then recorded. The frozen samples were then wrapped
[each] tightly in plastic sheet and scotch-taped to prevent any ice sublimation
during storage, Figure 5. Finally, the samples were stored in a cold room at –5
ºC, which is the testing temperature.
The above procedures utilized for preparing the samples yielded similar frozen
samples, with smooth surfaces, as shown in Figure 5, and no void gaps or air
bubbles on the surface were observed. Thus it is recommended, to be utilized
as standard procedures for preparing frozen sand samples for uniaxial and
triaxial creep, strain rate-controlled compression and stress- relaxation tests.
For different testing temperatures, it is recommended to prepare and store the
samples at the testing temperature. Temperature controlled deep freezers can
be utilized for storage of different frozen samples at different temperatures. This
can economies and speed the testing program and permit utilizing the cold room
for only freezing, disassembly and treatment of the frozen samples at each
desired temperature. Testing of frozen samples in the normal geotechnical
laboratory can be performed utilizing the Author’s Triaxial Cell with Self-Cooling
System [TCWSCS], (Youssef 1985 [174]).
Fig. 2.2 Initial load placed on top of each sample
Fig. 2 Freezing process of the water-saturated sand
(© Courtesy of Dr. Hamdy Youssef, The University of Montreal-Canada)
Fig. 3.1 Removing the frozen sand samples from the Mold
Each sample is contained in split plastic tube
Fig. 3.2 The freezing Mold and some extracted frozen sand samples
Fig. 3 Disassembly of the frozen samples from the Mold
(© Courtesy of Dr. Hamdy Youssef, The University of Montreal-Canada)
Fig. 4.1 Trimming of the frozen sample ends using an electric saw
Fig. 4.2 Surfacing the frozen sample ends using a Lathe machine
Fig. 4 Treatment of the frozen sand samples
(© Courtesy of Dr. Hamdy Youssef, The University of Montreal-Canada)
Fig. 5.1 Final treatment of the frozen soil samples
Fig. 5.2 Final treatment of the frozen sand samples
Fig. 5..Final treatment of the frozen sand samples
(© Courtesy of Dr. Hamdy Youssef, The University of Montreal-Canada)
2.2 Frozen Samples for Compressibility Tests
From the information given by Brodskaya 1962 [30], the Author concluded the
following procedures to prepare the frozen samples for compressibility, and
utilized the prepared samples for compressibility tests on frozen Ottawa sand
(20-30 mesh) tested at a temperature of –5 ºC:
i- The compressibility samples were prepared from cylindrical frozen sand
samples with a diameter of 7.20 cm (3”) and a length of 19.05 cm (7.50"),
prepared in a similar method as described in Section 2.1. The only difference
was that the wooden Mold surrounded only half of the sample in the Lathe
machine, as described in stage 2.1.4.
ii- An Odometer ring, with an inner diameter of 6.40 cm (2.52") by 2.025 cm
(0.80") in length, was driven smoothly inside the frozen sample, by means of a
hammer and the Lathe machine. The interior surface of the ring was coated with
silicon grease before introducing the sample, in order to reduce the friction
between the frozen sand and the Odometer inner surface. Such a measure
decreases to a negligible value the friction developed at the interface between
the soil and the Odometer (Silvestri et al. 1982 [117]).
iii- After driving the ring inside the frozen cylindrical sample, the sample was
removed from the Lathe machine. Using an electrical Saw, the frozen sample
was trimmed near the edge of the ring. The ring was then placed in the Lathe
machine again, and both ends of the sample were surfaced to the level of the
ring edge. A water level was utilized to make sure that the surfaces of the frozen
sand sample were parallel.
iv- The weight of the sample was recorded and its dimensions were exactly the
same as the Odometer length and diameter. The sample was then placed in the
Odometer apparatus and covered with snow [or ice] to prevent intergranular ice
sublimation.
The above procedures establish the standard for preparing frozen soil samples
for compressibility tests. Several frozen soil samples with different physical
properties can be prepared at different low temperatures and each set is stored
in different temperature controlled deep freezers to speed the testing program.
The Author prepared the frozen samples in the cold room of the Mining
Laboratory, evaluated the physical properties at the Geotechnical Laboratory,
and performed the tests in the cold room of the Structural Laboratory of The
University of Montreal-Canada.
Chapter 3
Testing Procedures
3.1 EXPERIMENTATION
Experimental results on frozen and unfrozen soils had been presented as output
of several investigation: (Terzaghi 1943 [126], 1952 [127], Thimus 2000 [128],
Andersland et al. 1994 [8], 1978 [7], Tsytovich 1975 [133], Phukan 1985 [100],
Jessberger 1979 [63], Bishop and Henkel 1978 [23], Bowles 1978 [26], Yong
1960 [158], Lambe and Whitman 1969 [81], Vinson 1978 [143], Sayles 1974
[111], Chamberlain et al. 1972 [34], Kaplar 1971 [73], Brodskaya 1962 [30],
Seed et al. 1967 [115], O’Connor and Mitchell 1978 [95], Vyalov et al. 1964
[149], Zhu et al. 1984 [194], Eckardt 1982 [41], Sadovsky et al. 1989 [109],
Shibata et al. 1985 [116], Bragg 1980 [27], Baker et al. 1983 [15]). However, it
is agreed upon that there is a need for developing standard laboratory testing
equipment, techniques, computerized data processing and documentation,
especially for testing frozen grounds (Baker et al. 1983 [15], Andersland et al.
1994 [8], Sayles et al. 1987 [188]).
Laboratory testing of ice and frozen soils required development of new testing
equipment, techniques as well as data reduction and graphics computer
programs. As contribution towards developing the needed standards, the
Author performed extensive laboratory testing on ice, unfrozen and frozen soils.
The output of Youssef’s experimental research provided extensive results for
triaxial strain-rate controlled compression of unfrozen and frozen soils, as well
as compressibility and stress- relaxation of frozen soils. The Author performed
experimental research work on the creep behavior and dynamic properties of
polycrystalline ice
The Author participated in developing Calgary- Canada apparatus for static and
dynamic creep testing of frozen samples utilizing the Resonant-Column method.
In addition, a new triaxial cell with self-cooling system [TCWSCS] and automatic
testing technique for measuring the volume change of frozen samples [AMVC-
FS] had been developed by the Author. The Author provided the logistics for
systematic and automated techniques for testing, reporting, analyzing,
presenting and documentation of the test results for frozen and unfrozen soils.
In this respect the Author developed and utilized a series of data reduction and
graphics computer programs, among them FROZENSOIL.1 and EFFECTIVE.
The research work permitted the Author to discover the mechanisms controlling
the volume change behavior of frozen soil samples during deformation under
uniaxial and triaxial stresses (Youssef 1979 [166], 1981 [170], 1982 [171],
1983 [164], 1984 [173], 1985 [165, 174], 1986 [175, 176, 178], 1987 [179],
1988 [188, 189], 2003 [194, 195, 196, 197]).
The objective of the present Chapter is to present the testing procedures for
the following types of tests on frozen soils:
1. Triaxial strain-rate controlled compression tests with volume change
measurements
2. Triaxial stress-relaxation, (constant volume tests), and
3. Compressibility tests.
Triaxial and uniaxial compression, as well as stress- relaxation type of tests are
usually performed by utilizing the conventional triaxial cell (Bishop and Henkel
1978[23]). For testing frozen samples, the cell as well as the laboratory
equipment (for example the compression machine) has to be placed in a
temperature controlled cold room. This necessitates initial expenses and
inconvenience especially for new laboratories. If simultaneous tests have to be
conducted at different low temperatures, several cold rooms will be needed. As
an alternative, triaxial cells with self- cooling systems [TCWSCS] can be utilized
with economical and flexibility advantages. The Author (Youssef 1983 [164],
1984 [173], 1985 [174], 1986 [178]) developed, supervised the construction
and calibrated the first Prototype of the [TCWSCS] at The University of
Montreal- Canada and designed the second version [TCWSCS-1] at Ruhr-
University, Bochum- Germany. The developed cell had been utilized for
laboratory testing of frozen Ottawa sand at –5 ºC in the normal geotechnical
laboratory at The University of Montreal, by placing the [TCWSCS] in a
compression machine and utilizing a refrigeration units to circulate the coolant
antifreeze around the tested frozen samples (Youssef 1983 [164], 1984 [173],
Lauzon 1984 [82]).
Several attempts had been made to measure the volume change of frozen
samples during testing in the triaxial cell (Bishop et al. 1987 [23], Bragg 1980
[27], O’Connor 1975 [95], Lade and Jessberger 198 [80]). However, most of the
previously developed techniques depend on manual recording and some are
valid only for uniaxial testing. A great amount of data on frozen soils did not take
into account the volume change measurement (Tsytovich 1975 [133], Vyalov et
al. 1980 [152], Sayles 1974 [111], Andersland et al. 1978 [7], 1994 [8]).
According to Ladanyi 1981 [78]: “Most of the available experimental data on
strength tests with frozen soils do not even contain sufficient information on
volume change during shear, so that it is not always clear whether the results
represent a behavior more on the drained or more on the undrained volume
constant side”.
From the review of the previous research, the Author concluded that, there is a
need to develop a new testing technique for measurement of the volume
change parameter. This technique would apply to loaded or strained frozen soil
sample while it is tested inside the triaxial cell, in stress or strain- rate controlled
uniaxial or triaxial tests. The technique would be based on use of industry
available instrumentation, in order to permit an easy utilization of the same
technique by researchers in different laboratories. Furthermore, it should allow
automatic monitoring of the volume change to avoid human errors, as well as to
minimize the time spent by researchers conducting the tests. The desired
instrumentation should be capable to operate in cold temperatures and to carry
out measurements while the sample is subjected to confining pressures.
Considering the above specific requirements, the Author developed the new
testing technique [AMVC-FS] at The University of Montreal- Canada for
accurate, simple and automatic measurements of the volume change
parameter. (Youssef 1983 [164], 1988 [189]) The Author successfully utilized
the new testing technique for uniaxial and triaxial strain- rate controlled
compression and triaxial stress- relaxation tests of frozen Ottawa sand.
The Author’s developed computer program FROZENSOIL.1 had been
extensively utilized for interpretation and documentation of the obtained
experimental results with fast speed, and provided valuable high quality
numerical and graphical output.
3.2 Laboratory Simultaneous Testing of Frozen Soils
The development of the triaxial cell with self- cooling system [TCWSCS] and the
new testing technique for automatic measurements of volume change of frozen
soil [AMVC- FS] permits proposing the following Laboratory System for Testing
Frozen Grounds [LSTFG], namely ice and frozen soils:
One cold room [CR] is to be utilized for the sample preparation (Chapter 2) at
the required specific temperature [Ti], and then this group of samples is stored
in a temperature-controlled freezer- frozen soil samples unit [FSSU] set at the
testing temperature. The cold room is now available for preparations of another
group of samples, which will be stored at another low temperature [Ti], in
another storage unit [FSSU], for another type of test or the same type of test at
different temperature. Again, the one cold room is available for preparation of
another group of frozen samples for storage in another [FSSU]. Thus
preparations of several group of frozen soil samples with different physical
properties, to be tested for different types of tests requires only one cold room.
This provides economization, especially when establishing new frozen ground
laboratories and expedites the testing program for any research or design
project.
For each type of test, the frozen sample is placed in the developed triaxial cell
[TCWSCS] which is connected to the instrumentation for the developed
automatic testing technique for measurement of volume change of frozen soils
[AMVC-FS] as shown schematically in Figure 6. From the start of each test,
during testing and up to the end of the test, all testing parameters [information]
are to be recorded with time by utilizing a data acquisition system. After each
test, the recorded experimental results are provided as an input to a data
reduction and graphics computer program (for example FROZENSOIL.1). The
output for each input data is the numerical listing of all the information of the
test followed by all the required graphics. This provides in very short time
knowledge about the results of the test and is an excellent way of computer
documentation.
In the same time, the graphics output allows information for the next test. This is
advantageous to the scientist, rather than waiting until the end of the testing
program for interpretation of all test results, and then find out that, it was best to
change this or that, or test more or less samples, for the experimental research
and or the engineering program.
Simultaneously, frozen samples can be drawn from another [FSSU], placed in
another [TCWSCS] and tested for another testing program. Thus depending on
the demands and finance, the proposed [LSTFG] system, can carry out several
testing programs on ice and frozen soils by utilizing several [TCWSCS] and one
cold room.
Figure 7 presents detailed schematic drawings of the developed triaxial cell
[TCWSCS] and the instrumentation utilized for the developed volume change
measurement technique [AMVC-FS]. The Author described in details the piping
connections and testing procedures (Youssef 1985 [174]). The Prototype of
Youssef’s triaxial cell is shown in Figure 8. Utilization of the same automatic
volume change measurements instrumentation, but with different technique, for
automatic measurement of volume change of unfrozen soil samples [AMVC-US]
had been utilized and published by the Author in the Geotechnical Testing
Journal, ASTM- USA (Youssef 1987 [179]). Testing frozen soil samples in the
developed triaxial cell [TCWSCS] is the same as utilizing the conventional triaxial
cell. However, in the second method the compression machine and the [AMVC-
FS] instrumentation have to be allocated in the cold room.
Fig. 6 Utilization of several units of the developed triaxial cell with self- cooling
and insulating systems [TCWSCS] for testing frozen samples at different
temperatures and for different types of material testing. (LTFG=
Laboratory system for testing frozen ground, FSSU= Frozen samples
storage unit)
Fig. 7 Triaxial cell with self-cooling system [TCWSCS] for testing ice and frozen
soils
Fig. 8 Prototype of the new triaxial cell with self-cooling system for testing
Ice and Frozen soils [TCWSCS]
(© Courtesy of Dr. Hamdy Youssef, The University of Montreal-
Canada)
3.3 Triaxial Compression Testing of Frozen Sand with Volume Change
Measurements
All tests were performed by the Author in the temperature well controlled cold
room [CR] at the Structural Laboratory of The University of Montreal- Canada,
due to its availability at the time of the testing program. The [CR] temperature
was set at the testing temperature of –5 ºC. The standard Wykeham- Farrance
compression machine with a capacity of 10,000 kgf (980 MN) was allocated in
the cold room. The differential pressure transducer utilized for the automatic
measurement of volume change [AMVC-FS] was also allocated in the cold room
[CR] and placed in the same level as the top of the compression machine
piston, by utilizing a horizontal metallic plate. This eliminate any errors in
measuring the volume change due to the upward movement of the machine
piston during the test, since the base of the volume change transducer will be
always in the same level as that of the base of the triaxial cell.
The volume change measurement transducer consists of two pressure
chambers separated by a metallic membrane (Figures 7 and 9). The pressure
chamber [I], which is connected to the burette tube, is also connected to the
base of the triaxial cell. The top of the burette is connected to the second [II]
pressure chamber. The strain gauges on the transducer metallic membrane
(separating chambers I and II) are connected to automatic data acquisition
system. A pressure transducer is connected to chamber [II] for measurement of
the applied air pressure. The same pressure transducer is connected to the
triaxial cell to check the cell pressure during testing. Several valves are placed
on the connection tubes to permit applying vacuum, air pressure and to empty
or to fill the triaxial cell as well as chamber [I] and the burette tube with the
coolant and confining liquid (antifreeze) as shown in the figures.
3.3.1 Testing Procedures
The tests were performed on frozen Ottawa sand samples (20-30 mesh) with
the dimension of 38.10 mm in diameter and 76.20 mm in length (chapter 2). At
–5 ºC, frozen sand is a two- phases material (Ice-Sand system), Andersland et
al. 1978[7]. The frozen sample covered by a rubber membrane, is placed in the
triaxial cell by freezing both ends of the sample to the machined- ruffed surfaces
of the base and top platen of the triaxial cell through precooled water films. The
ends of the rubber membrane are then rolled to the two cell platens to seal the
sand sample.
The triaxial cell is assembled and placed in the compression machine and on
the same metallic plate as that of the differential pressure transducer utilized for
the developed testing technique [AMVC-FS]. The piston cap of the triaxial cell is
in contact with the load cell, for measurement of the deviatoric stresses.
Chamber [I] of the [AMVC-FS], is connected through plastic (or copper) tube
with a valve to the interior of the cell (outside the sample). The burette tube is
connected through a valve to Chamber [I] and the top of the burette is
connected to the pressure Chamber [II].
As it is shown in Figure 9, the pressure Chamber [II] is connected to the vacuum
source to fill the burette tube with antifreeze. Chamber [II] is also connected,
through a valve, to the air pressure source and pressure transducer [PT], which
is also connected through another valve to the interior of the triaxial cell. Figure
10, presents the general layout (the experimental set- up) of the triaxial testing
equipment with the [AMVC-FS] instrumentation located in the temperature
controlled cold room.
Fig. 9 Schematic drawing of the experimental set-up for triaxial testing
of frozen soils with volume change measurement
Fig. 10.1 Experimental set-up of the triaxial compression and
triaxial stress-relaxation testing of frozen soils
(© Courtesy of Dr. Hamdy Youssef, The University of Montreal-
Canada)
Fig. 10.2 Experimental set-up for triaxial testing of frozen soils
utilizing kerosene as a transparent, coolant and confining liquid
(© Courtesy of Dr. Hamdy Youssef, The University of Montreal-
Canada)
Valve [1] between the triaxial cell and the pressure chamber [I] is closed.
Vacuum is applied through valve [8] and the antifreeze is introduced through
valves [5,6] to chamber [I] and the burette tube through valve [7], it is
recommended that the initial level of the antifreeze in the burette tube will be at
its mid height. Vacuum is applied through the top plate of the triaxial cell, and
the antifreeze is introduced around the frozen sample through valve [2] until the
cell is completely filled with the coolant and confining liquid without the inclusion
of any air bubbles. The pressure transducer [PT] is connected to the interior of
the triaxial cell through valve [4] and to the pressure chamber [II] through valve
[9]. Now, the experimental set- up is ready for starting the test on the frozen
sample. Before each triaxial test, the above connections and preparation
procedures had to be performed.
An air pressure equal to the test confining pressure [σ3 = σcell] is applied
through valve [9] to chamber [II], to the burette antifreeze and to chamber [I].
Valve [1] is opened so that the same confining pressure will be applied around
the frozen sample. Now σcell, σI and σII are the same and equal to the applied
confining pressure σ3. The gearbox of the machine is adjusted to apply a
controlled speed to the base platen in the upward direction at a constant rate
(strain- rate controlled compression test). The piston cap of the triaxial cell is
already in contact with the load cell for measurement of the deviatoric stresses
[σ1–σ3].
All connections and valves, applied confining pressure, the level of antifreeze in
the burette tube and its calibration chart are to be double-checked. The test
parameters: -TºC, σ3 , δ (the machine speed), and the burette tube liquid
height are recorded by the data acquisition system, these are the initial
conditions. The compression machine is then turned to the (ON) position. The
frozen soil sample compresses uniaxially at a constant strain rate [έ] up to a
strain [ε] of 20%. The volume change during deformation is observed by the
change in the burette antifreeze height [ΔH], these changes in height causes
changes in the pressure in chamber [I]. The difference in pressures [ơI – ơII]
results in stresses on the metallic membrane, which are recorded automatically
by the strain gauges connected to the data acquisition system. The load cell
readings are also simultaneously recorded with time throughout the test. Thus
for each triaxial test on frozen soil sample: the strain rate, the confining
pressure, the deviatoric stresses, and the volume change [εv %] are to be
recorded simultaneously with time.
For the series of the triaxial tests performed by the Author, the readings
were recorded every 20 seconds initially for 5 minutes, then every minute up to
a strain of 6% (after the failure strain), and finally every 2 minutes until the end
of the test at a strain of 20%.
The confining pressures applied were 00.00, 138.32, 207.00, 276.64, 365.90,
448.32, 517.77, and 552.30 kPa for all the frozen samples tested. The frozen
sand samples were tested at strain rates of: 3.30x 10-5 sec-1, 4x 10-4 sec-1,
1.60x 10-3 sec-1 and 6.50x 10-5 sec-1.
The above mentioned procedures for triaxial testing provide systematic
approach for Laboratory Testing of Frozen Soils [LTFS], with the outcome of
obtaining high quality and repeatable experimental results, this is in addition to
the advantages of expedition and economy in carrying out the testing program.
Thus, they are recommended for standardization.
3.3.2 Experimental Results and Analysis
The physical properties of the frozen sand samples tested are reported in Table
1, and typical results are presented in Figure 11. As it is seen in the figure, the
stress- strain curve shows a single peak at a strain level of about 3.50%. The
volume change shows an initial decrease followed by a steady increase near
the failure strain. The volume increases initially at a relatively steep slope, and
then continues to increase with milder slope until the end of test at a strain level
of 20%.
The initial voids ratio of the tested samples is reported in Table 1. The change
in the voids ratio attributable to the compressibility under the applied confining
pressure (up to 552.30 kPa) is very small and is negligible. Also, the table
presents data on the intergranular ice content in each sample, the volumetric
ratio between the ice content and solid particles, and the total and dry unit
weights for each frozen sample. The initial voids ratio varied between 0.56 and
0.72. A summary of the results is shown in Table 2 for comparison. The
reported information does include (for each test), the test conditions in terms of
the applied axial strain rate, the confining pressure, and the failure strain (the
strain corresponding to the maximum stress).
Table 2 shows the maximum stresses in terms of the major principal stress [σ1],
the deviatoric stress [σ1- σ3], the principal stress ratio [σ1/σ3], the normal
stress [p= ½ (σ1+ σ3)], the shear stress [q= ½(σ1- σ3)], the octahedral normal
stress [σoct = ⅓ (σ1 + 2σ3)], and the octahedral shear stress [τoct = √ ⅔ (σ1-
σ3)].
As it can be seen from the test results, the short- term strength of frozen sand
sample is influenced to a high degree by the applied strain rate [έ], and the
level of confining pressure [σ3] in addition to its being a function of its physical
properties, mainly the voids ratio [ei] and the degree of ice saturation [Si].
The effect of the applied strain rate on the strength of frozen sand is noticed by
comparing the experimental results of samples FS19 and FS39, both of which
have similar physical properties, as shown in Table 1, and are subjected to
identical testing conditions of confining pressure and temperature (Table 2).
The frozen soil sample FS19 was tested at the higher strain rate of 1.61x 10-3
sec-1, while FS39 was subjected to a strain rate of 3.19x 10 –5 sec-1, and the
resulting shear strength ratio is [τ19/ τ39] = 1.58. This indicates that the faster
the forced deformation rate, the higher the shear strength of the frozen soil.
This is due to the high viscosity of the intergranular ice phase; the strength of
ice depends largely on the duration of the applied load or the strain rate level. It
varies from several MPa, for the short- term strength under a high strain level,
to zero for long- term loading condition.
The variation of the voids ratio influences the shear strength of frozen sands. In
general, the smaller the void ratio (the denser the sample), the higher the shear
strength, as it is shown from comparing the results of samples FS47 and FS18.
The increase of confining pressure from 345.31 to 552.30 kPa causes the
increase of the shear strength of 21%; this can be attributed to the increase in
the strength of both the sand particles skeleton and the intergranular ice matrix
with the increase of the confining pressure.
Table 1 Physical properties of the frozen sand samples
Test Number Void Ratio, e Ice Content, W I % Degree of
Saturation Si % Volume of Sand grains, V s x 10- 6 m3 Volumetric ratio
of Ice to Sand Grains, Vi / Vs Total Unit Weight, gT kN / m3 Dry Unit
Weight, gD kN / m3
FS1FS2FS3FS4FS5FS6FS7FS8FS12FS14FS15FS18FS19FS19AFS20FS21FS
22FS23FS25FS26FS31FS32FS33FS35FS36FS37FS39FS40FS42FS43FS44F
S45FS46FS47FS48
0.710.690.710.680.710.720.710.680.640.630.600.690.640670.650.650.630.560
.580.610.630.620.640.660.630.650.640.650.680.640.700.630.670.670.58
24.3522.5422.9722.2522.2231.8321.7421.9220.9920.6620.3521.9820.9828.16
22.3420.6019.4917.8218.8617.8020.3421.1020.4220.3720.2620.3120.5522.51
21.7920.9122.9720.2521.7321.4718.55
99.8494.7293.5794.2091.1094.4888.9393.4394.5394.7597.6492.1594.7192.12
98.9992.1288.9892.1793.8884.2693.8797.5891.6489.7892.6590.0093.30100.0
92.4293.9394.7793.3093.3492.6493.30
50.9451.8150.9751.6550.7951.0452.1150.7052.4953.9654.0649.9653.9650.13
53.1954.2053.5656.5051.5754.2554.6654.2453.5953.4553.0053.3255.0954.72
51.5354.9250.4855.0451.6552.1055.85
0.700.650.660.640.640.680.630.630.610.600.590.640.610.610.650.600.560.52
0.540.510.590.610.590.590.590.590.590.650.630.610.660.590.630.620.54
19.3019.2019.1019.3019.0019.0018.9019.3019.5019.6019.9019.1019.5019.29
19.6019.4019.4020.0019.9019.4019.6019.8019.4019.3019.5019.3019.5019.70
19.2019.5019.2019.6019.3019.3020.00
15.6015.7015.5015.8015.5015.4015.5015.8016.1016.3016.5015.7016.2015.92
16.0016.1016.2017.0016.8015.5016.3016.3016.1016.0016.2016.0016.2016.10
15.8016.1015.6016.3015.8015.9016.80
Fig. 11 Typical results of triaxial compression test on frozen sand
with volume change measurements
Table 2 Test conditions and maximum stresses of the frozen sand samples
Test Number Test Conditions Maximum Stresses, kPa
Strain Ratee x 10-5 sec –1 Failure Strainef % ConfiningPressure,
s3 kPa (s1 - s3)max s 1max (s1/ s3)max toct, max soct
, max pmax qmax
FS1FS2FS3FS4FS5FS6FS7FS8FS12FS14FS15FS18FS19FS19AFS20FS21FS
22FS23FS25FS26FS31FS32FS33FS35FS36FS37FS39FS40FS42FS43FS44F
S45FS46FS47FS48-IK
3.263.283.283.293.253.273.253.383.313.233.253.38161.170.162.40.141.23.27
3.470.653.223.223.243.243.303.243.193.203.293.173.303.183.313.293.25
3.134.132.364.943.703.533.123.654.964.273.902.632.422.721.953.203.294.91
3.953.923.483.282.723.112.583.112.684.994.954.955.353.823.975.321.95
365.9483.6000.0552.3414.0483.6518.0207.0552.3276.6138.3345.3448.3448.3
448.3448.3448.3448.3448.3448.3448.3448.3448.3448.3448.3448.3448.3448.3
138.3138.3276.6276.6552.3552.3448.3
606077105587785068546410666858109064910080415057114401020010510
978510190115409590850173357130677971806531703072351054385958488
664178598421111905618
643382025587841372766902719660219627938181825409118931065610967
102421065112000100478958779275877236763769887430769211000873686
29692381418984117496075
17.2516.6514.9417.2414.0113.6328.5417.1033.3558.0315.3726.0223.3224.00
22.4133.3126.2621.9919.6017.0516.6015.8316.7115.2916.3816.8324.0761.96
61.2024.5528.8715.9620.8713.29
285736342634370132313022814327394273429037912384539148084954461
348055441452040083458336131963384307833143410492240524001313137
05397052732649
239330621862318027072629275021483584331528212038426938573960371
938554304365332912902283427172850263428002869393830062970249529
01337042922330
340343472794448838493697386231165095483141622880617555575712535
055546228525247084125402238474047372239724074567844394385360242
11477361563266
303038552794392534273205333429054532455040212528571851005255489
350975771479542513668356533903590326535153617522142984244332139
30421055932809
Figure 12 presents the experimental results of tests performed at the same
testing conditions of temperature (T= -5°C), confining pressure of 275.62 kPa
and strain rate of 3.30x 10-5 sec-1, for samples FS14, FS44, and FS45. The
influence of the physical properties of the frozen soils (Table 1) on their
properties is apparent. Although, samples FS14 and FS45 were tested under
the same conditions and both had the same initial voids ratio, it seems that for
sample FS44, the combination of the physical properties and the testing
conditions causes the intergranular ice matrix to fail at 2% strain, which results
in a general decrease in the total shear strength of the frozen sand sample. The
second peak strength occurs at a higher strain level (6%) in comparison to that
of samples FS14 and FS45, which had a failure strain in the order of 4%. The
volume change behavior during deformation shows that the initial density affects
the rate and magnitude of the volume increase. The denser the frozen sample,
the higher are the volume of cracks, and the resulting increase of the volume
change, εv%.
The observations for samples FS14 and FS45 do apply also to the experimental
results of samples FS15 and FS42, as shown in Figure 13. The applied
confining pressure is 138.32 kPa; the slight differences in the magnitudes of the
shear stresses and volumetric strains during deformation were due to the slight
variability in the initial physical properties. However, the general behavior for
both samples is essentially the same. The magnitudes of the volume change
during the decreasing phase were nearly identical, as shown in Figure 12.
The experimental results reported in Figure 14, show a comparison for samples
tested under the identical conditions of temperature, strain rate, and confining
pressure, however, the initial physical properties are different as can be seen
from Table 1. The influence of the initial voids ratio and the degree of ice
saturation on the short- term strength as well as the volume change behavior
can be traced as in the aforementioned manner.
Figure 15, presents the results of the frozen sand samples FS19, FS19A and
FS20 tested at a strain rate of 1.60x 10-3 sec-1, as compared to the results of
sample FS25 which was subjected to the slower strain rate of 3.47x 10-5 sec-1.
The four samples were subjected to the same confining pressure of 448.32 kPa
and a temperature of -5ºC. The influence of the applied strain rate is apparent
on both the shear stress- strain and the volumetric change behavior of the
frozen sand samples. The samples tested at a faster strain rate show sharp
peaks at a lower failure strain level (in the order of 2.5%). The shear stress ratio
of FS19 and FS25 is 1.20, and sample FS19 shows a brittle behavior.
Frozen sand samples FS19, FS19A, and FS20 show similar behavior. The slight
differences are due to the slight variability in the initial physical properties, as it
is shown in Table 1. From Figure 15, it is clear that increasing the applied strain
rate (i.e. increasing the volume of cracks that are initiated near the failure strain
from 1.95 % to 2.27% up to a strain level of about 10% with steep slope) will
cause the deformation to behave in a more brittle manner. The influence of the
physical properties on the volume change behavior is in agreement with the
previous information. The volume change behavior of Sample FS25 as
compared to the other samples shows similarity in general, but because it had
less magnitude as a result of the relatively smaller amount of cracks developed,
the volume increase starts at a relatively larger strain level, one that is close to
the failure strain of the sample and equal to 3.95%.
Fig. 12 Triaxial stress- strain- volume change behavior of frozen Ottawa sand
(σ3= 276.64 kPa)
Fig. 13 Triaxial behavior of frozen soil samples with volume change
measurement
(σ3= 138.32 kPa)
Fig. 14 Triaxial behavior of frozen sand samples with volume change
measurement
(σ3= 448.32 kPa)
Fig. 15 Triaxial behavior of frozen sand samples tested at different strain rates
3.3.3 Discovery of the Volume Change Behavior Mechanism of Frozen Soil
The reported results for the volumetric change behavior of frozen sand during
deformation, while subjected to triaxial stresses, generally show similar
behavior. When the frozen sample is forced to deform, it exhibits an initial
decrease in volume with a value of about 1%. Then, the rate of volume increase
becomes milder up to the end of the test.
Very few data have been reported for triaxial testing of frozen soils with volume
change measurements, and for the reported data, no explanation of the
mechanisms controlling the behavior has been given (Tsytovich 1975 [133],
Andersland et al. 1994 [8], 1978 [7], Lade and Jessberger 1980 [80]). It was
therefore found of interest to study the behavior, with an emphasis on the
mechanisms of deformation of frozen soils that causes a volume change, even
in a closed system (undrained) conditions.
In frozen soil mechanics science literature, one is faced with a fundamental
question: Is the performed test is a drained or undrained test? This question is
drawn from the unfrozen soil mechanics science, which defines the drained tests
as those performed on samples tested in an open system conditions (the water
phase is free to move in or out of the samples during deformation). In the case
of undrained tests, the sample volume is considered constant during the
deformation. In frozen soils, especially the two- phase material (e.g. sand- ice
system), the frozen sample is tested in a closed system. Thus, the volumes of
soil particles and ice matrix are constant throughout the test. However, the
sample exhibits a volume change during deformation. The observations arrived
at from the current research investigation are summarized as follows:
1. Because of the high viscosity of ice, the terminology of drained and
undrained triaxial testing that is adopted for unfrozen soils are not applicable to
frozen soils, especially at a relatively low temperatures when all or most of the
unfrozen water is transformed to ice.
2. The frozen soil samples deformed during shear exhibit volume change,
whether it is measured or not, and whether or not, the drainage valve is opened
or closed.
3. Since the volumes of ice and soil particles are constant during the test,
any volume increase is due to the increase of the volume of voids by initiations
and development of cracks.
4. From the results of more than 30 triaxial tests with volume change
measurements, in which the frozen samples were contained in a rubber
membrane, it was concluded that just before reaching the short- term strength
(the maximum stress observed on the stress- strain curve), the volume of the
sample starts to increase with a very mild slope, followed by a relatively steep
slope up to a strain level of about 10%. Then the rate of increase becomes
milder, up to the end of the test. This can be explained by the initiation of fissure
cracks before the peak strength, then the development of cracks increases with
a faster rate that is close to the peak strength of the frozen sample. Therefore,
the volume increase is explained by the development of cracks in the frozen soil
samples, in other words by the creation of voids gaps, since the ice and soil
volumes are constant and the frozen sample is tested in a closed system.
5. As a mean of verifying the volume change behavior explanation, some
tests (for example test FS48IK, Table 2) were performed on frozen sand
samples without using rubber membranes. Kerosene was utilized as a coolant,
transparent and confining liquid in the triaxial cell. As it is shown in Figure 16,
the visual observations were confirmed. When the kerosene occupied the voids
gaps (cracks) of the frozen sample, no increase in volume was recorded.
6. The frozen sand samples tested inside rubber membranes showed
initial compression more than 1%. From the results of the compressibility tests
on the same type of soil and at the same temperature of -5ºC, and from the
conclusions drawn from Brodskaya’s (1962[30]), major work on compressibility
of frozen grounds, as well as from the results reported for samples tested
without rubber membranes (Test FS48IK), it can be concluded that a major part
of the apparent recorded initial compressibility for our tests (and also, for others
tests, e.g. Lade et al. 1980[80] and O’Connor 1975[94]) was due to the
compressibility of the air bubbles contained between the frozen samples and the
rubber membrane (which are very difficult to avoid in frozen soil testing). It has
to be noticed that the stress- strain behavior of sample FS48IK cannot be
compared to the behavior of the other tested samples. In the test FS48IK, the
kerosene occupied the voids gaps once the cracks developed as a third phase,
with stresses equal to the confining pressures.
[a] Shear stress-strain behavior (σd x100 kPa vs. ε1 %)
[b] Volume change behavior (εv % vs. ε1 %)
Fig. 16 Triaxial testing of frozen sand for sample tested without rubber
membrane
utilizing kerosene as a coolant, transparent and confining liquid
7. When the results of test FS48IK are combined with those of test FS25
(for sample tested inside a rubber membrane), the following interesting
conclusions can be drawn: from the stress- strain curves shown in Figure 17, it
is observed that the two curves are almost identical, with the same elasticity
modulus E, prior to the initiations of the cracks in both frozen samples, up to the
point (A). At this point, which corresponds to a strain of about 2%, the volume
change behavior of sample FS25 starts to increase, and the stress- strain curve
of sample FS48IK achieves its peak. This is due to the starting of initiations of
cracks in the frozen sand sample during deformation, which causes the increase
in volume by creating voids gaps. After point (A), no increase in volume is
recorded in sample FS48IK, due to the presence of the kerosene in the voids
gaps. The magnitudes of (Vcr), as shown in Figure 17 between the volumetric
behaviors of the two samples are indications of the volumes of voids gaps
(cracks) in the frozen sample FS25 at specified strain levels. Both samples have
similar initial physical properties, as indicated in Table 1. These observations do
confirm the conclusions arrived at by the Author for the mechanisms controlling
the volume change behavior of frozen soils during deformation in shear, while
subjected to triaxial stresses.
Comparisons similar to that of samples FS48IK and FS25 are presented in
Figures 18 and 19 respectively. The indication of the start of the development
of the fissure cracks (corresponding to point A) as well as indication of the
magnitudes of the cracks (voids gaps) for each sample can be visualized.
Figure 20 presents photo of the actual sample. The indication of the start of the
development of the fissure cracks (corresponding to point A) as well as
indication of the magnitudes of the cracks (voids gaps) for each sample can be
visualized.from the frozen sample FS48IK during testing in the triaxial cell,
utilizing kerosene as a coolant, transparent and confining medium.
The research output presented, provides systematic procedures for Laboratory
Testing of Frozen Soils in the triaxial cell with Volume Change Measurements
and is recommended for standardization.
Fig. 17 Comparison between the results of sample tested without rubber
membrane
and sample tested with rubber membrane
(Vcr is indication of the volume of voids gaps, cracks)
Fig. 18 Comparison between the results of several samples tested
with rubber membranes and sample tested without rubber membrane
Fig. 19 Comparison between the experimental results of samples
FS45, FS14, FS44, FS47, FS25, FS43, and the results of sample
FS48IK
Fig. 20 Frozen sand sample FS48IK tested for triaxial compression
with volume change measurement utilizing kerosene as confining
medium
(© Courtesy of Dr. Hamdy Youssef, The University of Montreal-
Canada)
3.4 Triaxial Stress- Relaxation of Frozen Soils-(Constant-Volume Tests)
The Author performed the first time triaxial – stress relaxation tests on frozen
soils. The developed testing technique for automatic measurement of volume
change (AMVC-FS) permitted monitoring the volume of the frozen sample
during the stress- relaxation process to insure that there is no volume change
recorded, thus the test is true stress- relaxation test (constant- volume test).
The objective of the present section is to describe the testing procedures and
give examples of typical experimental results with analysis. Special emphasis is
given to the effect of the stress- relaxation strain level on the shear- strength
reduction after reloading the frozen sample; the observed mechanical behavior
is explained.
The highly viscous ice phase in frozen soil composite plays a major role in its
rheological behavior. The variation of stresses and or strains with time in the
frozen soil material is a rheological phenomenon. The parameters of a
rheological model, for a specific type of material can be obtained from creep or
stress- relaxation tests. Although, the stress- relaxation method is well known in
the creep literature for determining the creep parameters, it had been used very
little in the field of frozen soil testing (Andersland et al. 1994 [8], 1978 [7]), due
to the fact that the actual set- up of a relaxation test involves certain technical
difficulties (Rabtonov 1980 [101]). On the other hand, there exist an extensive
amount of experimental data on the creep behavior of frozen ground, since
creep testing can be performed with conventional equipment.
The long-term strength of specific type of frozen soils, tested at a certain
temperature and confining pressure can be determined from one stress-
relaxation test. In contrast, several creep tests will be required for the
determination of the shear strength reduction with time, under the above-
mentioned conditions. Thus, the stress- relaxation method is more
advantageous than the creep type of test. The same can be stated for the
rheological parameters. While these methods had been very well studied
experimentally for metals and other material (Gittus 1975[47], and Soo et al.
1980 [120]), very little is known on the triaxial stress- relaxation of frozen soils.
The only mention to laboratory stress- relaxation tests, are those reported in the
Russian literature and they are for uniaxial testing (Vyalov 1965 [148],
Grechishchev 1975 [53], and Tsytovich 1975 [133]). No data were reported
from triaxial stress- relaxation test utilizing the conventional triaxial cell.
The Author performed a series of triaxial stress- relaxation tests on frozen
Ottawa sand (20-30 mesh) at a temperature of -5ºC, under different confining
pressures and relaxation strain levels. In stress- relaxation tests on frozen soils,
we have:
εe + εc = εR = constant [3.1]
where εe is the elastic strain, εc is the creep strain, and εR is the stress-
relaxation strain, which is kept constant during the relaxation process. The
elastic strain is expressed by Hook’s law as follows:
εe = ơ / E [3.2]
where E is Young’s modulus of elasticity. The creep strain can be obtained from
one of the rheological models for frozen soils. Since, the creep phenomenon is
associated with that of the stress- relaxation, the creep strain can be expressed
by the following power function (Gittus 1975[47]):
εc = K (ơ1 – ơ3)n .
tb [3.3]
in which K, n, and b are experimental parameters, and ơ1 and ơ3 are the
principal major and minor stresses respectively. The power law is usually
adopted in the engineering theories of creep for metals at high temperatures.
Following Spence and Hult (1973 [121]) approach a general equation can be
derived for the stress-relaxation.
3.4.1 Testing Procedures
The triaxial stress- relaxation tests were performed on frozen Ottawa sand
samples with 3.81 cm in diameter and 7.62 cm length. The same experimental
set- up used for the triaxial compression tests (section 3.3.1, Figure 9) was
utilized. The testing procedures are as follows: first, a constant confining
pressure is applied to the frozen sample. Then, the sample is forced to deform
at a strain rate of 3.30x 10-5 sec-1 (which is the same strain rate level applied
for some of the triaxial compression tests on the same type of soil, Table 2) up
to a prescribed axial relaxation strain (εR). This strain is fixed by simply turning
the compression machine to the (OFF) position. The variation of deviatoric
stresses as well as the volume change is monitored as a function of time. At the
end of the relaxation period, the sample is reloaded with the same strain rate,
by turning the compression machine (ON), and monitoring the deformation up to
a strain level of 20%. Several relaxation cycles could be performed on the same
frozen soil sample at different relaxation strain (εR) levels.
Three different confining pressures were applied: 138.32, 275.64, and 448.32
kPa, which are the same pressures applied for most frozen samples tested in
triaxial compression (section 3.3.2).
3.4.2 Experimental Results and Analysis
The physical characteristics of the tested frozen samples are reported in Table
3. Typical experimental results, for triaxial stress- relaxation of frozen Ottawa
sand are presented in Figure 21. The frozen sample is deformed at a strain rate
of 3.30x10-5 sec-1 up to a relaxation strain, εR = 0.96%. Then, the strain is kept
constant (by turning the compression machine to the (OFF) position) until the
end of the relaxation process (5,119 minutes= about 85 hours), where the
variation of the stress difference became negligible. The compression machine
is then turned to the (ON) position and the frozen sample was then allowed to
deform again to the strain level of, ε1= 20%.
As it can be seen from Figure 21, when the sample was reloaded, it exhibits an
elastic behavior similar to that of the first loading. This was observed in all the
frozen soil samples tested. The deviatoric stress at the beginning of the
relaxation process (point ‘A’, Figure 21a) is referred to as the instantaneous
relaxation deviatoric stress (ơd0). The relaxation stress at any time (t) is
donated as (ơdt), the relaxed deviatoric stress at the time (t) is the difference
(ơd0-ơdt). Figure 21b, shows the variation of the unrelaxed deviatoric stress
with time (triaxial stress- relaxation curve). As it can be seen from the figure,
there is a rapid decrease in the shear stress at the first stage of the stress-
relaxation, which is then followed by a relatively slow rate of stress- reduction.
For all the tested frozen samples, the stress reduction at 30 minutes of the
relaxation process (ơd30 /ơd0) falls in the range of 30% to 60%. This wide
range is due to the differences in the applied confining pressures and the
relaxation strains. Furthermore, the magnitude of the instantaneous relaxation
stress (ơd0) is also influences the behavior. The effects of all the above-
mentioned factors on stress- relaxation behavior are investigated in the present
section.
Table 3 Physical Properties of the Frozen Sand Specimens
Test Number Voids Ratio, e Ice Content, Wi% Degree of
Saturation With Ice, Si % Volume of Sand Particles, Vsx10-6m3
Volumetric Ratio of Ice to Sand, Vi / Vs Total Unit Weight,gT, kN / m3
Dry unit Weight,gD, kN / m3
FS9RF210RFS11RFS13RFS16RFS17RFS24RFS27RFS28RFS29RFS25*
0.690.710.720.630.640.650.550.580.600.570.58
22.6223.1022.9520.8120.7021.5418.0118.6019.2318.8018.86
94.5094.0092.2095.5093.7095.9095.1092.4792.3095.7093.88
52.1350.1351.5052.8252.5151.5156.2956.7955.7756.6051.57
0.650.670.660.600.600.620.500.540.560.540.54
19.2019.1019.0019.7019.5019.5020.2019.9019.7020.0019.90
15.7015.5015.4016.2016.2016.1017.1016.8016.5016.7016.80
Fig. 21 Typical curves for triaxial stress- relaxation of frozen soils
The dotted curve in Figure 21a shows the results of the triaxial test performed
on a similar frozen sand sample tested in compression without stress- relaxation
(Test FS25, section 3.3.2, Tables 1 and 2). This comparison shows that the
elastic part of the behavior is identical for both samples. Due to the occurrence
of the stress- relaxation process in sample FS29R, its strength is lower than that
of the other frozen sample. This is in agreement with Tsytovich 1975 [133],
explanation for the process of relaxation in frozen soils. According to Tsytovich:
the stress- relaxation phenomenon is due to the reorientation of the ice crystals
and soil particles, as well as to the conversion of a part of the elastic strain to a
plastic strain (mostly due to a reduction of the cohesive bond). Since the stress-
relaxation occurs at the low strain level of 1%, and in the elastic part, that is
before initiation of micro cracks in the sample, the reduction in the strength is
relatively small (τFS25 / τFS29R = 1.28%). The volume change during the
relaxation process has been monitored and found of negligible value as shown
in Figure 22. Thus the performed relaxation test is true stress- relaxation test
with constant volumetric strain. Table 4, presents summary of the triaxial stress-
relaxation tests conditions and experimental results.
The experimental results obtained by the Author prove that, the shear stress
ratio (τt /τ0= σdt /σd0) is strongly dependent on the relaxation strain (εR):
τt /τ0 = f(εR, σ3, t, -T) [3.4]
Figure 23, present this relation from the experimental results obtained for the
tested frozen Ottawa sand samples at temperature of –5 °C, and are subjected
to confining pressure of 448.32 kPa (Table 4). The variations of the unrelaxed
shear stress ratio with respect to the instantaneous shear stress, versus the
relaxation strain are clearly shown for different relaxation times, tR (the time
from the start of the relaxation process). If for example, εR = 5%, after 60
minutes, the unrelaxed shear stress ratio (τ60 /τ0) will be 30%. Assuming that
τ0= 4.91 MPa, the value of τ60 will be 1.47 MPa, and the shear stress reduction
due to the relaxation process will be 70%. It is obvious from Figure 23, that the
relaxation strain level has a major influence at εR< 4%, which corresponds to
the elastic range of deformation, and is almost has negligible effect at εR> 7%.
For triaxial tests on almost identical frozen sand samples subjected to the same
conditions of confining pressure and temperature, the failure strain (εf) falls in
general in the range between 3% and 4%. The failure of the frozen samples
during triaxial relaxation testing is due to the progressive initiation of micro
cracks. It can be therefore suggested that when the relaxation strain is within
the elastic range of deformation, the axial strain at which the stress- relaxation
takes place (εR) does influence to a higher degree the magnitudes of the stress
reduction. Therefore, the relaxation strain parameter should be included in any
rheological equation describing the stress- relaxation of frozen soils. In a model
based on the hereditary creep theory, (Rabtonov 1980 [101], and Tsytovich
1975 [133]), the relaxation strain parameter, εR, is incorporated. This presents
the importance of the first time experimental results on the triaxial stress-
relaxation of frozen soils obtained by the Author.
In fact as Tsytovich pointed out, the stress- relaxation process is caused by
destruction of the cohesive bonds (between the ice matrix and soil particles)
and is related to the increase in the number of cracks within the frozen sample.
This explains the high rate of variation in the shear stress reduction with the
variation of the relaxation strain, for values less than the failure strain. (εR<
4%). Once the activities of cracks are stabilized, the destruction of the ice bonds
will be the major cause of the relaxation process, and εR will have a minor
influence for the relaxation strain more than 7%.
Test Number FS10R, T= -5 °C
Fig. 22 Triaxial stress- relaxation results on frozen Ottawa sand (Volume-
constant test)
Table 4 Unrelaxed deviatoric stresses as a function of time during the triaxial
stress- relaxation process
Sample Number ConfiningPressure, s3 kPa Failure Strain, ef %
RelaxationStrain, eR % InstantaneousDeviatoric stress,sd0 kPa
Deviatoric Stress, (sd,t kPa) with time t (t in minutes)
t = 10 t = 20 t = 30 t = 40 t = 50 t
= 60 t = 70 t = 80 t = 90 t = 100
FS9R 276.6 3.34 7.86 5890 3107 2551
2250 2041 1922 1809 1730 1685 1639 1592
FS10RFS10RFS10RFS10RFS10R 138.3138.3138.3138.3138.3
3.183.183.183.183.18 5.167.749.1310.5211.91
55423883272419731722 275016501000801 21501420850700
19001250750610 17001050680530 1530930530500
1360850500470379 1300470450 1270450430 1210430400
1150410380
FS11RFS11RFS11RFS11RFS11RFS11RFS11R
448.3448.3448.3448.3448.3448.3448.3
3.893.893.893.893.893.893.89 6.618.9511.0813.6115.7517.7019.25
5738351431882939281427212597
2970172016001345126012011172
2500135012601128108010301000 2239121011351010980940880
210010301010900860 19591050970900870820
18601010920850810782 900820750 1664860790730
890840750715 820685
FS13R 448.3 4.34 1.38 2899 1654 1217
997 791 601 454 322 220
FS16RFS16RFS16R 448.3448.3448.3 1.581.581.58
1.582.774.35 519150182658 35553020980 31452517780
28602234660 27212030600 25801872545 24701750525
23911636 23001480470 22491332 21801265420
FS17R 448.3 3.83 1.41 4634 3100 2724
2364 2240 2082 2040 1985 1926
FS24R 448.3 3.33 3.33 9670 6311 5588
5160 4913 4720 4530 4430 4300 4240
FS27R 448.3 4.21 4.21 10700 7130 6080
5600 5300 5020 4800 4680 4480 4320 4210
FS28R 448.3 3.46 4.43 8192 4065 3239
2800 2500 2340 2150 1940 1870
FS29R 448.3 4.21 0.96 3470 2461 2192
2050 1940 1865 1780 1740 1695 1740 1615
Table 4 Unrelaxed deviatoric stresses as a function of time during the triaxial
stress- relaxation process (continue)
Sample Number ConfiningPressure, s3 kPa Failure Strain, ef %
RelaxationStrain, eR % InstantaneousDeviatoric stress,sd0 kPa
Deviatoric Stress, (sd,t kPa) with time t (t in minutes)
t = 110 t = 120 t = 240 t = 360 t =
480 t = 600 t = 1200 t = 1800 t = 2400 t = 3000
FS9R 276.6 3.34 7.86 5890 1561
1400
FS10RFS10RFS10RFS10RFS10R 138.3138.3138.3138.3138.3
3.183.183.183.183.18 5.167.749.1310.5211.91
55423883272419731722 390370 360360 275 225
192 182
FS11RFS11RFS11RFS11RFS11RFS11RFS11R
448.3448.3448.3448.3448.3448.3448.3
3.893.893.893.893.893.893.89 6.618.9511.0813.6115.7517.7019.25
5738351431882939281427212597 1418835800665
1400802707701675651610 1120700655520 975600460
890530420 800510600 400
FS13R 448.3 4.34 1.38
2899
FS16RFS16RFS16R 448.3448.3448.3 1.581.581.58
1.582.774.35 519150182658 21501200400 21001104382
1800715245 1640610205 1440425180 1385405145
117034065 105529080 1003260 940220
FS17R 448.3 3.83 1.41 4634 1800 1707
1470 1275 1190 1120 865 760 680 580
FS24R 448.3 3.33 3.33 9670 4000 3438
2983 2590 2308 1600 1300 1175
FS27R 448.3 4.21 4.21 10700 4000 3180
2740 2350 2185
FS28R 448.3 3.46 4.43 8192 1790 1706
1200 920 550 370 290 200
FS29R 448.3 4.21 0.96 3470 1475 1404
1235 1125 1050 995 805 710 655 572
It is observed from the experimental results conducted at low confining
pressures of 138.32, and 276.66 kPa that, reloading the frozen soil samples
after the stress- relaxation process, shows almost no reduction in the shear
stress. This is shown in Figure 24 for samples FS9R and FS10R. The stress-
strain behavior is almost continuous, as if no stress- relaxation process had
been occurred. Figure 25 shows a different behavior to that observed in Figure
24, due to the higher applied confining pressure of 448.32 kPa to the tested
frozen sand samples. The test FS24R performed at a relaxation strain of 3.33%,
and test FS27R tested at relaxation strain of 4.21%, show that when the
relaxation occurs in the region of the failure strain, εf= 3 to 4%, a dramatic
strength reduction occurs on reloading. This reduction is due to the stress-
relaxation process, which destroys the ice cohesion bonds, and to the maximum
initiation of the voids gaps or cracks (at failure).
Strength reduction also occurs when the sample is subjected to several cycles
of stress- relaxation, for example Test FS11R. However, in the first relaxation
cycle the strength reduction is maximum for the same reasons as mentioned
above. The relative reduction in the following cycles is almost negligible. The
magnitude of the strength reduction, or the stress losses, in the first cycle for
sample FS11R, is less than that for the two other frozen samples as shown in
Figure 25. This is due to the fact that (εR1) occurs after the peak strength when
the progression of cracks starts to stabilize. It can be concluded from the above
that the shear strength recovery after the stress- relaxation process is
dependent on: the physical properties of the frozen soil, the applied confining
pressure, as well as the level of the relaxation strain with respect to the failure
strain. The relative magnitude of the relaxation strain factor shows whether the
relaxation process occurs before or after initiation of the microscopic or
macroscopic cracks in the tested frozen sample.
Vyalov 1979 [151], reported numerical values for the amount of the shear
strength reduction with time ((τ0- τt)/τ0), for frozen soils in general. As an
approximation, during the first 30 minutes, a 60% reduction occurs. There is a
70% reduction during the first hour; during the first 8 hours the reduction is
80%. This range of strength reduction with time is in agreement with the
numerical values reported in Table 4, and Figure 23 for each relaxation strain
(εR). The general agreements of Youssef’s experimental results and those of
Vyalov’s on stress- relaxation of frozen soils are of interest. Although, Vyalov
1979 [151] did not give any indication of the level of the stress- relaxation strain,
it was found by the Author that this level is of importance as illustrated in Figure
23.
Fig. 23 Shear stress ratio of frozen Ottawa sand as a function of time and
relaxation strain
Fig. 24 Stress-strain behavior after the stress-relaxation process of frozen soils
Fig. 25 Stress- strain behavior of frozen sand samples with relaxation strain
near
the peak stress
Figure 26 presents the relation between the deviatoric stresses and the
relaxation time in the logarithmic scales for frozen sand samples FS16R,
FS17R, and FS29R (Table 4) tested at the same low temperature and confining
pressure. The relaxation strain for each sample is indicated on the figure.
The experimental results of Test FS11R are shown in Figure 27, in the form of
(ơd vs. logt). The curves observed for different relaxation cycles are similar in
shape; these curves approach an average value of 382.60 kPa. A large drop in
the deviatoric stress is observed in the first cycle, followed by a relatively
smaller reduction (a milder slope) at a higher relaxation strain level. It is
observed that, reloading the frozen sand samples contribute to the partial
closing of cracks. For the relaxation strains of 13.60% and 15.75%, the
experimental curves are almost identical.
In conclusions, the Author’s first time experimental results on triaxial stress-
relaxation of frozen soils are presented in numerical and graphical forms. The
detailed presentation was made available by utilization of the developed
computer program FROZENSOIL.1. The testing procedures followed, are
recommended for standardization. Now, it is possible to study the rheological
behavior of any type of frozen ground, at any low temperature and confining
pressure in the triaxial cell, following the above-mentioned Laboratory Testing
procedures. It is also possible to obtain, and in a very short time, all the
required numerical and graphical experimental results with analysis, as the
computer program FROZENSOIL.1 output. This is also, the perfect
documentation for the complete testing program.
Fig. 26 Relations between the deviatoric stresses and the relaxation time in
logarithmic
scales
Fig. 27 Results on the triaxial stress-relaxation of frozen Ottawa sand with
several
relaxation cycles at different relaxation strains
3.5 Compressibility of Frozen Soils
The Author performed compressibility tests on frozen Ottawa sand at a
temperature of –5 οC, the sample preparations are presented in section 2.2.
The objective of the present section is to demonstrate the testing procedures
followed and present typical experimental results. The time dependent
settlement of foundations constructed on permafrost (ice and frozen soils) are
due to both the compressibility and creep phenomenon, in which compressibility
constitutes less than 30% of the total deformation which is a considerable
amount (Vyalov 1959 [146], Brodskaya 1962 [30], Tsytovich 1975 [133], and
Andersland et al. 1994 [8]). Thus, the compressibility test is important type of
test for Laboratory Testing of Frozen Soils. For ground freezing engineering
projects, the compressibility tests are of importance for design.
Brodskaya 1962 [30], performed compressibility tests on ice and frozen clay as
well as frozen sand samples, at different low temperatures and subjected to
different stresses. Based mainly on the US Department of Commerce 1977 [30]
Technical Translation, the Author devoted extensive amount of time for
clarifying and compilation of Brodskaya’s experimental results (Youssef 1983
[164]), especial emphasis was given to the compressibility of frozen sand. Table
5, presents summary of Brodskaya’s work for different types of sands and ice
samples tested at a temperature range of –0.40oC to –4.20oC, and for applied
constant stresses up to 2.00 MPa. The frozen samples physical properties and
the compressibility coefficients (mv) are illustrated for each sample tested.
Figure 28, presents Brodskaya’s experimental results on frozen Igarka (USSR)
sand in term of strain (ε %) vs. (p), the applied pressure. As it can be observed
from the figure, the compressibility curve for frozen soils is different from the
typical consolidation curve for the unfrozen soils. The typical compressibility
curve for frozen soil shows two gently sloping segments (AA1 and A2D) at both
ends with (S-shape) in between the two lines. Brodskaya and Tsytovich, showed
that the S- curve can be approximated by a straight line (A1A2), and explained
the deformation mechanisms of frozen grounds subjected to confined
compression, (Tsytovich 1975 [133]).
3.5.1 Testing Procedures
The frozen sand samples were tested for compressibility utilizing the
conventional Odometer (fixed ring Odometer), Bowles 1978 [26]. The only
difference with unfrozen soil testing is that, a large bottom porous stone with
large diameter 10.60 cm (4”) was utilized. This allowed enough space for the
unfrozen water (which occurs during testing due melting of the ice matrix), to be
stored in the porous stones. The frozen sample was loaded for one minute
under the maximum experimental load to eliminate the possible non- uniformities
of the sample surface. The deformation was measured by micrometer with an
accuracy of 0.002 mm. The loads were then applied with the increasing values
of: 446.36, 892.71, 1339,10, 1785.42, and 2231.78 kPa.
Table 5 Compressibility of frozen ground- Data on ice and frozen Igarka (USSR)
sand
Experimental data compiled by the Author (Youssef 1983)
J Type of Frozen Ground[Frozen sands and ice] Ho mm Wi %
T-°C THours gTkN/m3 Compressibility Coefficients, mv x10-6 (kPa)
-1Corresponding to the Applied Stresses in MPa
0 -0.1 0.1 -0.2 0.2 -0.4 0.4
-0.8 0.8 -1.2 1.2 -1.6 0.6 -2.0
1 Sandy loam of massive 61 26.8 0.4 1189 18.8
24 29 26 14 - - -
2 Texture [ natural] 61 23.2 3.5 1208 19.0
06 14 18 23 - - -
3 Sandy loam of massiveTexture [artificial] 30 51.6 4.0
7248 - 22 22 71 26 14 9 13
4 Fine-grained sand[artificial 30 21.5 3.8 217
18.7 10 14 50 14 - - -
5 Medium grained sand 31 27.1 4.2 283 18.7
15 15 10 7 - - -
6 [artificial] 30 22.0 4.0 410 18.6 3 3
3 9 7 - -
7 30 20.6 0.6 120 19.9 11 11 6
4 2 - -
8 32.5 26.7 0.4 166 --- 36 32 20
12 - - -
9 31 27.1 0.6 498 18.6 28 28 14
6 - - -
10 Ground ice 30 100 4.2 269 8.9 9 9
6 3 - - -
11 34.30 100 4.0 5328 8.5 14 14
20 25 25 - -
12 30 100 0.5 765 8.8 12 14 17
- - - -
Fig. 28 Compression curves of frozen sands and ice (after Brodskaya 1962[30]
(for test numbers refer to Table 5)
The value of the maximum stress of 2231.78 kPa, corresponds to the maximum
pressure admissible for frozen soils, Tsytovich 1975[133]. Readings of the
compressibility (settlement) were recorded every 0.10, 0.25, 0.50, 1.00, 2, 5,
15, 30, and 60 minutes from the start of each step of loading, and then every
hour for 7 hours. Therefore, several readings were taken with maximum interval
of 12 hours, until the deformation was stabilized. The stabilization criterion
adopted was that, the deformation difference should be equal to or less than
0.002 mm in 24 hours. The maximum recorded period for one step of loading
was 246 hours, about 10 days.
3.5.2 Experimental Results and Analysis
The Author’s results on compressibility of frozen sand (20- 30 mesh), with initial
voids ratio of 0.727, ice content of 17.56%, total initial unite weight of 1.80
gm/cm3 (17.66 kN/m3), and degree of saturation with ice of 69.80%, tested at a
temperature of –50C, show similar mechanical behavior to Brodskaya’s (USSR)
results on frozen sand.
Figure 29 presents the deformation (δH) and strains (ε1%), as a function of time
(t) for the applied stresses (p= ơ1). As can be seen from the figure, for each
stress level, the deformation stabilized at the end of each loading interval,
almost horizontal tangent to the curve. The test duration for the frozen Ottawa
sand was 800 hours (33.36 days), while Brodskaya’s tests on Igraka sand
(USSR) was only 17 days. The small magnitudes of the deformations
(settlements) according to Tsytovich’s 1975 [133] classification indicate that,
this type of frozen sand is reliable for construction.
Figure 30, shows the compressibility coefficient (mv) varies slightly with the
applied loads. The S- shape of the compressibility curve can be approximated
by a straight segment (A1A2), as can be seen from the p vs. ε1 diagram, with
the critical pressure (pcr) located at point (B). The values of (mv) for each
stress increment are listed as follows:
Stress interval: 0-.455 .455- .91 .91- 1.37 1.37- 1.82 1.82- 2.28
mvx 10-6 kPa-1 3.44 3.82 3.69 3.82
2.29
Fig. 29 Compressibility of sand- ice system, typical deformations and strains
Fig. 30 Compression curve of frozen Ottawa sand at –50C
The value of (mv) increases and then decreases, this indicates that, the critical
pressure (pcr) is between 9.10 and 13.70 kg/cm2 (0.893 and 1.344 MPa). The
small variation in mv means that, the S- shape of the curve is more flat due to
the low ice content. The higher magnitudes of the compressibility coefficients,
(for the stresses from 4.55 to 18.20 kg/cm2 (0.446 to 1.785 MPa)), are
represented by the steeper slope of the curve (A1A2) where plastic irreversible
deformation dominates.
In Test number 6, from Brodskaya’s results (Table 5), carried out under
conditions comparable to that of the present study (Wi= 22%, T= -40C), the
coefficient of compressibility recorded is 3x 10-4 cm2/kg (3x 10-6 kPa-1, in the
interval of 0- 4 kg/cm2 (0- 0.392 MPa). This compares well with the value of 3.44
x 10-6 kPa-1 according to the Author’s experimental results on frozen Ottawa
sand.
At higher stress levels, the values of (mv) found by Brodskaya are 2 to 3 times
higher than those for our test, this can be attributed to the higher ice content
and higher temperature in Brodskaya’s test. Furthermore, the difference in the
type of sands could also have an influence on the experimental results.
In addition to the USSR investigators, Zhu et al. 1982 [195], presented
experimental results on compressibility of Lanzhaou (China) frozen sands,
however, without detailed description of the sample preparations and testing
procedures.
In conclusions, it is possible to perform compressibility tests on frozen soils with
different physical properties and at different low temperatures in the
conventional Odometer apparatus located in the cold room as described above.
The experimental results are important for design of constructions in the cold
regions and for utilizing artificial ground freezing techniques for special
engineering projects.
Chapter 4
Compressibility of Frozen Grounds
Data Processing And Documentation
4.1 Introduction
The present chapter describes in details: the data recording, processing, and
documentation of typical compressibility test of frozen soils.
Table 6, is to be utilized for identification and recording the physical properties
of the frozen sample prior and after the test. As it can be seen from the table,
the first data recording is: the test and soil type, the low temperature, the
Odometer and Ring numbers and their calibration factors. The frozen sample
dimensions prior to testing are also recorded. From the sample total initial
weight and volume, the frozen soil initial unit weight is calculated.
After successful testing of the frozen soil sample for compressibility, the final
total and dry weights of the sample are to be recorded in the same table. From
the above information, the ice content and the weight of ice, which departed
from the sample during testing, can be calculated. The numerical data in Table
6 are for typical compressibility test of frozen Ottawa sand. The specific gravity
from the soil mechanics literature for sand is 2.65, knowing (Gs) in addition to
the dry weight and initial volume, the initial voids ratio (ei) is to be calculated
and recorded. For the frozen grounds testing program for compressibility,
Table 6, information sheet is basically necessary and to be included as the first
page for documentation of each test.
4.2 Data Recording During Testing
The only data to be measured during performing the compressibility test on
frozen soils are those of the deformation settlement with time under each static
load. Table 7, presents typical example for recording the elapsed times from the
start of each load application and the deformations (δH) as a result of the
applied stress (p= ơ1= 1.82 MPa). The stress was calculated by dividing the
applied vertical static load (in the Odometer apparatus) of 53.20 kg (1.82 MPa),
to the frozen sample area (A= 32.17 cm2) and multiplies the result by the
Odometer load factor (F= 11). The deformation (δH) was calculated by
multiplying the readings of the Micrometer divisions by its calibration factor
(0.002 mm).
As it can be seen from the table, the testing for the load level started on
October 28th and the deformation achieved stabilization on November 5th.
Hence, it was the time to start applying the next load of 66.50 kg (2.275 MPa),
and record the new deformations with time. The stabilization criterion adopted
was that, the deformation differences should be equal to or less than 0.002 mm
in 24 hours.
Table 6 Compressibility Testing of Frozen Soils-Test and Frozen Sample
Identifications
TYPE OF TEST: Compressibility of Frozen SandType of Soil : Ottawa
Sand [ 20-30 mesh ]TEMPERATURE: -50COEDOMETER NO.: 1RING
NO. : 1LOAD FACTOR [F]: F= 11, [ơ= p = (P/A) x 11 kg/cm2 ]
MICROMETERCALIBRATION FACTOR [ F1]: F1 [ 1 Division ] = 0.002mm
D = FROZEN SAMPLE DIAMETER = 6.40 cmA = FROZEN SAMPLE
AREA = 32.17 cm2H = FROZEN SAMPLE INITIAL HEIGHT =2.
025 cmV = FROZEN SAMPLE INITIAL VOLUME = 65.144 cm3Before TestingWT
= FROZEN SAMPLE INITIAL TOTAL WEIGHT = 117.49 gmsgT = FROZEN
SAMPLE INITIAL UNIT WEIGHT = WT / V = 1.80 gm / cm3After TestingWTf = F.
S. FINAL TOTAL WEIGHT = 111.63 gmsWIc = ICE WEIGHT DUE TO
COMPRESSIBILITY = WT - WTf= = 117.49 – 111.63 = 5.86 gmsWd =
SAND SAMPLE DRY WEIGHT = 99.94 gmsWI = F.S. INITIAL ICE
WEIGHT= WT - Wd = 17.55 gmsWi = ICE CONTENT = WI / Wd = 17.56 %WIf =
F.S. ICE WEIGHT AFTER COMPRESSIBILITY = = WI - WIc = 17.55 –5.86 =
11.69 gmsGs = SPECIFIC GRAVITY OF SAND = 2.65ei = F.S. INITIAL VOIDS
RATIO = ([GsV] / Wd) -1 = 0.727
Table 7 Compressibility of Frozen Ottawa Sand, T= -50C
Example of Data Recording (ơ3= 1.82 MPa)
Time Readings Elapsed TimeMinutes Micrometer Reading
DeformationdHx10-3 mm
Initial Adjusted
October 28, 198112:0712:071712:072512:07512:08012:09012:10012:11012:
13013.110October 29, 198110.0510.51October 30, 198108:5111:
4314.4416.4417.45October 31, 198112:1720:10November 1,198100:0922:
15November 2,198109:4114:4816:10November 3,198117:10November
4,198110:26November 5,198111:3013.2015.2518.06
0.000.170.250.501.002.003.004.006.0010012541300258027722963308331444
2564729469562956981734873708870990811410115201170511865
238.70239.60239.70239.80239.90239.90239.90240.00240.00240.40242.60242
.70243.80243.90244.10244.60244.60245.00245.20245.30245.90246.20246.28
246.40247.00247.70256.30256.40256.50256.70
49.8050.7050.8050.9051.0051.0051.0051.1051.1051.5053.7053.8054.9055.00
55.2055.7055.7056.1056.3056.4057.0057.3057.5057.508.10558.8067.4067.50
67.6067.80
99.90101.40101.60101.80102.00102.00102.00102.20102.20103.00107.40107.
60109.80110.00110.40111.40111.40112.20112.60112.80114.00114.60115.001
15.00116.20117.60134.80135.00135.20135.60
* Frozen Ottawa Sands, Temperature=-5°C
.Figure 29, shows the measured deformations with time for the five pressure
levels applied to the tested frozen Ottawa sand sample. The curves for the axial
strain (ε1%) which were calculated by dividing the measured deformations to
the initial sample height of: H= 20.25 mm, are also presented on the same
figure. Figure 30, presents the second typical graphics of compressibility
results, namely the variations of the axial strains with the applied stresses. As it
can be seen from the figure, the compression curve consists of three slopes
(OA1, A1A2, and A2D). The middle slope (A1A2) is approximation of the S-
shape curve with reversal point at (B), which is indication of the level of the
critical pressure (pcr).
4.3 Calculations of the Compressibility Coefficients
The coefficient of compressibility (m) and the coefficient of volumetric
compressibility (mv) are the relationships between the difference of the voids
ratio and the applied stress increment, and defined as follows:
m= Δe/Δ p = tanα [4.1]
where (α) is the angle of the slope of the voids ratio increment (ej- ej+1), and
the pressure (stress) increment (pj+1 – pj), and mv is equal to:
mv= m/(1+ei) [4.2]
where ei is the initial voids ratio.
Table 8, presents the numerical values of the coefficients of volumetric
compressibility (mv) for the tested frozen Ottawa sand (20- 30 mesh), at the
temperature of –50C. As it can be seen from the table, knowledge of the
deformation (δ Hj) permits calculations of (Gs Vj) and hence the voids ratio (ej):
ej= (Gs Vj / Wd)- 1 [4.3]
this allows calculations of the values of (mj) and (mvj ).
For an example, for the pressure interval (0.00- 0.455 MPa):
e1= (172.37/ 99.94)- 1= 0.7247, and
m = (ei – e1)/ (p1 – pi )= (0.7274- 0.7247)/ (0.455- 0.00)= 5.934x 10-3 MPa-1 ,
and
mv= m/(1+ei)= (5.93x 10-3)/ (1.7274)= 3.44x 10-6 kPa-1
Tsytovich 1975 [133] divided the soils (frozen and unfrozen) on basis of their
compressibility to three principal groups:
[1] Those with little compressibility m≈ 0.01 MPa-1
[2] Those with moderate compressibility m< 0.50 MPa-1
[3] Those with high compressibility m> 0.50 MPa-1
From the experimental results presented on compressibility of frozen
Ottawa sand at –50C, it is clear that, this type of frozen ground is in the first
group and is considered reliable and good ground to support structural
foundations.
For constructions in the cold regions and for the design of artificially frozen
ground projects, predicting the compressibility settlements is of importance. This
requires Laboratory Testing of Frozen Soils for compressibility at the field
temperature and applied stresses. This can be achieved by following the
information given in section 2.2, for sample preparations, section 3.5, for testing
procedures and the present chapter for data processing.
The Author recommends the above-mentioned testing method for
standardization. This will permit the exchange of knowledge among professional
engineers, researchers and academics with interest in the frozen soil science
research and development.
Table 8 Compressibility of Frozen Ottawa Sand
Calculations of the Compressibility Coefficients
j LoadingPressures1 MPa Micrometer Readings Deformationd H x
103mm Straine1% VolumeDecreased Vj, cm3 SampleVolumeVj ,
cm3 GsVj Coefficient ofCompressibilityMvx10-6 kPa-1
Initial Adjusted
012345 0.00o.4550.911.371.822.28
188.90203.40221.80238.70256.70265.70
0.0014.5032.9049.8067.8076.40 0.0029.0065.8099.80135.60152.80
0.000.1430.3250.4930.6700.755 0.000.0930.2120.3210.4360.492
65.14465.04564.93064.82364.71064.650
172.630172.370172.070171.780171.480171.320
0.003.443.823.693.822.29
* Frozen Ottawa Sands, Temperature =-5°C, Test duration: October 6 to
November 11
Chapter 5
Youssef’s FROZENSOIL.1
Data Processing and Documentation
Triaxial Results of Frozen Soils
As a first step to develop software package for data reduction, analysis and
documentation- computer programs with graphics output for: Laboratory Testing
of Frozen Soils, the Author developed the computer program FROZENSOIL.1.
The program is capable of interpretation of the triaxial and uniaxial compression
and stress- relaxation experimental results with (or without) volume change
measurements. The program had been tested and extensively utilized by the
Author for numerical and graphics interpretations of more than fifty tests on
frozen soils and proved to be very useful for analyzing and plotting the
experimental results with higher accuracy and speed than utilizing the classical
methods for data processing and analysis.
The logical flow chart and listing of the program are presented in this chapter.
Typical numerical and graphics outputs for both type of tests, are presented in
detail to give standard examples to be followed by academics and engineers
performing and analyzing test results on frozen soils. The documentation and
exchange of knowledge, will contribute to the development of frozen soil
mechanics science.
5.1 Data Recording and Decoding
The testing procedures for both types of tests are described in chapter 3-
sections 3.3.1, and 3.4.1. During testing, the experimental results were
recorded with time utilizing a data acquisition system (Figure 31, for example).
The data were recorded automatically on a paper tape, the paper tape was
decoded upon completing each test utilizing (9825B HP, Hewlett Packard) Desk
Top computer, with a (9883A Acquisition- control unit, a 3497A Data Reader,
and a 9871A line printer) as shown in Figure 32. This simple and systematic
data recording permits obtaining as many experimental result points on each
curve, as necessary for accuracy by adjusting the recording time intervals at the
start and during performing each test. The numerical outputs of the
experimental results from the Desk Top computer are utilized as input for the
computer program FROZENSOIL.1.
5.2 Program FROZENSOIL.1 Identification
The computer program has been developed to run on virtually any computer
that has an ANSI FORTRAN IV compiler, except for free FORMAT reading of
data. The plotting routines utilized are those of a standard CALCOMP plotter.
The storage requirements are 104K for compilation and 87K for execution on
IBM 4341 main- frame computer. The program is written as a main program that
reads the input data and uses subroutines performing calculations and
graphics. The program requires only the normal control cards for particular
operating system.
Fig. 31 Data acquisition for recording the results of triaxial testing of frozen
soils
(© Courtesy of Dr. Hamdy Youssef, The University of Montreal-Canada)
Fig. 32 Desktop computer utilized for Data Decoding. Of the experimental
results.
(© Courtesy of Dr. Hamdy Youssef, The University of Montreal-Canada)
5.3 FROZENSOIL.1 Flow Chart
The computer program flow chart is presented in Figure 33. First the program
FROZENSOIL.1, reads the test Number, the initial readings of the load cell, the
type of test (with or without volume change measurements). Once the type of
test is defined by an (IF) statement, the frozen sample physical properties and
the test conditions (parameters, for example the confining pressure and
temperature) are read and recorded. The program then calculates the frozen
soil sample parameter (for example: the area, volume, and unit weight). Second,
FROZENSOIL.1 reads as an input the experimental test results with time (for
example, the load cell readings and the volume change differential pressure
transducer outputs). The subroutine (CALCUL) takes care of the stresses,
strains and time scales calculations, for each set of data. The subroutine
(GRAPHICS) is recalled for plotting all the required experimental curves for data
reduction and analysis.
FROZENSOIL.1 print the frozen sample and test information, as well as the input
experimental data and calculates the stresses and strains for each time of
reading, with graphics output of the required stress- strain, and stress- time
relations in several scales and forms. This does speed and simplify the
experimental analysis and documentation of each test results, and therefore the
entire testing program. These are the easily accessible and necessary
experimental results, for the required further analysis to investigate the
mechanical (short- term and long- term) behaviors of frozen soils and provides
the required design parameters for constructions on and by utilizing of frozen
grounds at the field temperature and applied stresses.
5.4 Listing of the Computer Program FROZENSOIL.1
The computer program FROZENSOIL.1 and the associated subroutines
(CALCUL) and (GRAPHICS) are listed in the following pages with the objective
to be recommended for utilization as a standard example to be followed for data
processing and analysis of laboratory triaxial and uniaxial testing results of
frozen soils. The symbols decoding and the title for each program statements
group are printed to simplify the utilization of the program.
Fig. 33 Flow chart of the Computer Program FROZENSOIL.1
Laboratory Testing of Frozen Soils under triaxial conditions
C PROGRAM: FROZENSOIL.1
C TRIAXIAL AND STRESS-RELAXATION TESTING OF FROZEN SOILS
C DATA REDUCTION AND GRAPHICS COMPUTER PROGRAM
C
C
C Dr. HAMDY YOUSSEF, THE UNIVERSITY OF MONTREAL-CANADA
C
C
C
C SYMBOLS DECODING
C
C T = TEMPERATURE
C DELTAD = MACHINE SPEED
C SIGMA3 = CONFINING PRESSURE
C
C L = LENGTH
C WT = TOTAL WEIGHT
C WD = DRY WEIGHT
C GS = SOIL SOLIDS SPECIFIC GRAVITY
C GI = ICE SPECIFIC GRAVITY
C
C AMVL1 = LOAD CELL CALIBRATION FACTOR(Yl= M1*X1)
C AMVL2 = LOAD CELL CALIBRATION FACTOR(Y2= M2*X2)
C TIME(I)= TIME OF READING
C LMV(I) = LOAD CELL OUTPUT
C VMV(I) = BURETTE TUBE OUTPUT (VOLUME CHANGE MEASUREMENTS)
C
C IREL(I)= 0 THE DATA LINE IS NOT A RELAXATION ONE
C IREL(I)# 0 THE DATA LINE IS A RELAXATION ONE
C
REAL P(250), Q(250), SIGMOC(250),TAUOCT(250),STRRAT(250),
1STRAIN(250), L,LMV(250),LOADK(250),SIGMAD(250),
2SIGMA1(250), OCTSTR(250),VMV(250),VOLSTR(250),
3SIGMAI(250), TIMEI(250),SORTT(250),LOGT(250),X(250),Y(250)
INTEGER TIME(250), IREL(250)
COMMON TESTNO
C
C ITEST= 1 TEST UNCONSOLIDATED UNDRAINED
C ITEST= 2 TEST UNCONSOLIDATED DRAINED
C IPLOT= 0 NO PLOTTING OUTPUT
C IPLOT# 0 PLOTTING OUTPUT
C
C CHECK TYPE OF TEST
C
C
READ(5,*) TESTNO
WRITE(6,500) TESTNO
500 FORMAT(1X,'TEST NUMBER = S',F6.0,///)
C
READ(5,*) LMVI
READ(5,*) ITEST,IPLOT
IF(ITEST.NE.1) GO TO 1
WRITE(6,600)
600 FORMAT(1X,'TEST UNCONSOLIDATED UNDRAINED')
C
GO TO 100
1 CONTINUE
IF(ITEST.EQ.2) GO TO 2
WRITE(6,601)
601 FORMAT(1X,'ITEST PARAMETER WRONG')
GO TO 106
2 WRITE(6,602)
602 FORMAT(1X,'TEST UNCONSOLIDATED DRAINED')
C
100 CONTINUE
IF(IPLOT.NE.0) GO TO 3
WRITE(6,603)
603 FORMAT(///,' NO PLOTTING OUTPUT ')
GO TO 101
3 WRITE(6,604)
604 FORMAT (1X,' PLOTTING OUTPUT OPTION ')
C
101 CONTINUE
C
C READING OF THE SAMPLE AND TEST PARAMETERS
C
C
IF(ITEST.EQ.2) GO TO 4
C
C TESTS WITHOUT VOLUME CHANGE MEASUREMENTS
C READING THE SAMPLE AND TEST DATA
C
C
WRITE(6,501)
501 FORMAT (1X,'SAMPLE AND TEST DATA')
READ (5,*) L,D,WT,WD,GS,GI,AMVL1,AMVL2,DELTAD,
1GAMAW,T,SIGMA3
WRITE(6,605) L,D,WT,WD,GS,GI,AMVL1,AMVL2,DELTAD,
1GAMAW,T,SIGMA3
605 FORMAT(' L= ',F13.5,/,’ D= ',F13.5,/,’ WT= ',F13.5,/,
+’ WD= ',F13.5,/,’ GS= ‘,F13.5,/,’ GI= ',F13.5,/,
+ ‘AMVL1=’,F13.5,/,
+’ AMVL2= ‘,F13.5,/,’ DELTAD= ',F13.5,/,’ GAMAW= ‘,F13.5,
+/,’TEMPERATURE= ‘,F13.5,/,‘SIGMA3= ',F13.5,///)
GO TO 102
C
C TESTS WITH VOLUME CHANGE MEASUREMENTS
C READING THE SAMPLE AND TEST DATA
C
C
4 WRITE(6,502)
502 FORMAT(1X,’ SAMPLE AND TEST DATA ‘)
READ(5,*) L,D,WT,WD,GS,GI,AMVL1,AMVL2,AMVV,DELTAD,
+GAMAW,T,SIGMA3
WRITE(6,6O6) L,D,WT,WD,GS,GI,AMVL1,AMVL2,AMVV,DELTAD,
+GAMAW,T,SIGMA3
606 FORMAT (1X,' L= ',F13.5,/,’ D= ‘,F13.5,/,’ WT= ' ,F13.5,
+/,' WD= ‘,F13.5,/,’ GS= ‘,F13.5,/,’ GI= ‘,F13.5,/,
+’ AMVL1= ‘,F13.5,/,’ AMVL2= ',F13.5,/,’ AMVV= ‘,F13.5,
+/,’ DELTAD= ' ,F13.5,/,’ GAMAW= ‘,F13.5,/,' TEMPERATURE= ‘,
+F13.5,/,’ SIGMA3= ',F13.5,///)
102 CONTINUE
C
C CALCULATIONS OF THE SAMPLE PARAMETERS
C
C
A= 0.7854* D* D
V= A* L
GAMAT= WT/V
GAMAD= WD/V
WICE= WT- WD
WI= (WICE/WD)* 100.
VICE= WICE/(GI* GAMAW)
VSOLID= WD/(GS* GAMAW)
VVOIDS= V- VSOLID
SI= (VICE/VVOIDS)* 100.
VOIDSR= GS*V/WD- 1.
VISR= VICE/VSOLID
STRANR= DELTAD/(L*60.)
C
WRITE(6,503)
503 FORMAT(1X,‘SAMPLE INFORMATION ')
WRITE(6,607) A,V,GAMAT,GAMAD,WICE,WI,VICE,VSOLID,VVOIDS,
+SI,VOIDSR,VISR,STRANR
607 FORMAT (‘ A= ',F13.5,/,’V= ‘,F13.5,/,‘GAMAT= ',F13.5,/,
+’ GAMAD= ',F13.5,/,' WICE= ',F13.5,/,' WI= ',F13.5,/,
+’ VICE= ‘,F13.5,/,’ VSOLID= ',F13.5,/,' VVOIDS= ‘,F13.5,/,
+’ SI= ',F13.5,/,’ VOIDSR= ‘,F13.5,/,’ VISR= ',F13.5,/,
+' STRANR= ‘,F13.7,///)
I= 0
IF(ITEST.EQ.2) GO TO 103
WRITE(6,50)
50 FORMAT (1X,‘R’,2X,‘TIME’,5X,‘LMV',//)
104 I= I+1
C
C TESTS WITHOUT VOLUME CHANGE MEASUREMENTS
C READING THE TIME AND TEST OUTPUT IN MV
C
READ(5,*,END=999) IREL(I),TIME(I),LMV(I)
WRITE (6,608) IREL(I),TIME(I),LMV(I)
LMV(I) = LMV(I)- LMVI
608 FORMAT(1X,I1,1X,I5,1X,F13.5)
GO TO 104
999 NT=I-1
CALL CALCUL(STRANR,A,AMVL1,AMVL2,SIGMA3,NT,IREL,TIME,LMV,
+LOADK,SIGMAD,SIGMA1,P,Q,SIGMOC,TAUOCT,STRRAT,STRAIN,
OCTSTR,
+SIGMAI,TIMEI,SQRTT,LOGT)
WRITE (6,506)
C
C CALCULATIONS OF STRESSES AND STRAINS
C
C
DO 5 I= 1,NT
IF(IREL(I).NE.0) GO TO 6
WRITE(6,609)I,IREL(I),TIME(I),SIGMAD(I),SIGMA1(I)
+,P(I),Q(I),
+SIGMOC(I),TAUOCT(I),STRRAT(I),STRAIN(I),OCTSTR(I)
609 FORMAT(1X,I3,1X,Il,1X,I5,9(1X,F5.2))
GO To 5
506 FORMAT (3X,'N',2X,'R',2X,'TIME',1X,'SIGMD',
+1X,'SIGM1',3X,'P',4X,'Q',3X,'SIGOC',1X,
+'TAUOC',1X,'S1/S3',1X,’STRAIN',1X,'OCSTR’,6X,
+'SIGMI' ,4X,'TIMEI',8X,'SQRTT',5X,’LOGT',///)
6 CONTINUE
IF (TIME(I).GT.1)GO TO 60
WRITE(6,550)
550 FORMAT(lX, 'STRESS- RELAXATION RESULTS ',/)
60 WRITE(6,610) I,IREL(I),TIME(I),SIGMAD(I),SIGMA1(I),
+P(I),Q(I),SIGMOC(I),TAUOCT(I),STRRAT(I),STRAIN(I),
+OCTSTR(I),SIGMAI(I),TIMEI(I),SQRTT(I),LOGT(I)
610 FORMAT (1X,I3,1X,I1,1X,I5,9(1X,F5.2),1X,F10.4,1X,F10.7,
+2(1X,F10.3)
5 CONTINUE
GO TO 105
C
C TESTS WITH VOLUME CHANGE MEASUREMENTS
C READING OF THE SAMPLE AND TEST DATA
C
103 WRITE(6,507)
507 FORMAT(1X,'R’,3X,'TIME’,7X,'LMV’,11X,'VMV’,///)
2103 I= I+1
READ (5,*, END=998) IREL(I),TIME(I),LMV(I),VMV (I)
WRITE(6,611) IREL(I),TIME(I),LMV(I),VMV(I)
LMV(I) = LMV(I)- LMVI
611 FORMAT(1X,I1,2X,I5,2(1X,F13.5))
GO TO 2103
C
C CALCULATIONS OF STRESSES, STRAINS, AND VOLUME CHANGE
C
C
998 NT= I-1
CALL CALCUL(STRANR,A,AMVL1,AMVL2,S1GMA3,NT,IREL,TIME,LMV,
+LOADK,SIGMAD,SIGMA1,P,Q,SIGMOC,TAUOCT,STRRAT,STRAIN,
OCTSTR,
+SIGMAI,TIMEI,SQRTT,LOGT)
VOLUM1= AMVV* VMV(1)
WRITE(6,508)
DO 7 I= 1,NT
VOLUM= AMVV* VMV(I)
DELTVA= VOLUM- VOLUM1
IF(IREL(I).NE.0) GO TO 8
DELTVP= .01937* TIME(I)
DELTAV= DELTVA-DELTVP
VOLSTR(I)= (DELTAV/V)* 100.
508 FORMAT(3X,'N',2X,'R’,2X,’TIME',1X,'SIGMD',
+1X,‘SIGM1',3X,'P',4X,‘Q',3X,'SIGOC’,1X,'TAUOC’
+,1X,’S1/S3',1X,'STRAIN',1X,'OCTST',1X,’VOLSTR’,///)
WRITE(6,612) I, IREL(I),TIME(I),SIGMAD(I),SIGMA1(I),
+P(I),Q(I),SIGMOC(I),TAUOCT(I),STRRAT(I),STRAIN(I),
+OCTSTR(I),VOLSTR(I)
612 FORMAT(1X,I3,1X,I1,1X,I5,9(1X,F5.2),1X,F6.2)
GO TO 7
8 CONTINUE
DELTAV= DELTVA
VOLSTR(I)= (DELTAV/V)* 1O0.
IF(TIME(I).GT.1)GO TO 9
WRITE(6,509)
509 FORMAT(2X,'N',2X,‘R',3X,‘TIME',1X,'SIGMD',2X,
+'SIGM1',5X,'P',5X,'Q',3X,'SIGMOC',2X,'TAUOC',
+2X,’S1/S3',2X,'STRAIN',2X,'OCTSR',2X,’VOLSTN’,
+3X, 'SIGMI',5X,'TIMEI’,6X,'SQRTT',5X,'LOGT’,///)
9 WRITE(6,613)I,IREL(I),TIME(I),SIGMAD(I),SIGMA1(I),
+P(I),Q(I),SIGMOC(I),TAUOCT(I),STRRAT(I),STRAIN(I),
+OCTSTR(I),VOLSTR(I),SIGMAI(I),TIMEI(I),SQRTT(I),LOGT(I)
613 FORMAT(1X,I3,1X,I1,1X,I5,10(1X,F6.2),2X,F6.4,3(1X,F10.3))
7 CONTINUE
105 CONTINUE
C GRAPHICS OUTPUT OF THE EXPERIMENTAL RESULTS
C
IF(IPLOT.EQ.0) GOTO 106
CALL PLOT (0,0,14)
CALL SPMESS (27,'PLUME L3 ENCRE NOIRE s.v.P.’)
CALL FACTOR (1./2.54)
C
C PLOT THE GRAPHIC OF STRAIN vs. SIGMAD
CALL GRAPH (STRAIN,SIGMAD,NT,’STRAIN(%)',9,’DEVI.STRESS',
+11,0.,2.,0.,10.,1)
C
C PLOT THE GRAPH1C OF STRAIN vs. STRRAT
CALL GRAPH (STRAIN,STRRAT,NT,'STRAIN(%)‘,9,’SIGM1/SIGM3’,
+11,0.,2.,0.,3.,1)
C
C PLOT THE GRAPHIC OF STRAIN vs. OCTSTR
CALL GRAPH (STRAIN,OCTSTR,NT,’STRAIN(%)’,9,'OCT.STRESSES’,
+12,0.,2.,0.,3.,1)
C
C PLOT THE GRAPH1C OF STRAIN vs. SIGMOC
CALL GRAPH (STRAIN,SIGMOC,NT,'STRAIN(%)',9,'SIGMA OCT.’,
+10,0.,2.,0.,5.,1)
C
C PLOT THE GRAPHIC OF STRAIN vs. TAUOCT
CALL GRAPH (STRAIN,TAUOCT,NT,'STRAIN(%)’,9,'TAU OCT.',
+8,0.,2.,0.,5.,1)
C
C PLOT THE GRAPH1C OF STRAIN vs. VOLSTR
IF(ITEST.EQ.2) CALL GRAPH (STRAIN,VOLSTR,NT,'STRAIN(%)',9,
+'VOL.STRAIN’,10,0.,2.,-5.,2.,1)
C
C DRAW THE STRESS-RELAXATION CURVES
C
I=1
1100 IF(I.LE.NT) GOTO 1101
GOTO 1102
1101 CONTINUE
1200 IF(IREL(I).EQ.0) GOTO 1201
GOTO 1202
1201 I= I+1
IF(I.GT.NT) GOTO 1000
GOTO 1200
1202 CONTINUE
N= 0
ND= I
NF= ND
1300 IF(IREL(I).EQ.1) GOTO 1301
GOTO 1302
1301 N= N+1
X(N)= TIME(I) *1.
Y(N)= SIGMAD(I)
NF= NF+1
I= I+1
IF(I.GT.NT) GOTO 1010
GOTO 1300
1302 CONTINUE
1010 CONTINUE NF= NF-1
C PLOT THE GRAPHIC OF TIME VS. SIGMAD
CALL GRAPH(X,Y,N,’TIME’,4,’DEVI.STRESS',11
+ ,0.,0.,0.,10.,1)
C
C PLOT THE GRAPHIC OF LOG(TIME) VS. SIGMAD
CALL GRAPH(X,Y,N,’LOG(TIME)‘,9,’DEVI.STRESS’,11 ,0.,0.,
+0. ,10. ,2)
C
C PLOT THE GRAPHIC OF TIMEI VS. SIGMAD
N= 0
DO 1020 J= ND,NF
N= N+1
1020 X(N)= TIMEI (J)
CALL GRAPH(X,Y,N,’1/TIME’ ,6,’DEVI.STRESS’ ,11,0. ,0.,0.
,10.,1)
C
C PLOT THE GRAPHIC OF SQRTT VS. SIGMAD
N= 0
DO 1030 J=ND,NF
N= N+1
1030 X(N)= SQRTT (J)
CALL GRAPH(X,Y,N,’SQRT(TIME) ‘,10,’DEVI.STRESS’,11,0.,0.,
+ 0.,10. ,1)
C
C PLOT THE GRAPHIC OF LOG(TIME) VS. SIGMAI
N= O
DO 1040 J= ND,NF
N= N+1
X(N)= TIME (J)
1040 Y(N)= SIGMAI(J)
CALL GRAPH(X,Y,N,’LOG(T1ME) ‘,9,’1/DEVI.STRESS’,13,
+ 0.,0.,0.,0.03,2)
C
C PLOT THE GRAPHIC OF TIMEI VS. SIGMAI
N= O
DO 1050 J= ND,NF
N= N+1
1050 X(N)= TIMEI(J)
CALL GRAPH(X,Y,N,’1/TIME’,6,’1/DEVI.STRESS’,13,
+ 0.,0.,0.,0.03,1)
1000 GOTO 11OO
1102 CONTINUE
C END OF PLOTTING
C
CALL PLOT (0., 0.,999)
106 CONTINUE
RETURN
END
C
C SUBROUTINE TO CALCULATE STRESSES AND STRAINS
C
C
SUBROUTINE CALCUL
+(STRANR,A,AMVL1,AMVL2,S1GMA3,NT,IREL,TIME,LMV,
1LOADK,SIGMAD,SIGMA1,P,Q,SIGMOC,TAUOCT,STRRAT,STRAIN,
OCTSTR,
2SIGMAI,TIMEI,SQRTT,lOGT)
C
REAL P(NT),Q(NT),SIGMOC(NT),TAUOCT(NT),STRRAT(NT),
1STRAIN(NT),LMV(NT),LOADK(NT),SIGMAD(NT),SIGMA1(NT),
2OCTSTR(NT),SIGMAI(NT),TIMEI(NT),SQRTT(NT),LOGT(NT)
INTEGER TIME(NT), IREL(NT)
DO 4 I= 1,NT
C
IF(LMV(I)-100.) 1,1,2
1 LOADK(I)= 0.454* AMVL1* LMV(I)
GOTO 3
C
2 LOADK(I)= 0.454* AMVL2* LMV (I)
C
3 SIGMAD(I)= LOADK(I)/A
SIGMA1(I)= SIGMAD(I)+ SIGMA3
P(I)= (SIGMA1(I)+ SIGMA3)/2.
Q(I)= SIGMAD(I)/2.
SIGMOC(I)= (SIGMA1(I)+2.*SIGMA3)/3.
TAUOCT(I)= SIGMAD(I)*0.4714
STRRAT(I)= SIGMA1 (I)/SIGMA3
STRAIN(I)= STRANR*TIME(I)*6000.
OCTSTR(I)= TAUOCT(I) /SIGMOC(I)
C
IF(IREL(I).EQ.0) GOTO 4
IF(SIGMAD(I).EQ.0) SIGMAI (I) = 0.
SIGMAI(I)= 1./SIGMAD (I)
IF(TIME(I).EQ.0) TIME(I)= 1
TIMEI(I)= 1./TIME (I)
TT= 1.*TIME(I)
SQRTT(I)= SQRT(TT)
LOGT(I)= ALOG10 (TT)
STRAIN(I)= STRAIN (I-1)
C
4 CONTINUE
RETURN
END
C
C GRAPHICS SUBROUTINE
C
C
SUBROUTINE GRAPH(X,Y,NT,TITX,ITITX,TITY,ITITY,XMIN,DX,
+YMIN,DY,IAXEX)
C
C X : ARRAY CONTAINING X VALUES TO BE PLOTTED
C Y : ARRAY CONTAINING Y VALUES TO BE PLOTTED
C NT: TOTAL NUMBER OF POINTS TO BE PLOTTED
C TITX : TITLE ON X AXIS
C ITITX: NUMBER OF CHARACTERS IN TITX
C TITY : TITLE OF Y AXIS
C ITITY: NUMBER OF CHARACTERS IN TITY
C XMIN : DEFAULT MINIMUM VALUE OF BEGINNING X AXIS
C DX : DEFAULT VALUE OF 1 CM IN X AXIS
C YMIN : SAME AS XMIN FOR Y AXIS
C DY : SAME AS DX FOR Y AXIS
C IAXEX: IF = 1 THE GRAPHIC IS LINEAR IN X AND Y
C IF = 2 THE GRAPHIC IS SEMI-LOGARITHMIC IN X AXIS
C
REAL X(1),Y(1),TITX(1),TITY(1)
COMMON TESTNO
X(NT+1)= XMIN
X(NT+2)= DX
Y(NT+1)= YMIN
Y(NT+2)= DY
IF(DX.EQ.0.0.AND.IAXEX.EQ.1)CALL SCALE(X,10.,NT,1)
IF(Dx.EQ.0.0.AND.IAXEX.NE.1)CALL SCALG(X,10.,NT,1)
IF(DY.EQ.0.0)CALL SCALE(Y,10.,NT,1)
C
C DRAW A 11” x 8.5” FRAME
CALL PLOT(0.,-27.94,-3)
CALL RECT(O.,0.,27.94,21.59,0.,3)
C DRAW THE INNER FRAME
CALL PLOT(4.,2.,-3)
CALL RECT(0.,0.,21.94,15.59,0.,3)
C DRAW THE AXIS
CALL PLOT(2.8,6.,-3)
IF(IAXEX.EQ.1)CALL AXIS(0.,0.,TITX,-ITITX,10.,0.,X(NT+1),
+X(NT+2))
IF(IAXEX.NE.1)CALL LGAXS(0.,0.,TITX,-ITITX,10. ,0.,X(NT+1),
+X(NT+2))
CALL AXIS(0.,0.,TITY,ITITY,10.,90.,Y(NT+1) ,Y(NT+2))
IF(IAXEX.EQ.1)CALL LINE(X,Y,NT,1,1,3)
IF(IAXEX.NE.1)CALL LGLIN(X,Y,NT,1,1,3,-1)
CALL PLOT(-6.8,-8.,-3)
CALL SYMBOL(5.0,23.,0.5,’TEST NUMBER= S',0.,15)
CALL NUMBER(12.5,23.,0.5,TESTNO,0.,-1)
CALL PLOT(25.,27.94,-3)
CALL SEPARE
RETURN
END
5.5 FROZENSOIL.1-Input Data and Output Results
Before start testing frozen soil sample in the triaxial cell, the sample dimensions
as well as its total weight are recorded. The test temperature and confining
pressure applied are also recorded, along with the speed of the compression
machine (d) for the predetermined controlled (constant) strain rate. The
calibration factors of the load cell, and that of the deferential pressure
transducer utilized for volume change measurements are to be also recorded.
At the start of the testing procedures, the initial reading of the load cell, and that
of the antifreeze height in the volume change transducer burette tube has to be
recorded. During testing, the time of each experimental reading, the deviatoric
stress, and the volume change (the change of the liquid height in the burette)
are recorded for a preset chosen time intervals and recorded automatically by
utilizing a data acquisition system.
The triaxial cell piston cross- section area is determined for the calculations of
the actual volume change of the frozen sample by subtracting the volume
change due to the piston penetration. The dry weight of the frozen sample (Wd)
has to be determined after completing the test by placing the sample in a
porcelain dish in a heated oven, and then measure the dry weight of the soil
particles. For each sample tested, the test number is identified.
The above procedures have to be followed for each test type: with or without
volume change measurements, and with or without stress- relaxation cycle (or
cycles). For the stress- relaxation tests, the level (or levels) of the relaxation
strain (eR) has to be introduced as input to the computer program. All the
above parameters are the data entry (input) to the developed program
FROZENSOIL.1.
The entry data are introduced to the computer program through four input
cards (statements) followed by set of statements (cards), each for the
experimental results at the time of recording. These are in the following order:
First Card: Test number
Second Card: Initial reading of the load cell (LMV(I)),and initial reading of the
volume change differential pressure transducer reading* (VMV(I).
Third Card: Type of test: (with or without volume change measurements), and
the plotting option: (ITEST, and IPLOT).
Fourth Card: The sample and test data (L, D, WT, GS, GI, AMVL1, AMVL2,
AMVV*, DELTAD, GAMAW, T, and SIGMA3)
Data set cards: Relaxation index (IRE> 0 for stress relaxation tests), the time of
reading, the load cell reading (LMV(I)), and the volume change reading (VMV(I)).
* For test, with volume change measurements.
The number of the reading of the point, n (I= 1,n) has a maximum of n= 248 sets
(experimental points results on each output curve for the tested frozen sample).
All data entry are in a free format, unless the readings formats are modified. For
sand, the specific gravity (Gs) is equal to 2.65, for ice Gi= 0.917,and GAMAW
(gw)= 1 gm/cm3. The specific gravity for other type of soils can be recalled from
the soil mechanics literature.
The frozen sample dimensions (L, D) are in cm, the weights (WT, WD) are in
gm, the confining pressure (s3= scell) is in kg/cm2, the temperature (T) is in 0C,
the load cell calibration factors (AMVL1, AMVL2) are in kg/mV, and the volume
change differential pressure transducer calibration factor (AMVV) is in cm3/mV,
where mV is in mille volt.
The FROZENSOIL.1 input data and the calculated experimental results, are to
be printed with all the required graphics plotted in the computer program output.
Typical results for both types of tests namely, strain rate compression and
stress- relaxation are presented in detail in the present chapter. These are for
test number (FS2- Tables 1, 2), and test number (FS29R- Tables 3).
5.5.1 Triaxial Constant Strain Rate Compression Tests
Typical FROZENSOIL.1 Output- Test FS2
Test Number= FS2
Test with Volume Change Measurements
Sample and Test Data
L= 7.75
D= 3.79
WT= 168.24
WD= 137.30
GS= 2.65
GI= 0.917
AMVL1= 3.60
AMVL2= 3.87
AMVV= 0.0925
DELTAD= 0.0152
GAMAW= 1.00
Temperature= -5
SIGMA3= 4.926
Sample Information
A= 11.28
V= 87.43
GAMAT= 1.924
GAMAD= 1.57
WICE= 30.94
WI= 22.535
VICE= 33.74
VSOLID= 51.81
VVOIDS= 35.62
SI= 94.72
VOIDSR= 0.651
VISR= 0.651
STRANR= 0.0000328
Table 9. Triaxial Compression Tests-FROZENSOIL.1 Input Data
N R TIME LMV VMV
1 0 0 00.00 377.00
2 0 1 18.00 377.00
3 0 2 70.00 376.00
4 0 3 121.00 376.00
5 0 4 172.00 375.00
6 0 5 224.00 375.00
7 0 6 271.00 374.00
8 0 7 314.00 374.00
9 0 8 351.00 374.00
10 0 9 380.00 373.00
11 0 10 402.00 373.00
12 0 11 403.00 374.00
13 0 12 427.00 374.00
14 0 13 443.00 374.00
15 0 14 455.00 374.00
16 0 15 466.00 375.00
17 0 16 474.00 376.00
18 0 17 482.00 376.00
19 0 18 487.00 376.00
20 0 19 492.00 377.00
21 0 20 494.00 378.00
22 0 21 495.00 378.00
23 0 23 490.00 380.00
24 0 25 481.00 383.00
25 0 30 444.00 389.00
26 0 35 397.00 396.00
27 0 40 349.00 403.00
28 0 45 303.00 410.00
29 0 50 272.00 416.00
30 0 55 251.00 423.00
31 0 60 237.00 428.00
32 0 65 223.00 433.00
33 0 70 214.00 438.00
34 0 75 206.00 442.00
35 0 80 200.00 446.00
36 0 83 198.00 448.00
37 0 86 190.00 450.00
Table 10. Triaxial compression tests-FROZENSOIL.1 Output results
N R TIME SIGMAD SIGM1 P
Q SIGOC
1 0 0 0.00 4.93 4.93 0.00 4.93
2 0 1 2.61 7.53 6.23 1.30 5.80
3 0 2 10.14 15.07 10.00 5.07 8.31
4 0 3 18.84 23.77 14.35 9.42 11.21
5 0 4 26.79 31.71 18.32 13.39 13.86
6 0 5 34.89 39.81 22.37 17.44 16.55
7 0 6 42.21 47.13 26.03 21.10 18.99
8 0 7 48.90 53.83 29.38 24.45 21.23
9 0 8 54.66 59.59 32.26 27.33 23.15
10 0 9 59.18 64.11 34.52 29.59 24.65
11 0 10 62.61 67.53 36.23 31.31 25.80
12 0 11 62.76 67.69 36.31 31.38 25.85
13 0 12 66.50 71.43 38.18 33.25 27.09
14 0 13 68.99 73.92 39.42 34.50 27.92
15 0 14 70.86 75.79 40.36 35.43 28.55
16 0 15 72.57 77.50 41.21 36.29 29.12
17 0 16 73.82 78.75 41.84 36.91 29.53
18 0 17 75.07 79.99 42.46 37.53 29.95
19 0 18 75.84 80.77 42.85 37.92 30.21
20 0 19 76.62 81.55 43.24 38.31 30.47
21 0 20 76.94 81.86 43.39 38.47 30.57
22 0 21 77.09 82.02 43.47 38.55 30.62
23 0 23 76.31 81.24 43.08 38.16 30.36
24 0 25 74.91 79.84 42.38 37.46 29.90
25 0 30 69.15 74.07 39.50 34.57 27.98
26 0 35 61.83 66.75 35.84 30.91 25.54
27 0 40 54.35 59.28 32.10 27.18 23.04
28 0 45 47.19 52.11 28.52 23.59 20.66
29 0 50 42.36 47.29 26.11 21.18 19.05
30 0 55 39.09 44.02 24.47 19.55 17.96
31 0 60 36.91 41.84 23.38 18.46 17.23
32 0 65 34.73 39.66 22.29 17.36 16.50
33 0 70 33.33 38.25 21.59 16.66 16.04
34 0 75 32.08 37.01 20.97 16.04 15.62
35 0 80 31.15 36.07 20.50 15.57 15.31
36 0 83 30.84 35.76 20.34 15.42 15.20
37 0 86 29.59 34.52 19.72 14.80 14.79
Table 10. Triaxial compression tests-FROZENSOIL.1 Output results (continue)
N R TIME TAUOC S1/S2 STRAIN OCTST
VOLSTR
1 0 0 0.00 1.00 0.00 0.00 0.00
2 0 1 1.23 1.53 0.20 0.21 .02
3 0 2 4.78 3.06 0.39 0.58 0.15
4 0 3 8.88 4.83 0.59 0.79 0.17
5 0 4 12.63 6.44 0.79 0.91 0.30
6 0 5 16.45 8.08 0.98 0.99 0.32
7 0 6 19.90 9.57 1.18 1.05 0.45
8 0 7 23.05 10.93 1.38 1.09 0.47
9 0 8 25.77 12.10 1.57 1.11 0.49
10 0 9 27.90 13.01 1.77 1.13 0.62
11 0 10 29.51 13.71 1.97 1.14 0.64
12 0 11 29.59 13.74 2.16 1.14 0.56
13 0 12 31.35 14.50 2.36 1.16 0.58
14 0 13 32.52 15.01 2.56 1.16 0.61
15 0 14 33.40 15.39 2.75 1.17 0.63
16 0 15 34.21 15.73 2.95 1.17 0.54
17 0 16 34.80 15.99 3.15 1.18 0.46
18 0 17 35.39 16.24 3.34 1.18 0.48
19 0 18 35.75 16.40 3.54 1.18 0.50
20 0 19 36.12 16.55 3.74 1.19 0.42
21 0 20 36.27 16.62 3.93 1.19 0.34
22 0 21 36.34 16.65 4.13 1.19 0.36
23 0 23 35.97 16.49 4.52 1.18 0.19
24 0 25 35.31 16.21 4.92 1.18 0.08
25 0 30 32.60 15.04 5.90 1.17 0.60
26 0 35 29.15 13.55 6.88 1.14 1.23
27 0 40 25.62 12.03 7.87 1.11 1.86
28 0 45 22.24 10.58 8.85 1.08 2.49
29 0 50 19.97 9.60 9.83 1.05 3.02
30 0 55 18.43 8.94 10.82 1.03 3.65
31 0 60 17.40 8.49 11.80 1.01 4.07
32 0 65 16.37 8.05 12.78 0.99 4.48
33 0 70 15.71 7.77 13.77 0.98 4.90
34 0 75 15.12 7.51 13.75 0.97 5.22
35 0 80 14.68 7.32 15.73 0.96 5.53
36 0 83 14.54 7.26 16.32 0.96 5.67
37 0 86 13.95 7.01 16.91 0.94 5.82
Fig. 34 FROZENSOIL.1: Triaxial compression results
Deviatoric stresses as a function of strain
Fig. 35 FROZENSOIL.1: Triaxial compression results
Major to minor stress ratio as a function of strain
Fig. 36 FROZENSOIL.1: Triaxial compression results
Octahedral stresses ratio as a function of strain
Fig. 37 FROZENSOIL.1: Triaxial compression results
Octahedral normal stresses as a function of strain
Fig. 38 FROZENSOIL.1: Triaxial compression results
Octahedral shear stresses as a function of strain
Fig. 39 FROZENSOIL.1: Triaxial compression results
Volume change as a function of strain
5.5.2 TRIAXIAL STRESS-RELAXATION OF FROZEN SOILS
TYPICAL TEST RESULTS (FS29R)
TEST NUMBER= FS29R
Test without Volume Change Measurements
Sample and Test Data
L= 7.966
D= 3.766
WT= 178.20
WD= 150.00
GS= 2.65
GI= 0.917
AMVL1= 3.60
AMVL2= 3.87
DELTAD= 0.01524
GAMAW= 1.00
Temperature= -5
SIGMA3= 4.571
Sample Information
A= 11.139
V= 88.734
GAMAT= 2.008
GAMAD= 1.6904
WICE= 28.20
WI= 18.80
VICE= 30.752
VSOLID= 56.603
VVOIDS= 32.13
SI= 95.711
VOIDSR= 0.568
VISR= 0.5433
STRANR= 0.0000319
Table 11. Triaxial stress-relaxation tests-FROZENSOIL.1 Input data
N R TIME LMV
1 0 0 0
2 0 1 11
3 0 2 63
4 0 3 110
5 0 4 156
6 0 5 220
7 1 1 212
8 1 2 195
9 1 3 186
10 1 4 179
11 1 5 173
12 1 6 169
13 1 7 165
14 1 8 162
15 1 9 159
16 1 10 156
17 1 11 154
18 1 12 152
19 1 13 150
20 1 14 148
21 1 15 147
22 1 16 145
23 1 17 143
24 1 18 142
25 1 19 141
26 1 20 139
27 1 22 137
28 1 24 135
29 1 26 133
30 1 28 131
31 1 30 130
32 1 32 128
33 1 34 127
34 1 36 125
35 1 38 124
36 1 40 123
37 1 42 121
Table 11. Triaxial-stress-relaxation tests-FROZENSOIL.1 Input data (continue)
N R TIME LMV
38 1 46 120
39 1 51 118
40 1 56 115
41 1 61 113
42 1 66 111
43 1 71 110
44 1 76 108
45 1 81 107
46 1 86 105
47 1 91 104
48 1 96 103
49 1 101 102
50 1 111 100
51 1 116 99
52 1 121 98
53 1 126 97
54 1 131 96
55 1 136 96
56 1 141 95
57 1 146 94
58 1 151 93
59 1 156 93
60 1 161 92
61 1 166 92
62 1 176 90
63 1 186 89
64 1 206 87
65 1 226 86
66 1 246 84
67 1 256 83
68 1 266 83
69 1 296 81
70 1 326 79
71 1 356 77
72 1 386 76
73 1 416 74
74 1 446 73
75 1 476 72
76 1 506 71
Table 11. Triaxial stress-relaxation tests-FROZENSOIL.1 Input data
(continue)
N R TIME LMV
77 1 536 70
78 1 566 69
79 1 596 68
80 1 626 67
81 1 656 66
82 1 686 65
83 1 716 64
84 1 746 63
85 1 776 63
86 1 806 62
87 1 866 61
88 1 896 60
89 1 926 59
90 1 956 59
91 1 986 58
92 1 1016 59
93 1 1046 57
94 1 1076 56
95 1 1106 56
96 1 1136 56
97 1 1166 55
98 1 1196 55
99 1 1226 54
100 1 1286 54
101 1 1316 53
102 1 1376 52
103 1 1406 52
104 1 1436 52
105 1 1466 52
106 1 1496 52
107 1 1526 52
108 1 1556 50
109 1 1706 50
110 1 1946 47
111 1 2186 46
112 1 2426 44
113 1 2906 39
114 1 3386 39
115 1 3626 34
Table 11. Triaxial-stress-relaxation tests-FROZENSOIL.1 Input data (continue)
N R TIME LMV
116 1 3866 30
117 1 4106 22
118 1 4346 20
119 1 4586 21
120 1 4826 20
121 1 5066 20
122 1 5119 20
123 0 6 48
124 0 7 117
125 0 8 183
126 0 9 242
127 0 10 293
128 0 11 338
129 0 12 375
130 0 13 405
131 0 14 427
132 0 15 442
133 0 16 453
134 0 17 461
135 0 18 467
136 0 19 470
137 0 20 473
138 0 22 474
139 0 24 467
140 0 26 455
141 0 28 440
142 0 30 419
143 0 32 391
144 0 34 366
145 0 36 346
146 0 38 329
147 0 40 315
148 0 44 292
149 0 48 275
150 0 52 261
151 0 56 250
152 0 60 236
153 0 65 233
Table 11. Triaxial-stress-relaxation tests-FROZENSOIL.1 Input data (continue)
N R TIME LMV
154 0 70 229
155 0 75 227
156 0 80 225
157 0 85 223
158 0 90 233
159 0 95 221
160 0 100 219
Table 12. Triaxial-stress-relaxation tests-FROZENSOIL.1 Output
results
N R TIME SIGMAD SIGM1 P Q SIGOC
TAUOC S1/S2 STRAIN OCSTR SIGMI TIMEI
SQRTT LOGT
1 0 0 0 4,57 4,57 0 4,57 0 1 0
0
2 0 1 1,61 6,18 5,38 0,81 5,11 0,76
1,35 0,19 0,15
3 0 2 9,24 13,81 9,19 4,62 7,65 4,36
3,02 0,38 0,57
4 0 3 17,35 21,92 13,25 8,68 10,35
8,18 4,8 0,57 0,79
5 0 4 24,61 29,18 16,87 12,3 12,77
11,6 6,38 0,77 0,91
6 0 5 34,7 39,27 21,92 17,35 16,14
16,36 8,59 0,96 1,01
7 1 1 33,44 38,01 21,29 16,72 15,72
15,76 8,32 0,96 1 0,0299 1 1 0
8 1 2 30,76 35,33 19,95 15,38 14,82
14,5 7,73 0,96 0,98 0,0325 0,5 1,414 0,301
9 1 3 29,34 33,91 19,24 14,67 14,35
13,83 7,42 0,96 0,96 0,0341 0,333 1,732 0,477
10 1 4 28,23 32,8 18,69 14,12 13,98
13,31 7,18 0,96 0,95 0,0354 0,25 2 0,602
11 1 5 27,29 31,86 18,21 13,64 13,67
12,86 6,97 0,96 0,94 0,0366 0,2 2,236 0,699
12 1 6 26,66 31,23 17,9 13,33 13,46
12,57 6,83 0,96 0,93 0,0375 0,1666 2,449 0,778
13 1 7 26,03 30,6 17,58 13,01 13,25
12,27 6,69 0,96 0,93 0,0384 0,1429 2,646 0,845
14 1 8 25,55 30,12 17,35 12,78 13,09
12,05 6,59 0,96 0,92 0,0391 0,125 2,828 0,903
15 1 9 25,08 29,65 17,11 12,54 12,93
11,82 6,49 0,96 0,91 0,0399 0,111 3 0,954
16 1 10 24,61 29,18 16,87 12,3 12,77
11,6 6,38 0,96 0,91 0,0406 0,1 3,162 1
17 1 11 24,29 28,86 16,72 12,15 12,67
11,45 6,31 0,96 0,9 0,0412 0,0909 3,317 1,041
18 1 12 23,97 28,55 16,56 11,99 12,56
11,3 6,25 0,96 0,9 0,0417 0,0833 3,464 1,079
19 1 13 23,66 28,23 16,4 11,83 12,46
11,15 6,18 0,96 0,9 0,0423 0,0769 3,606 1,114
20 1 14 23,34 27,92 16,24 11,67 12,35
11 6,11 0,96 0,89 0,0428 0,0714 3,742 1,146
Table 12. Triaxial-stress-relaxation tests-FROZENSOIL.1 Output results
(continue)
N R TIME SIGMAD SIGM1 P Q SIGOC
TAUOC S1/S2 STRAIN OCSTR SIGMI TIMEI
SQRTT LOGT
21 1 15 23,19 27,76 16,16 11,59 12,3
10,93 6,07 0,96 0,89 0,0431 0,0667 3,873 1,176
22 1 16 22,87 27,44 16,01 11,44 12,19
10,78 6 0,96 0,88 0,0437 0,0625 4 1,204
23 1 17 22,56 27,13 15,85 11,28 12,09
10,63 5,93 0,96 0,88 0,0443 0,0588 4,123 1,23
24 1 18 22,4 26,97 15,77 11,2 12,04
10,56 5,96 0,96 0,88 0,0446 0,0556 4,243 1,255
25 1 19 22,24 26,81 15,69 11.12 11,98
10,48 5,87 0,96 0,87 0,045 0,0526 4,359 1,279
26 1 20 21,92 26,5 15,53 10,96 11,88
10,34 5,8 0,96 0,87 0,0456 0,05 4,472 1,301
27 1 22 21,61 26,18 15,38 10,8 11,77
10,19 5,73 0,96 0,87 0,046 0,0455 4,69 1,342
28 1 24 21,29 25,86 15,22 10,65 11,67
10,04 5,66 0,96 0,86 0,047 0,0417 4,9 1,38
29 1 26 20,98 25,55 15,06 10,49 11,56
9,89 5,59 0,96 0,86 0,0477 0,0385 5,1 1,415
30 1 28 20,66 25,23 14,9 10,33 11,46
9,74 5,52 0,96 0,85 0,0484 0,0357 5,29 1,417
31 1 30 20,5 25,08 14,82 10,25 11,41
9,67 5,49 0,96 0,85 0,0488 0,0333 5,477 1,417
32 1 32 20,19 24,76 14,67 10,09 11,3
9,52 5,42 0,96 0,84 0,0495 0,0312 5,657 1,505
33 1 34 20,03 24,6 14,59 10,02 11,25
9,44 5,38 0,96 0,84 0,0499 0,0294 5,831 1,531
34 1 36 19,72 24,29 14,43 9,86 11,14
9,29 5,31 0,96 0,83 0,0507 0,0278 6 1,556
35 1 38 19,56 24,13 14,35 9,78 11,09
9,22 5,28 0,96 0,83 0,0511 0,0263 6,164 1,58
36 1 40 19,4 23,97 14,27 9,7 11,04
9,15 5,24 0,96 0,83 0,0515 0,025 6,325 1,602
37 1 42 19,09 23,66 14,11 9,54 10,93 9
5,18 0,96 0,82 0,0524 0,02381 6,481 1,623
38 1 46 18,93 23,5 14,03 9,46 10,88
8,92 5,14 0,96 0,82 0,0528 0,02174 6,782 1,663
39 1 51 18,61 23,18 13,88 9,31 10,78
8,77 5,07 0,96 0,81 0,0537 0,01961 7,141 1,708
40 1 56 18,14 22,71 13,64 9,07 10,62
8,55 4,97 0,96 0,81 0,0551 0,0179 7,483 1,748
Table 12. Triaxial-stress-relaxation tests-FROZENSOIL.1 Output results
(continue)
N R TIME SIGMAD SIGM1 P Q SIGOC
TAUOC S1/S2 STRAIN OCSTR SIGMI TIMEI
SQRTT LOGT
41 1 61 17,82 22,39 13,48 8,91 10,51
8,4 4,9 0,96 0,8 0,0561 0,0164 7,81 1,785
42 1 66 17,51 22,08 13,33 8,75 10,41
8,25 4,83 0,96 0,79 0,0571 0,0152 8,124 1,82
43 1 71 17,35 21,92 13,25 8,68 10,35
8,18 4,8 0,96 0,79 0,0576 0,0141 8,426 1,851
44 1 76 17,03 21,61 13,09 8,52 10,25
8,03 4,73 0,96 0,78 0,0567 0,0132 8,718 1,881
45 1 81 16,88 21,45 13,01 8,44 10,2
7,96 4,69 0,96 0,78 0,0593 0,01235 9 1,908
46 1 86 16,56 21,13 12,85 8,28 10,09
7,81 4,62 0,96 0,77 0,0604 0,01163 9,274 1,934
47 1 91 16,4 20,97 12,77 8,2 10,04
7,73 4,59 0,96 0,77 0,061 0,011 9,539 1,959
48 1 96 16,25 20,82 12,69 8,12 9,99
7,66 4,55 0,96 0,77 0,0616 0,0104 9,798 1,982
49 1 101 16,09 20,66 12,62 8,04 9,93
7,58 4,52 0,96 0,76 0,0622 0,0099 10,05 2,004
50 1 111 14,67 19,24 11,91 7,34 9,4
6,92 4,21 0,96 0,73 0,0682 0,009 10,536 2,045
51 1 116 14,53 19,1 11,83 7,26 9,41
6,85 4,18 0,96 0,73 0,0688 0,00862 10,77 2,064
52 1 121 14,38 18,95 11,76 7,19 9,36
6,78 4,15 0,96 0,72 0,0695 0,00827 11 2,083
53 1 126 14,23 18,8 11,69 7,12 9,32
6,71 4,11 0,96 0,72 0,0703 0,00794 11,23 2,1
54 1 131 14,09 18,66 11,61 7,04 9,27
6,64 4,08 0,96 0,72 0,071 0,0076 11,45 2,117
55 1 136 14,09 18,66 11,61 7,04 9,27
6,64 4,08 0,96 0,72 0,071 0,0074 11,66 2,134
56 1 141 13,94 18,51 11,54 6,97 9,22
6,57 4,05 0,96 0,71 0,0717 0,0071 11,87 2,149
57 1 146 13,79 18,36 11,47 6,9 9,17
6,5 4,02 0,96 0,71 0,0725 0,00685 12,08 2,154
58 1 151 13,65 18,22 11,39 6,82 9,12
6,43 3,99 0,96 0,71 0,0733 0,0066 12,288 2,169
59 1 156 13,65 18,22 11,39 6,82 9,12
6,43 3,99 0,96 0,71 0,0733 0,0064 12,49 2,193
60 1 161 13,5 18,07 11,32 6,75 9,07
6,36 3,95 0,96 0,7 0,0741 0,00621 12,689 2,207
Table 12. Triaxial-stress-relaxation tests-FROZENSOIL.1 Output results
(continue)
N R TIME SIGMAD SIGM1 P Q SIGOC
TAUOC S1/S2 STRAIN OCSTR SIGMI TIMEI
SQRTT LOGT
61 1 166 13,5 18,07 11,32 6,75 9,07
6,36 3,95 0,96 0,7 0,0741 0,00602 12,884 2,22
62 1 176 13,21 17,78 11,17 6,6 8,97
6,22 3,89 0,96 0,69 0,0757 0,00568 13,266
2,246
63 1 186 13 17,63 11,1 6,53 8,92 6,16
3,86 0,96 0,69 0,0766 0,00538 13,638 2,27
64 1 206 12,77 17,34 10,95 6,38 8,83
6,02 3,79 0,96 0,68 0,0783 0,00485 14,353
2,314
65 1 226 12,62 17,19 10,88 6,31 8,78
5,95 3,76 0,96 0,68 0,0792 0,00443 15,033
2,354
66 1 246 12,32 16,9 10,73 6,16 8,68
5,81 3,7 0,96 0,67 0,0811 0,0041 15,684 2,391
67 1 256 12,18 16,75 10,66 6,09 8,63
5,74 3,66 0,96 0,67 0,0821 0,00391 16 2,408
68 1 266 12,18 16,75 10,66 6,09 8,63
5,74 3,66 0,96 0,67 0,0821 0,00376 16,31 2,425
69 1 296 11,88 16,46 10,51 5,94 8,53
5,6 3,6 0,96 0,66 0,0841 0,00338 17,205 2,471
70 1 326 11,59 16,16 10,37 5,8 8,43
5,46 3,54 0,96 0,65 0,0863 0,0031 18,055 2,513
71 1 356 11,3 15,87 10,22 5,65 8,34
5,33 3,47 0,96 0,64 0,0885 0,00281 18,87 2,551
72 1 386 11,15 15,72 10,15 5,58 8,29
5,26 3,44 0,96 0,63 0,0897 0,0026 19,647 2,587
73 1 416 10,86 15,43 10 5,43 8,19 5,12
3,38 0,96 0,62 0,0921 0,0024 20,4 2,62
74 1 446 10,71 15,28 9,93 5,36 8,14
5,05 3,34 0,96 0,62 0,0934 0,00224 21,12 2,65
75 1 476 10,56 15,14 9,85 5,28 8,09
4,98 3,31 0,96 0,62 0,0947 0,0021 21,817 2,678
76 1 506 10,42 14,99 9,78 5,21 8,04
4,91 3,28 0,96 0,61 0,096 0,00198 22,494 2,704
77 1 536 10,27 14,84 9,71 5,14 7,99
4,84 3,25 0,96 0,61 0,0974 0,001866 23,152
2,729
78 1 566 10,12 14,7 9,63 5,06 7,96
4,77 3,21 0,96 0,6 0,0988 0,001767 23,791
2,753
79 1 596 9,98 14,55 9,56 4,99 7,9 4,7
3,18 0,96 0,6 0,1002 0,00168 24,413 2,775
80 1 626 9,83 14,4 9,49 4,92 7,85 4,63
3,15 0,96 0,59 0,1017 0,0016 25,02 2,797
Table 12. Triaxial-stress-relaxation tests-FROZENSOIL.1 Output results
(continue)
N R TIME SIGMAD SIGM1 P Q SIGOC
TAUOC S1/S2 STRAIN OCSTR SIGMI TIMEI
SQRTT LOGT
81 1 656 9,68 14,25 9,41 4,84 7,8 4,56
3,12 0,96 0,59 0,1033 0,001524 25,613 2,817
82 1 686 9,54 14,11 9,34 4,77 7,75 4,5
3,09 0,96 0,58 0,1049 0,001458 26,192 2,836
83 1 716 9,39 13,96 9,27 4,7 7,7 4,43
3,05 0,96 0,57 0,1065 0,0014 26,76 2,86
84 1 746 9,24 13,81 9,19 4,62 7,65
4,36 3,02 0,96 0,57 0,1082 0,00134 27,313
2,873
85 1 776 9,24 13,61 9,19 4,62 7,65
4,36 3,02 0,96 0,57 0,1082 0,00129 27,86 2,89
86 1 806 9,1 13,67 9,12 4,55 7,6 4,29
2,99 0,96 0,56 0,11 0,00124 28,39 2,906
87 1 866 8,95 13,52 9,05 4,48 7,55
4,22 2,96 0,96 0,56 0,112 0,001155 29,428
2,938
88 1 896 8,8 13,37 8,97 4,4 7,51 4,15
2,93 0,96 0,55 0,114 0,00112 29,93 2,952
89 1 926 8,66 13,23 8,9 4,33 7,46 4,08
2,89 0,96 0,55 0,116 0,00108 30,43 2,967
90 1 956 8,66 13,23 8,9 4,33 7,46 4,08
2,89 0,96 0,55 0,1155 0,001046 30,919 2,98
91 1 986 8,51 13,08 8,83 4,26 7,41
4,01 2,86 0,96 0,54 0,1175 0,00101 31,4 2,984
92 1 1016 8,66 13,23 8,9 4,33 7,46
4,08 2,89 0,96 0,55 0,116 0,00098 31,88 3,017
93 1 1046 8,36 12,93 8,75 4,18 7,36
3,94 2,83 0,96 0,54 0,1196 0,00096 32,34 3,02
94 1 1076 8,22 12,79 8,68 4,11 7,31
3,87 2,8 0,96 0,53 0,122 0,00093 32,802 3,032
95 1 1106 8,22 12,79 8,68 4,11 7,31
3,87 2,8 0,96 0,53 0,122 0,00091 33,,26 3,044
96 1 1136 8,22 12,79 8,68 4,11 7,31
3,87 2,8 0,96 0,53 0,122 0,00088 33,71 3,055
97 1 1166 8,07 12,64 8,61 4,03 7,26
3,8 2,77 0,96 0,52 0,124 0,00086 34,15 3,067
98 1 1196 8,07 12,64 8,61 4,03 7,26
3,8 2,77 0,96 0,52 0,1239 0,000836 34,583
3,078
99 1 1226 7,92 12,49 8,53 3,96 7,21
3,73 2,73 0,96 0,52 0,1262 0,000816 35,014
3,088
100 1 1286 7,92 12,49 8,53 3,96 7,21
3,73 2,73 0,96 0,52 0,1262 0,00078 35,861
3,109
Table 12. Triaxial-stress-relaxation tests-FROZENSOIL.1 Output results
(continue)
N R TIME SIGMAD SIGM1 P Q SIGOC
TAUOC S1/S2 STRAIN OCSTR SIGMI TIMEI
SQRTT LOGT
101 1 1316 7,78 12,35 8,46 3,89 7,16
3,67 2,7 0,96 0,51 0,1286 0,00076 36,277 3,119
102 1 1376 7,63 12,2 8,39 3,81 7,11
3,6 2,67 0,96 0,51 0,1311 0,000727 37,094
3,139
103 1 1406 7,63 12,2 8,39 3,81 7,11
3,6 2,67 0,96 0,51 0,1311 0,000711 37,497
3,148
104 1 1436 7,63 12,2 8,39 3,81 7,11
3,6 2,67 0,96 0,51 0,1311 0,000696 37,86 3,157
105 1 1466 7,63 12,2 8,39 3,81 7,11
3,6 2,67 0,96 0,51 0,1311 0,000682 38,288
3,166
106 1 1496 7,63 12,2 8,39 3,81 7,11
3,6 2,67 0,96 0,51 0,1311 0,00067 38,68 3,175
107 1 1526 7,63 12,2 8,39 3,81 7,11
3,6 2,67 0,96 0,51 0,1311 0,00066 39,064 3,184
108 1 1556 7,34 11,91 8,24 3,67 7,02
3,46 2,6 0,96 0,49 0,1363 0,000643 39,446
3,192
109 1 1706 7,34 11,91 8,24 3,67 7,02
3,46 2,6 0,96 0,49 0,1363 0,00059 41,304 3,232
110 1 1946 6,9 11,47 8,02 3,45 6,67
3,25 2,51 0,96 0,47 0,145 0,000514 44,113
3,289
111 1 2186 6,75 11,32 7,95 3,37 6,82
3,18 2,48 0,96 0,47 0,1482 0,000458 46,755
3,34
112 1 2426 6,46 11,03 7,8 3,23 6,72
3,04 2,41 0,96 0,45 0,1549 0,000412 49,254
3,385
113 1 2906 5,72 10,29 7,43 2,86 6,48
2,7 2,25 0,96 0,42 0,1748 0,000344 53,907
3,463
114 1 3386 5,72 10,29 7,43 2,86 6,48
2,7 2,25 0,96 0,42 0,1748 0,000295 58,189 3,53
115 1 3626 4,99 9,56 7,07 2,49 6,23
2,35 2,09 0,96 0,38 0,2005 0,000276 60,216
3,559
116 1 3866 4,4 8,97 6,77 2,2 6,04 2,07
1,96 0,96 0,34 0,2272 0,000259 62,177 3,587
117 1 4106 3,23 7,8 6,18 1,61 5,65
1,52 1,71 0,96 0,27 0,3098 0,000244 64,078
3,613
118 1 4346 2,93 7,51 6,04 1,47 5,55
1,38 1,64 0,96 0,25 0,3408 0,00023 65,924
3,618
119 1 4586 3,08 7,65 6,11 1,54 5,6
1,45 1,67 0,96 0,26 0,3245 0,000218 67,72
3,661
120 1 4826 2,93 7,51 6,04 1,47 5,55
1,38 1,64 0,96 0,25 0,3408 0,000207 69,469
3,684
Table 12. Triaxial-stress-relaxation tests-FROZENSOIL.1 Output results
(continue)
N R TIME SIGMAD SIGM1 P Q SIGOC
TAUOC S1/S2 STRAIN OCSTR SIGMI TIMEI
SQRTT LOGT
121 1 5066 2,93 7,51 6,04 1,47 5,55
1,38 1,64 0,96 0,25 0,3408 0,0002 71,176 3,705
122 1 5119 2,93 7,51 6,04 1,47 5,55
1,38 1,64 0,96 0,25 0,3408 0,0002 71,547 3,709
123 0 6 7,04 11,61 8,09 3,52 6,92 3,32
2,54 1,15 0,48
124 0 7 18,45 23,03 13,8 9,23 10,72
8,7 5,04 1,34 0,81
125 0 8 28,86 33,44 19 14,43 14,19
13,61 7,31 1,53 0,96
126 0 9 38,17 42,74 23,66 19,09 17,29
17,99 9,35 1,72 1,04
127 0 10 46,21 50,79 27,68 23,11 19,98
21,79 11,11 1,91 1,09
128 0 11 53,31 57,88 31,23 26,66 22,34
25,13 12,66 2,1 1,12
129 0 12 59,15 63,72 34,15 29,57 24,29
27,88 13,94 2,3 1,15
130 0 13 63,88 68,45 36,51 31,94 25,86
30,11 14,98 2,49 1,16
131 0 14 67,35 71,92 38,25 33,68 27,02
31,75 15,73 2,68 1,17
132 0 15 69,72 74,29 39,43 34,86 27,81
32,86 16,25 2,87 1,18
133 0 16 71,45 76,02 40,3 35,73 28,39
33,68 16,63 3,06 1,19
134 0 17 72,71 77,28 40,93 36,36 28,81
34,28 16,91 3,25 1,19
135 0 18 73,66 78,23 41,4 36,83 29,12
34,72 17,11 3,44 1,19
136 0 19 74,13 78,7 41,64 37,07 29,28
34,95 17,22 3,63 1,19
137 0 20 74,61 79,18 41,87 37,3 29,44
35,17 17,32 3,83 1,19
138 0 22 74,76 79,34 41,95 37,38 29,49
35,24 17,36 4,21 1,2
139 0 24 73,66 78,23 41,4 36,83 29,12
34,72 17,11 4,59 1,19
140 0 26 71,77 76,34 40,45 35,88 28,49
33,83 16,7 4,97 1,19
Table 12. Triaxial-stress-relaxation tests-FROZENSOIL.1
Output results (continue)
N R TIME SIGMAD SIGM1 P Q SIGOC
TAUOC S1/S2 STRAIN OCSTR
141 0 28 69,4 73,97 39,27 34,7 27,7
32,72 16,18 5,36 1,18
142 0 30 66,09 70,66 37,62 33,04 26,6
31,15 15,46 5,74 1,17
143 0 32 61,67 66,24 35,41 30,84 25,13
29,07 14,49 6,12 1,16
1440 0 34 57,73 62,3 33,44 28,86 23,81
27,21 13,63 6,5 1,14
145 0 36 54,57 59,15 31,86 27,29 22,76
25,73 12,94 6,89 1,13
146 0 38 51,89 56,46 30,52 25,95 21,87
24,46 12,35 7,27 1,12
147 0 40 49,69 54,26 29,41 24,84 21,13
23,42 11,87 7,65 1,11
148 0 44 46,06 50,63 27,6 23,03 19,92
21,71 11,08 8,42 1,09
149 0 48 43,38 47,95 26,26 21,69 19,03
20,45 10,49 9,18 1,07
150 0 52 41,17 45,74 25,15 20,58 18,29
19,41 10,01 9,95 1,06
151 0 56 39,43 44 24,29 19,72 17,72
18,59 9,63 10,71 1,05
152 0 60 37,22 41,8 23,18 18,61 16,98
17,55 9,14 11,48 1,03
153 0 65 36,75 41,32 22,95 18,38 16,82
17,32 9,04 12,44 1,03
154 0 70 36,12 40,69 22,63 18,06 16,61
17,03 8,9 13,39 1,03
155 0 75 35,8 40,38 22,47 17,9 16,51
16,88 8,83 14,35 1,02
156 0 80 35,49 40,06 22,32 17,74 16,4
16,73 8,76 15,31 1,02
157 0 85 35,17 39,74 22,16 17,59 16,3
16,58 8,69 16,26 1,02
158 0 90 36,75 41,32 22,95 18,38 16,82
17,32 9,04 17,22 1,03
159 0 95 34,86 39,43 22 17,43 16,19
16,43 8,63 18,17 1,01
160 0 100 34,54 39,11 21,84 17,27 16,09
16,28 8,56 19,13 1,01
Fig. 40 FROZENSOIL.1 Triaxial stress- relaxation results.
Major to minor stress ratio as a function of strain
Fig. 41 FROZENSOIL.1 : Triaxial stress- relaxation results
Deviatoric stresses as a function of log- time
Fig. 42 FROZENSOIL.1 : Triaxial stress- relaxation results
Deviatoric stresses as a function of inverse of time
Fig. 43 FROZENSOIL.1: Triaxial stress- relaxation results
Deviatoric stresses as a function of square root of time
Fig. 44 FROZENSOIL.1: Triaxial stress- relaxation results
Inverse of deviatoric stresses as a function of log of time
Fig. 45 FROZENSOIL.1: Triaxial stress- relaxation results
Inverse of deviatoric stresses as a function of inverse of time
Chapter 6
Conclusions
Geotechnical engineering for cold regions and the utilization of ground freezing
techniques worldwide for special civil and mining engineering projects,
necessitate establishing of the frozen soils mechanics science. Theoretical
frozen soil mechanics requires experimental parameters. Thus, developing
theoretical models necessitate laboratory testing of frozen soils. This, calls for
developing standards for: (1) samples preparations, (2) testing techniques, and
(3) data processing, for all types of tests as well as, for different types of soils
tested at the same field temperature and loading conditions. The present book
provide the required standards recommended by the Author for the following
types of tests: (1) triaxial and uniaxial strain rate controlled compression tests
with volume change measurements, (2) compressibility tests, and (3) triaxial and
uniaxial stress- relaxation tests (constant volume long- term tests).
REFERENCES
Aerni, K., Mettier, K. (1980): Ground Freezing for the Construction of the Three-
Lane Milchbuck Road Tunnel in Zurich, Switzerland. 2nd Int. Symposium on
Ground Freezing, Trondheim, Norway, pp. 889-895.
Akili, W. (1966): Stress Effect on Creep Rates of a Frozen Clay Soil from Stand
Point of Rate Process Theory. Ph.D. Thesis, Michigan State University, USA.
Alkire, B.D. (1972): Mechanical Properties of Sand-Ice Materials. Ph.D. Thesis,
Michigan State University, USA.
Al- Moussawi, H.M. (1988): Thermal Contraction and Crack Formation in Frozen
Soils. Ph.D. Thesis, Michigan State University, USA.
AlNouri, I. (1969): Time-Dependent Strength Behaviour of Two Soil Types at
Lowered Temperatures. Ph.D. Thesis, Michigan State University, USA.
ASTM (1989): Classification of Soils for Engineering Purposes. Soil and Rocks
(Standards Vol. 4), The American Society for Testing and Materials,
Philadelphia, USA.
Andersland, O., Anderson, D. (eds.) (1978). Geotechnical Engineering for Cold
Regions. McGraw-Hill Book Company, New York, USA.
Andersland, O., Ladanyi, B. (eds.) (1994): An Introduction to Frozen Ground
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Author Index
Adachi, T., 116, 123
Aerni, K., 111, 123
Aitken, G. W., 123
Akili, W., 111. 123
Alkire, B.D., 111, 123
Al Moussawi, H. M., 111, 123
Al Nouri, i., 111, 123
American Society for Testing and Materials, ASTM, 15, 111, 119, 120, 123
American Society for Civil Engineers, ASCE, i, 115, 116, 120, 123
Andersland, O. B., 1, 13, 14, 18, 32, 38, 51, 111, 117, 123
Anderson, D. M., 1, 111, 117, 123
Arteau, J., 3, 111, 123
Assur, A., i, 111, 123
Atkinson, H. J., 111, 123
Aziz, K. A., 111, 123
Baker, T. H. W., 13, 111, 112, 120, 123
Barnes, P., 112, 123
Barnsby, L. P.,
Bishop, A. W., 13, 14, 112, 123
Bourbonnais, J., 112, 123
Bowles, J.E., 13, 51, 112, 123
Braun, B., 2, 112, 123
Bragg. R. A., 13, 14, 112, 123
Brodskaya, A. G., iii, 10, 13, 33, 51, 53, 54, 55, 112, 123
Brown, R. J. E., 112, 113, 114, 121, 123
Careaga, J., 2, 112, 123
Carbee, D. L., 121, 123
Chaichanavong, T., 117, 123
Chamberlain, E. J., 13, 112, 119, 123
Cheatham, J., 116, 123
Cole, D. M.,119, 123
Czajkowski, R. L., 112, 123
Dahlin, B., 114, 123
Diekman, N., 114, 123
Dillon, H. B., 112, 123
Dokuchayev, V., 112, 123
Dorman, Ya. A., 116, 123
Dumont- Villares, A., 112, 123
Department of the Army, USA CRREL, I, 3, 112, 113, 114, 115, 116, 117, 118,
123
Dokichayev, V., 112, 118, 123
Eckardt, H., 112, 113, 124
El Ansary,A., 120, 124
El Din, G. A., 112, 124
Eranti, E., 113, 124
Farouki, O. T., 113, 124
French, R., 121, 124
Frederking, V., 116, 124
Fremond, M., 113, 124
Gallavresi, F., 111, 124
Gavrillo, I. G., 116, 124
Gittus, V., 39, 113, 124
Glen,J. W., 113, 124
Gold, L. W., 113, 124
Goodman, M. A., 113, 124
Goughnour, R. R., 113, 124
Grechishev, S. Ye.,
Green, S., 116, 124
Groves, C., 112, 124
Handegord, G. O. P., 114, 124
Hanna,A. M., 113, 120, 124
Haynes, F., 113, 124
Henkel, D. J., 13, 112, 113, 124
Hirayama, M., 116, 124
Hobbs, P., 113, 124
Holtz, R. D., 113, 124
Howard, A. K., 114, 124
Hooke, R., 114, 124
Houston, W. N., 114, 124
Hult, J. A. H., 39, 115, 116, 124
Hutcheon, N. B., 114, 124
Jackson, R. H., 114, 124
Jagow, H., 114, 124
Jessberger, H. L., 2, 13, 14, 32, 111, 114, 120, 124
Johnston, G. H., 114, 124
Jones, A., 114, 124
Jones, S. J., 114, 124
Jumikis, A. R., 114, 124
Kaplar, C. W., 13, 114, 124
Kalafut, j., 113, 124
Karalius, J., 113, 124
Kauper, M., 114, 124
Khakimov, R., 117, 124
Kiayi, Z., 121, 124
Kinosita, S., 111, 118, 120, 124
Konard, J. M., 112, 124
Kovacs, W. D., 113, 124
Knutsson, S., 114, 124
Krabbe, W., 114, 124
Kudryavtsev, V. A., 114, 125
Kuhlemeyer, R., 120, 121, 125
Lacerda, W. A., 114, 125
Ladanyi, B., 14, 111, 114, 125
Lambe, T. W. 13, 125
Lauzon, V., 14, 114, 125
Lee, K.. L.,113, 115, 116, 125
Linell, K.A., 115, 125
Lunardini, V. J., 115, 125
Macchi, A., 112, 125
Maksimayak, R. V., 116, 125
McRoberts, E., 115, 125
Massoud, N., 113, 125
Mayer, E., 112, 125
Mellor, M., 114, 115, 116, 125
Mettier, K., 11, 125
Morgavi, R., 116, 125
Nash, 112, 125
Nersasora, A. Z., 116, 125
Nixon, J. F., 115, 125
O’Connor, M. J., 13, 14, 33, 115, 125
Parameswaran, V. R., 15, 125
Perham, 112, 125
Perkapskaia, N., 115, 125
Perkins, T. K., 115, 116, 125
Petrov, K. I., 116, 125
Phillllipp Holzmann- Germany,
Phukan, A., 13, 115, 125
Rabtonov, Yu. N., 38, 43, 115, 125
Razbegin, V. N., 116, 125
Reubhan, D., 115, 125
Rendulic, L., 115, 125
Roggensack, W. D., 115, 125
Roscoe, K. H.,. 115, 125
Ruedrich, R. A., 115, 116, 125
Sadovsky, A. V., 13, 116, 125
Sarkisyan, R. M., 116, 125
Sayles, F. H., 3, 13, 14, 111, 116, 120, 125
Schofield, A. N., 115, 116, 125
Schwarz, J.R., 116, 125
Seed, B. H., 13, 115, 116, 125
Sego, D., 111, 120, 125
Shibata, T., 13, 116, 126
Silvestri, V., 10, 116, 126
Simonsen, E., 116, 126
Skelton, 116, 126
Smith, L. B., 116, 126
Soo, J. N.., 39, 116, 126
Spence, J., 39, 115, 116, 126
Steinemann, S.,
Sheynkman, D., 118, 126
Shushrina, Ye. P., 118, 126
Stoss, K., 2, 116, 126
Sumgin, M., 117, 126
Takahashi, T., 116, 126
Taylor, D. W., 116, 126
Terzaghi, K., 13, 116, 117, 126
Thimus, J. F., 13, 117, 126
Trimble, J., 117, 126
Tryde, P., 111, 116, 126
Tsytovich, N. A., 1, 2, 13, 14, 39, 46, 51, 111, 116, 117, 118, 120, 126
Turcott, R. 117, 126
Udd, J. E., 117, 126
Valk, J., 116, 126
Vaudrey, K. D., 116, 126
Vermeer, P. A., 13, 117, 126
Vinson, T., 13, 117, 118, 126
Vyalov, S. S., 1, 13, 14, 39, 46, 51, 111, 116, 117, 118, 120, 126
Walker, J., 112, 126
Warketin, B. P., 118, 126
Weaver, J. S., 118, 126
Whitman, R. V., 13, 114, 126
Williams, P. J., 118, 126
Wind, H., 118, 126
wroth, C. P., 115, 116, 126
Yong, R. N., 118, 126
Yashima, A., 116, 126
Yoshioka, I., 116, 126
Youssef, H., iii, iv, 3, 4, 6, 8, 9, 13, 14, 15, 16, 18, 20, 38, 46,51, 52, 53, 63, 64,
66,
67, 113, 116, 118, 119, 120, 121, 126
Zhu, Y. 55, 121, 126
Zmwang, W., 121, 126
Subject Index
Artificial freezing, 116, 117, 127
Coefficient of compressibility, 55, 60, 127
Cohesion, 46, 116, 127
Cold regions, i, 1, 55, 60, 109, 111, 113, 114, 115, 116, 117, 118, 119, 120,
121, 127
Compressibility coefficients, ii, iii, 51, 52, 55, 60, 61, 127
Compressibility of frozen soils, ii, 51, 112, 127
Compression tests, iii, 13, 39, 78, 79, 80, 81, 109, 127
Computer program FROZENSOIL.1, i, iii, v, 2, 14, 48, 63, 65, 66, 127
Cooling system, iv, 6, 13, 14, 17, 118, 127
Creep, 5, 13, 38, 38, 39, 43, 51, 111, 112, 113, 114, 115, 116, 117, 118, 119,
120, 121,
127
Data processing, i, ii, iii, 2, 13, 57, 60, 63, 65, 109, 127
Deviatoric stresses, v, 18, 19, 22, 39, 48, 82, 103, 104, 105, 106, 107, 108,
109, 127
Experimental results, i, ii, iv, v, 2, 13, 14, 15, 22, 23, 27, 38, 40, 43, 46, 48, 51,
53, 54,
55, 60, 63, 64, 65, 73, 77, 127
Frozen sand, ii, iii, iv, v, 4, 5, 7,8, 9, 10, 15, 18, 22, 23, 24, 25, 26, 27, 30, 31,
32, 33,
34, 38, 40, 41, 43, 46, 48, 51,52, 53, 54, 55, 58, 111, 112, 114, 115, 116,
117,
118, 120, 127
Frozen soils, i, ii, iii, iv, v, 1, 2, 13, 14, 15, 17, 18, 19, 20, 21, 22, 27, 32, 33, 38,
39, 40,
42, 43, 46, 47, 48, 51, 53, 55, 57, 58, 60, 63, 64, 65, 66, 67, 88, 109, 111,
112,
113, 114, 115, 116, 117, 118, 119, 120, 121, 127
frozen grounds, i, ii, iii, 1, 2, 13, 14, 15, 16, 33, 38, 48, 51, 52, 57, 60, 65, 111,
112,
113, 15, 117, 118, 120, 127
ground freezing. i, ii, 1, 2, 51, 109, 111, 112, 113, 114, 115, 116, 117, 118, 120,
121,
127
Ice, i, ii, iii, iv, v, 1, 2, 5, 11, 13, 14, 15, 17, 18, 22, 23, 24, 27, 32, 33, 38, 40,
41, 43,
46, 51, 52, 53, 54, 55, 57, 58, 67, 70, 77, 78, 88, 111, 112, 113, 114, 115,
116,
117, 118, 119, 120, 121, 127
Ice content, 2, 22, 24, 41, 54, 55, 57, 58, 127
Instantaneous relaxation stress, 40, 127
Insulation, 5, 127
Mechanical behaviour of frozen soils, 114, 127
Mechanical properties of frozen soils, 116, 127
Octahedral stresses, v, 84, 127
Permafrost, ii, 1, 51, 111, 112, 113, 114, 115, 116, 117, 118, 120, 121, 127
Permeability, 2, 127
Relaxation strain, v, 38, 39, 40, 41, 43, 46, 47, 48, 50, 77, 127
Sample preparation, i, ii, 2, 3, 14, 55, 60, 112, 127
Saturation, ii, iv, 3, 4, 23, 24, 27, 27, 41, 54, 127
Seasonally frozen ground, 113, 127
Shear strength, 23, 27, 38, 46, 112, 113, 115, 127
Simultaneous testing , ii, iv, 14, 127
Strength, 2, 14, 22, 23, 27, 32, 38, 40, 46, 111,112,113, 114, 115, 116, 117,
118, 121,
127
Stress ratio, v, 22, 27, 40, 41, 47, 83, 102, 127
Temperature, i, 1, 2, 3, 5, 6, 10, 11, 13, 14, 15,16, 18, 23, 27, 32, 33, 38, 39,
40, 43, 48,
51, 54, 57, 58, 59, 60, 61, 65, 67, 69, 77, 78, 88, 109, 111, 112, 128
Thaw, 1, 117, 128
Thermal, 1, 2, 111, 113, 114, 115, 116, 128
Triaxial tests, i, iv, v, 18, 19, 21, 22, 32, 34, 64, 119, 128
Voids ratio, 22, 23, 27, 41, 54, 57, 58, 60, 128
Volume, i, ii, iv, v, 1, 2, 13, 14, 15, 17, 19, 22, 24, 25, 27, 28, 29, 30, 32, 33, 34,
35, 38,
39, 41, 57, 58, 60, 61, 6 3, 65, 66, 67, 69, 71, 72, 77, 78, 87,109, 113,
114, 115,
116, 119, 120, 121, 128
Water content, 2, 113, 128
Weight, 5, 11, 22, 24, 41, 54, 57, 58, 65, 67, 77, 128