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Scholars' Mine Scholars' Mine
Masters Theses Student Theses and Dissertations
1970
Multi-stage shear testing of a cohesionless soil Multi-stage shear testing of a cohesionless soil
Robert Clyde Gullic
Follow this and additional works at: https://scholarsmine.mst.edu/masters_theses
Part of the Civil Engineering Commons
Department: Department:
Recommended Citation Recommended Citation Gullic, Robert Clyde, "Multi-stage shear testing of a cohesionless soil" (1970). Masters Theses. 7188. https://scholarsmine.mst.edu/masters_theses/7188
This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected].
MULTI-STAGE SHEAR TESTING OF A COHESIONLESS SOIL
BY
ROBERT CLYDE GULLIC, 1946-
A
THESIS
submitted to the faculty of
UNIVERSITY OF MISSOURI - ROLLA
in partial fulfillment of the requirements for the
Degree of
MASTER OF SCIENCE IN CIVIL ENGINEERING
Rolla, Missouri T2486
1970 c.l 132 pages
18799(J
ABSTRACT
The multi-stage test is a procedure by which a soil's
shear strength parameters can be evaluated by the use of
a single sample of the material. The object of the
investigation is to evaluate to what extent multi-stage
testing can be used on a cohesionless material. Three
types of tests, using conventional and multi-stage
procedures are evaluated. They are: direct shear/
consolidated drained, triaxial compression/consolidated
drained and triaxial compression/consolidated undrained
shear tests.
It was found that multi-stage testing can easily be
performed and the shear strength parameter, ~f obtained
from these tests are in good agreement with those
obtained from the conventional shear tests. Only fair
to poor agreement was found for dilatancy, void ratio at
failure and strain at failure. Five different testing
procedures were used in the direct shear/consolidated
drained/multi-stage testing and it was found that the
results of these tests depend upon the procedure used.
ii
iii
ACKNOWLEDGEMENT
The author wishes to express his appreciation to his
advisor, Dr. William D. Kovacs, for his guidance and counsel
during the preparation of this paper.
The writer is particularly grateful to Professor John
B. Heagler and Dr. Floyd Cunningham for their valuable
assistance in correction of the manuscript and participation
in the oral committee.
Special gratitude is due Mr. H. Hollingsworth whose
assistance during the design and construction of equipment
was more than invaluable.
The author also wishes to thank Mrs. Diane Jones for
her assistance in typing the manuscript.
Particular appreciation is due the authorts wife,
Suzanne, without whose help and understanding this thesis
could not have been finished.
TABLE OF CONTENTS
ABSTRACT t • • • • • , • •
. . . ACKNOWLEDGEMENT
LIST OF FIGURES
LIST OF TABLES
. . ~ . ' . . . . . . . . . . . . . . . . . . . . . .
LIST OF SYMBOLS . . . . . " . . I. INTRODUCTION .
II. REVIEW OF LITERATURE . . . . III. MATERIALS . . . . . .
IV. EQUIPMENT AND TESTING PROCEDURES .
V. DIRECT SHEAR/CONSOLIDATED DRAINED TESTS
A. Equipment . . . . . . . . . . . . . . . . B. Sample Preparation . . . c. Testing Procedure . . . . . . . .
1 . Procedure "A" . . . 2. Procedure "B" . . . . . . . . . 3. Procedure "C" . . . . . . . . . 4. Procedure "D" . . . . . 5. Procedure "E" . . . . . .
D. Test Results . . . . . . . . . . . . 1. Conventional Tests
Page
ii
iii
vi
ix
X
1
4
17
22
25
25
25
28
29
29
32
32
32
32
36
2. Direct Shear/Consolidated Drained/ Multi-Stage Tests . . . . . . . . . 36
E. Comparison of Results . . . . . . . . . . 59
iv
Page
VI. TRIAXIAL COMPRESSION TESTS/CONSOLIDATED
VII.
DRAINED . . . . . . . . . , . . . . . . . 7 2
Equipment . . . . . . . . . A.
B. Sample Preparation ............. C. Testing Procedures . . . . . . D. Test Results
1. Conventional Tests ....
2. Multi-Stage Tests
E. Comparison of Results .
TRIAXIAL COMPRESSION TESTS/CONSOLIDATED UNDRAINED . . . . , , . . . , . . . . .
A. Equipment .. , . . . . . . . . . . . B. Sample Preparation
C. Testing Procedure . . . . . . . . . . D. Test Results . . . . . . . . . . . . . . E. Comparison of Results .
72
72
76
77
77
82
82
VIII. CONCLUSIONS
90
90
90
90
91
92
97
99 IX. APPENDICES .
1. DETAILED TEST PROCEDURES - DIRECT SHEAR/ CONSOLIDATED DRAINED . . . . . . . . . . 100
2 . DETAILED TEST PROCEDURES - TRIAXIAL COMPRESSION/CONSOLIDATED DRAINED
3. DETAILED TEST PROCEDURES - TRIAXIAL
108
COMPRESSION/CONSOLIDATED UNDRAINED 112
4. BACK PRESSURE - VOLUME CHANGE APPARATUS 117
X. BIBLIOGRAPHY . . . . . . . . . . . . . . . 119
121 XI. VITA . . . . . . . .
v
LIST OF FIGURES
Figure
1. Idealized Representation of Nunez's Multi-Stage Procedure
2. Grain Size Distribution Curve
3. Relationship Between Dry Density and Relative Density . • .
4. Back Pressure - Volume Change Apparatus
5. Equipment for Direct Shear Testing .
6. Direct Shear Equipment Ready for Testing .
7 .
8.
9.
10.
11.
Idealized Representation of Procedure "A"
Idealized Representation of Procedure "B"
Idealized Representation of Procedure "C"
Idealized Representation of Procedure "D"
Idealized Representation of Procedure "E"
12. Typical Results From Conventional Direct Shear Tests
13.
14.
15.
16.
17.
18.
Relationship Between and Void Ratio . Typical Test Results
Typical Test Results
Typical Test Results
Typical Test Results
Typical Test Results
Angle of Internal Friction
Using Procedure A . Using Procedure B . Using Procedure c . Using Procedure D . Using Procedure E .
19. Relationship Between Horizontal Deflection at Failure and Normal Stress For 40% Relative Density · ·
vi
Page
14
18
21
23
26
27
30
31
33
34
35
43
44
46
47
48
49
50
52
20. Relationship Between Horizontal Deflection at Failure and Normal Stress For 60%
vii
Relative Density 53
21. Relationship Between Horizontal Deflection at Failure and Normal Stress For 80% Relative Density 54
22. Relationship Between Dilatancy and Normal Stress For 40% Relative Density 56
23. Relationship Between Dilatancy and Normal Stress For 60% Relative Density 57
24. Relationship Between Dilatancy and Normal Stress For 80% Relative Density 58
25. Relationship Between Void Ratio and Normal Stress 60
26. Mohr Failure Envelopes For 40% Relative Density 61
27. Mohr Failure Envelopes For 60% Relative Density 62
28. Mohr Failure Envelopes For 80% Relative Density 63
29. Mohr Failure Envelopes Corrected For Dilatancy For 40% Relative Density 65
30. Mohr Failure Envelopes Corrected For Dilatancy For 60% Relative Density 66
31. Mohr Failure Envelopes Corrected For Dilatancy For 80% Relative Density 67
32. Summary of Corrected and Uncorrected Mohr Envelopes For 40% Relative Density
33. Summary of Corrected and Uncorrected Mohr Envelopes For 60% Relative Density
34. Summary of Corrected and Uncorrected Mohr Envelopes For 80% Relative Density
35. Triaxial Compression/Consolidated Drained Equipment Ready for Testing .
Failure
Failure
Failure
68
69
70
73
36. Typical Results From Conventional Triaxial Compression/Consolidated Drained Tests 80
37. Mohr Circles From Typical Conventional Tests 81
38. Relationship Between the Angle of Internal Fric-tion at Failure and Void Ratio at Failure . 83
39. Typical Multi-Stage Test Results ..•.
40. Relationship Between the Deviator Stress at Failure and Void Ratio at Failure . . . .
41. p-q Diagram For 60% Relative Density~ TX/CD
42. p-q Diagram For 80% Relative Density, TX/CD
43. Stress Path Representation of Triaxial Compression/Consolidated Undrained Test
44. p-q Diagram For 60% Relative Density, TX/CU
45. Photomicrographs of Lane Spring Sand .
viii
84
86
87
88
93
94
96
46. Direct Shear Sample in Place Ready for Testing . 101
47. Direct Shear Device Disassembled . 102
LIST OF TABLES
Table
I. Soils Used in Multi-Stage Testing by Other Investigators . . . . . . . . . .
II. Physical Properties of Lane Spring Sand
III. Test Results for Direct Shear Tests
IV. Test Results for Triaxial Shear Tests
ix
Page
7
19
• • 3 7
• • 7 8
4>f
4> I
c Cl
(J I
1
u
ad ' (a 1 - a 3 ) max
a I ( a I - a I ) max d ' 1 3
(a 1 I I a 3 I ) max
(a 11 a 3 ) max
LL
PI
TX/CD
TX/CU
DS/CD
TX/CD/MS
TX/CU/MS
LIST OF SYMBOLS
angle of internal friction at failure
effect angle of internal friction
cohesion intercept
effective cohesion intercept
major principal stress
effective major principal stress
confining pressure
change in confining pressure
pore water pressure
normal stress
maximum deviator stress
maximum effective deviator stress
maximum effective stress ratio
maximum stress ratio
liquid limit
plasticity index
triaxial compression/consolidated drained
triaxial compression/consolidated undrained
direct shear/consolidated drained
triaxial compression/consolidated drained/multi-stage
triaxial compression/consolidated undrained/multi-stage
X
DS/CD/MS
A
1\Ht.
p'
q
o:f
p
e. 1
Tf
MS
xi
direct shear/consolidated drained/ multi-stage
cross sectional area of sample
change in height of sample
energy for dilatancy
change in horizontal deflection
change in volume
volume after consolidation
abscissa stress point
effective abscissa stress point
ordinate stress point
failure line from p-q diagram
angle of Kf-line
back pressure
change in height of water in burette
applied back pressure
initial void ratio
void ratio after consolidation
void ratio at failure
shear stress at failure
multi-stage
I. INTRODUCTION
Shear strength parameters are needed in the design
of foundations, evaluation of slope stability of earth dams
and many other areas of the field of soil mechanics. Most
engineers rely on conventional tests such as the triaxial
compression test and the direct shear test to obtain these
parameters. The office or design engineer must choose the
appropriate type of test and drainage conditions to simulate
the field conditions so as to obtain a failure envelope and
evaluate values of cohesion, C, and the angle of internal
friction, $f.
In the process of running these tests two or three
samples must be obtained, representative of the material.
The samples must be prepared and tested individually.
Difficulties arise in securing three representative
samples from the same layer. Sometimes several samplings
must be made at the same depth or in the same layer to
obtain the necessary samples for testing. This standard
practice is both time consuming and expensive.
To reduce time and expense in laboratory testing it
is possible to use one representative soil sample to
evaluate the shear strength parameters C and $f. This
method of evaluating the soil parameters by the use of
only a single sample has come to be known as the
multi-stage test. In this test a sample is consolidated
1
and sheared to failure as in a conventional test. The cell
pressure or normal stress is then changed and the sample
allowed to come to equilibrium, The sample is then again
sheared to failure. The process is then repeated for
other stages. This has the obvious advantage in reducing
the time and cost of sample preparation and set up. Lumb
(1964) points out that it is particularly advantageous
when testing brittle or stony soil which must be carved
to shape or in a case with saturated sand where the
sampling is both difficult and expensive,
Multi-stage testing is not a relatively new testing
procedure; the first published work was in 1950 by DeBeer.
Most of the work has been done on cohesive material with
a few scattered tests on cohesionless material and looks
very promising.
The objective of this investigation is to evaluate
to what extent multi-stage testing can be used. This will
be done by evaluating the work by other investigators along
with this study.
The material used in this investigation is a clean
free draining sand. This material was chosen since most
of the previous work has been done on cohesive material.
To evaluate the shear properties, the direct shear test
and triaxial tests will be used. Different testing
procedures will be used in order to ascertain the shear
behavior of this material.
2
Three types of tests, using conventional and multi
phase procedures, will be evaluated. They are: direct
shear/consolidated drained, triaxial compression/
consolidated drained and triaxial compression/consolidated
undrained. Frictionless end platens were not used for
the triaxial compression tests in this study. Because of
the simplicity and ease of adaption of the direct shear
equipment, this test will be used to evaluate the effect
of different testing procedures.
3
II. REVIEW OF LITERATURE
DeBeer (1950) performed the original multi-stage
triaxial test and called it the "Cell Test". This test
procedure has not been universally accepted as it presents
several problems in the laboratory. One serious objection
is that the behavior of the soil sample is dependent on
the degree of flexibility1 of the testing cell (Kenny and
Watson, 1961).
DeBeer assumed that when a state of failure occurred
within a soil mass, one of two things occurred: either
sliding occurs along a surface or a plastic remoulding
takes place. With either of these phenomenon, the maximum
principal stress ratio is obtained. DeBeer thus attempts
to determine by direct means the lateral supporting
pressure just satisfying the equilibrium of a sample under
a given axial stress.
DeBeer used the following test procedure: a membrane
protected sample is placed within a cell and the cell is
completely filled with water. The sample is then loaded
axially and a manometer is used to measure the resulting
lateral stress. The lateral supporting pressure is then
decreased under a given axial load by allowing a small
amount of water to escape from the cell. This is continued
1Flexibility is understood to mean the relationship between cell expansion and change in confining pressure.
4
until further reduction of the lateral pressure is not
possible and the sample is at failure. The critical stress
ratio is at a maximum at this point. By increasing the
axial load in steps and repeating the process of decreasing
the lateral supporting pressure a number of combinations
of the ultimate stresses is obtained. From these data a
series of Mohr circles can be drawn and a Mohr envelope
evaluated.
Taylor (1950) presented a more conventional triaxial
type of testing method. The first stage proceeds as a
normal triaxial test, taking the sample to failure.
Failure is defined as the point of maximum principal stress
ratio. Then the chamber pressure is increased without
unloading and the sample is failed in a second stage of
loading. The steps are repeated a third and possibly a
fourth time.
Taylor tested undisturbed, partially saturated
samples of low plasticity silty clay. All tests were
run undrained with no change of water content permitted
during shear. Pore pressures were measured.
Taylor concluded from his testing that a multi-stage
test gives at least as much information as a series of
normal tests and that it gives better information unless
all the samples used in the normal tests are exactly alike.
The procedure has its limitations in testing soils that
are sensitive to change of structure during shearing. The
5
first stage of shearing destroys the structure and latter
phases are not indicative of the sensitive structure.
DeBeer tested a number of soils ranging from a fine
sand, silt, peat and clay, Taylor confined his study to
only low plasticity silty clays, These soils and other
types tested by the authors in this review are summarized
1n Table I.
Fleming (1952) ran undrained triaxial compression
tests on a decomposed phyllite. This material in its
natural state varies from a compacted soil to a hard rock.
The material used for the samples was a silty sand ranging
from clay size to 3/16 inch. His multi-stage procedure is
the same as that presented by Taylor (1950). Fleming
showed that the procedure gave very good results and that
the whole testing procedure depends on the definition of
failure, i.e. the point at which the principal stress ratio
is a maximum. He concluded that the multi-stage testing
procedure may be limited to soils having moderate cohesion.
Kenny and Watson (1961) ran both consolidated drained
and consolidated undrained triaxial tests on saturated clay
samples to determine the shear strength parameters, C' and
¢'. Their multi-stage procedure is the same as that
presented by Taylor (1950). They found that for the
consolidated undrained tests with pore pressure measurement
the values of ct and ¢ 1 determined by multi~stage compare
favorably with conventional tests. These tests were run
6
TABLE I
Soils Used in Multi-Stage Testing by Other Investigators
i Soil Unified Reference Type Class. LL PI Activity Test Remarks
~eBeer (1950) Boon Clay CH 94.0 58.7 I ----- "Cell" Organic content: 5%
Fine Sand SP ---- ---- ----- "Cell"
Clay CH 90.6 59.6 ----- "Cell"
Silt ML 26.4 8.3 ----- "Cell"
Peat OH 320.0 65.5 ----- "Cell" Organic content: 82%
:
Taylor (1950) Silty-Clay CL 36.0 18.0 ----- TX/CD Low plasticity
Fleming (1952) Decomposed ML 2 2. 8 3.1 ----- TX/CD Phyllite
Kenny & Watson Ottawa CH 52.8 26.2 <0.70 TX/CU Sensitivity (1961) 20+
Cornwall CL 2 7. 7 14.1 0.58 TX/CU Sensitivity I TX/CD 10+ i
Beauharnois CH 69.9 41.8 0.70 TX/CU I
1 TX/CD --
-...]
TABLE I continued
Beauharnois CL 43.5 19.3 <0.70 I TX/LU 2
St. Catha-rines CL 46.0 25.9 0.43 TX/CU Sensitivity
2
Wallaceburg CL 40.5 17.2 0.57 TX/CU Sensitivity 4
Allanburg CL 28.5 15.0 <0.50 TX/CU Sensitivity 3
Schmertmann Ottawa SP ---- ---- ---- CPS (1962 & 1963) Sand
95% ML 29 4 0.07 CPS Kaolinite I
Residual ML 37 9 0.45 CPS Clay
Leda Clay CL 36 12 ---- CPS
Mixture CL 30 14 1. 08 CFS
Blue Clay CL 38 19 0.36 CPS
Kaolin MH 52 21 0.35 CFS Powder
Mixture CH 150 105 1. 24 CPS ~-- --- -- ---------- -· - -- -~~- ----
00
TABLE I continued
Parry (1963 Clayey Silt CL 47 I 24 0.86 TX/CU
Clay CH 54 I 25 0.42 TX/CU
Silty Clay CL 49 30 0.71 TX/CU
Clay CH 77 54 0.90 TX/CU
Silty Sand CL 47 28 ---- TX/CU
Clay Sand ML 18 3 '-1--- TX/CD
Silty Clay CL 30 12 0.52 TX/CU
Clay CH 51 26 0.52 TX/CU
Sandy Clay CL 43 30 1. DO TX/CU
Silty Clay CH 59 39 0.81 TX/CU
Clay CH 92 66 0.85 TX/CU I
I
Nunez (1963 "Silty CL 16 9 ---- TX/CU/CD First two !
& 1970) Soil" stages undrain-ed, last stage drained
Lumb (1964) Silty Sand SM -- -.- -..--- TX/CD Undisturbed 56 to 92%
Silts ML -- -- ---- TX/CD saturated
\0
on soils having activities less than 0.75. The activity
of a clay is defined as the quantity derived by dividing
the plasticity index (liquid limit minus the plastic limit)
by the per cent clay by weight finer than 2 microns
(Skempton, 1953). No conclusion could be made for higher
activity soils. For the fully drained tests the multi
stage tests could only be applied for soil having "low"
sensitivities.
Schmertmann (1962) presented a type of multi-stage
test which he called the CFS test (Cohesion-Friction-
Strain Test). In this he attempts to determine the
strain mobilization of the cohesion and friction components
of soil's resistance to shear stress. The procedure
consists of subjecting a specimen, which has been placed
in a triaxial cell, to a constant rate of compressional
strain and controlling the pore pressures induced in it.
By controlling the pore pressures a constant value of o1 •,
the effective major principal stress may be maintained.
In the procedure he alternates between two values of o 1 '
in such a way that two stress-strain curves are obtained-
one for each o1 '. The CFS test is neither a drained nor
undrained test. There are small changes in volume in
conjunction with changes in o 1 ' at the same strain, but
yet the test is not free draining because of the imposed
pore pressure control. Schmertmann found good correlation
between the CFS test on a single specimen and tests run
10
on two specimens. He concluded that it was successful for
all the soil types tested. These soils included: Ottawa
sand, cohesive samples prepared by a "Vac-Aire" extrusion
machine and two natural undisturbed soils. A undisturbed
soil sample can be defined as one in which the soil
structure has not been changed during the sampling
operation (Lambe and Whitman, 1969). There is no such
thing as a truly undisturbed sample. Over consolidated
soil or soils which are at equilibrium under a stress less
than that to which it was once consolidated were not
tested. In general, the higher the plasticity index the
more difficult the performance of the test. The CFS test
must be run very slowly, often taking several days or
weeks.
Schmertmann (1963) continued with his curve hopping
testing, changing its name to the IDS test (Independent-
Dependent-Strain Test) instead of the CFS test. It is the
same testing procedure only the terminology is changed.
It is the imposed change in effective stress that controls
the curve hopping. Variations can be made in the test
by using different manners of changing the effective
stress. Schmertmann gives the examples of two levels of
a 1 ' wherein the pore pressure is suitably controlled, or
two levels of pore pressure or confining stress in
drained tests, or two levels of constant volume in
undrained tests with pore pressure measured.
11
Parry (1963) tested undisturbed samples with a multi
stage procedure like that of Taylor (1950). He tested
mostly clay soils with a few clayey sands and clayey silt
samples. Except for one drained test on a clayey sand
sample, all other tests were undrained triaxial tests.
Parry concludes that any variation between the results of
the multi-stage and conventional tests seem to be random.
The multi-stage tests gave more consistant results than
the conventional tests due largely to the inconsistancy
of the individual samples in the conventional tests.
Parry found one instance in which the multi-stage test
failed in the first stage. The soil was a very hard and
brittle desiccated soil and fell completely apart. He
did have good results from testing other highly desiccated
samples.
12
Nunez (1963, 1970) studied the shear parameters
obtained from multi-stage triaxial tests run on silty soils
of low plasticity, normally consolidated soft clays and
over consolidated clays. The multi-stage procedure used
by Nunez consisted of taking the same soil sample to
failure at different confining pressures. His procedure
for performing a consolidated undrained triaxial test
consisted of three steps or stages. The first step
consists of running a conventional test with pore pressure
measurements, to failure. For this step, failure was
assumed at (cr 1 - cr 3 ) maximum. Reasons for Nunez's choice
13
of failure criteria will be discussed later. Figure 1
shows an idealized representation of the procedure. From
step one with confining pressure a 3 (1) and pore pressure
u(l) at failure he went to step two with a 3 (2) = a 3 (1) +
6a 3 , letting it develop all the pore pressure corresponding
to 6a 3 • The change in pore pressure 6u is different than
6a 3 due to the previous triaxial state of stress. The
pore pressure is then dissipated totally and a new pore
pressure is induced in the sample equal to the previous
total pressure minus the increment 6a 3 corresponding to
the increase in the confining pressure. The value of
6a 1 (2) is then increased until failure is reached in step
two. Once failure is reached the pore pressure is once
again dissipated totally. He then goes to step three and
proceeds as if he were performing a drained test. In this
manner he obtains two determinations to define the value
of the shear strength parameters in terms of effective
pressures with a measurement of pore pressures and one
determination where the pore pressure is equal to zero.
Nunez found that in normally consolidated clays and
in sensitive clays, it is not desirable to go to
(a 1 '!a 3 ') maximum in the first two steps. Large axial
deformations are required to reach this failure criteria.
The test is stopped at (a 1 - a 3 ) maximum. In over
consolidated clays, he found no problem in obtaining
reasonably low axial strains at which (a 1 ' - a 3 ') is
,-.. 'M U)
~=!.. ..__.
(!)
~ :::s U) U) (!)
~ ~=!..
bll s::
•M s::
'M 4-1 s:: 0 u
,-., •M tf)
~=!.. '--'
(!)
~ :::s tf)
tf)
(!)
~ ~=!..
(!)
~ 0
~=!..
0
0
14
Stage 1 ______ _,,_.1,._• St~ge 2~Stage 3-+ I I cr (3)
1 Consolidation ~ ~----------~----~
: a 3 (1) llcr3 \r-1--------~ _l_
Time (Min.)
FIGURE 1. Idealized Representation of Nunez's Multi-Stage Procedure
I
____ r
15
maximum. Nunez concluded that for the undisturbed samples
or remoulded samples tested, the observed scatter of results
was similar to that obtained in conventional testing.
Multi-stage triaxial drained tests on undisturbed
partially saturated residual soil were carried out by
Lumb (1964). The residual soils were derived from the
decomposition of igneous rocks. The soils were silty
sands and silts with clay content rarely exceeding 20%.
Lumb's procedure differed from Taylor (1950) in that he
used various sequences of applying lateral pressures. He
tested specimens going from the lowest to highest pressure,
highest to lowest pressure and from a intermediate
pressure to the highest and then to the lowest pressure.
Lumb found no significant difference in the deviator
stress at failure between the multi-stage and conventional
test values for different sequences of applying o3 . In
the cases of failure strains, compressibility, and
dilatancy, the sequence of applying o3 strongly affected
the results. Excellent agreement was found between the
multi-stage and conventional tests with respect to
deviator stress at failure, drained cohesion and drained
angle of shearing resistance; only fair to poor agreement
was found for the strain at failure, compressibility and
dilatancy.
Lumb feels that the most important information sought
from triaxial testing is the soil strength. For the soils
studied, the multi-stage tests give results that are
practically indistinguishable from the conventional tests.
The main limitation of the multi-stage test is however,
the maximum axial strain that can be applied to a specimen
in ordinary commercially available triaxial test cells.
For undisturbed soils this is not serious. One may have
trouble with remoulded samples because of the high strains
at failure.
16
III. MATERIALS
"The general behavior of all cohesionless granular material is essentially the same, and differs only in the absolute values which are peculiar to each material. For this reason the behavior of cohesionless soils in general may be represented in the laboratory by tests on a sand fine enough to form conveniently into a test specimen." (Lee, 1965)
The sand used in this study was obtained from Lane
Springs Recreation Area on the Little Piney River in
Phelps County, Missouri. The sand is a uniformly graded
medium to fine sand. The grain size distribution curve for
this material is shown in Figure 2.
The physical properties of the material are given in
Table II. The specific gravity was found by averaging four
tests which were run in accordance with ASTM test
designation D854-58. The minimum density and maximum void
ratio were found by averaging three tests run in accordance
with ASTM test designation D2049-69. The minimum void
ratio and maximum vibrated density were found by two
methods. The first method was in accordance with ASTM
test designation D2049-69. A known weight of material was
placed in a known volume mold. It was then placed on a
shaker vibrating table and 57 pounds of weight was placed
on the material. The material was vibrated at 3600 vibra-
tions per minute and a double amplitude of 0.004 inches.
The double amplitude used was very close to the minimum
17
.j.J
...c:: b.O
•..-l Q)
:s: :>-. ~
!-< Q)
!=: •..-l I:.L.
.j.J
!=: Q)
u !-< Q)
~
100
80
60
40
20
0 10
"'~'~
I'
\
\ '-
5 1 0.5 0.1 0.05 0.01
Grain Size in Millimeters
Lane Spring Sand Source: Lane Spring Recreation Area
Little Piney River Phelps County, Missouri
FIGURE 2. Grain Size Distribution Curve
18
19
TABLE II
Physical Properties of Lane Spring Sand
Specific Gravity . 2.64
Minimum Void Ratio . 0.487
Maximum Void Ratio . . 0.751
Minimum Dry Density 93.9 lb./cu. ft.
Maximum Dry Density . 110.7 lb. I cu. ft.
Grain Size Distribution
Coefficient of Uniformity, Cu . . 1.6
Coefficient of Curvature, Cc 1.1
Unified Classification . SP
value of the specification. It was felt that because a
series of weights was used instead of a solid weight an
increase in the amplitude would cause a force greater than
lG to be exerted and that the weights would bounce against
one another thus not transmitting the energy to the
material. The method was used for both dry and completely
submerged sand. The values obtained by this method
appeared low when compared to values obtained in the
second method described below. The second method used was
vibrating the material in a 2 inch high, 2.5 inch diameter
direct shear specimen mold. The material was deposited
in two layers, each layer being vibrated for two minutes
by an electric engraving tool vibrator. The final minimum
void ratio was taken as the average of four tests. The
relationship between density, void ratio versus relative
density, is presented in Figure 3.
20
120
-+..J
4-!110 . ::s u --..0
M
>-.100 -+..J •r-1 !/)
s::: Q)
Q
t; 90 Q
Relative Density %
Lane Spring Sand
80 ~--~--~----L----L--~----~---L--~----._--~ 0.751 0.698 0.646 0.594 0.541 0.487
Void Ratio
FIGURE 3. Relationship Between Dry. Density and Relative Density
21
22
IV. EQUIPMENT AND TESTING PROCEDURES
The three types of tests performed in this study are the
direct shear/consolidated drained, triaxial compression/
consolidated drained and the triaxial compression/consoli
dated undrained.
The direct shear tests were performed on a Karol-Warner
Direct Shear machine (Model KW580) in conjunction with a
strain gage load cell (500 lb. capacity). This combination
produces a maximum horizontal shear force of 102 psi and a
maximum normal stress of 326 psi on a 2.5 inch diameter
sample.
The triaxial compression/consolidated drained tests were
performed using a conventional triaxial cell and a Geonor
triaxial loading machine. The triaxial compression/consoli
dated undrained tests were also performed using a similar
triaxial cell but with a Farnell constant rate of strain
testing machine. Further description of the equipment will
be given in later chapters.
As part of this investigation, an apparatus was designed
and constructed to measure volume changes and back pressure
within a triaxial sample. The apparatus is shown in
Figure 4. Description of the operation of the apparatus and
its calibrations are given in Appendix 4.
The principles of multi-stage testing are the same for
the direct shear and triaxial machines. The multi-stage test
23
A. Volume Change Burette
B. Back Pressure Burette
C. Cell Pressure Burette
D. Monitoring Gauge
FIGURE 4. Back Pressure - Volume Change Apparatus
24
is a method of testing wherein a single sample is brought
to failure under different confining stresses. In the basic
procedure a sample is consolidated under a predetermined
cell pressure or normal load. The sample is then sheared
at a constant rate of strain until a predetermined failure
criteria is met. The cell pressure or normal load is then
changed and the sample is allowed to come to equilibrium
under this new load. The sample is then again sheared to
failure. This process is repeated one or more times.
Since a large portion of this study deals with various
testing procedures using this equipment, further details
are given in the next three chapters which describe these
tests and their results.
25
V. DIRECT SHEAR/CONSOLIDATED DRAINED TESTS
A. Equipment
All direct shear tests in this investigation were per
formed with a Karol~Warner Direct Shear machine (Model KW580).
The normal load is applied to the sample by an air piston.
Shear loads are applied either by hand or motor drive. In
this investigation, the motor drive was used. The speed of
the motor is controlled by a Karol-Warner variable speed
drive (Model KWDV-3). The shear loads were monitored by a
strain gauge load cell of 500 lb. capacity in conjunction
with a Budd strain indicator (Model HW-1).
Figure 5 shows the equipment used in the direct shear
testing. Item A in the figure is on the Karol-Warner Direct
Shear machine. The letter A is just below the water
reservoir holding a sample inside ready for testing. Item
B denotes the variable speed drive which controls the speed
of the motor C. The Budd strain indicator is marked D
which monitors the strain gauge load cell at item E. The
direct shear machine with sample in place ready for testing
is shown in Figure 6.
B. Sample Preparation
Samples for the direct shear test were cylindrical in
shape. The diameter is 2.493 inches by 1.016 inches in
height. The following procedure is used to prepare samples
of desired density. The upper and lower frames or rings of
26
FIGURE 5. Equipment for Direct Shear Testing
27
FIGURE 6. Direct Shear Equipment Ready for Testing
28
the shear box are fastened together by using alignment pins.
The rings are placed on top of a porous stone which had been
placed in the· reservoir. The frames are then filled approxi
mately half full of deaired water. Additional water is
added as required so that when a predetermined weight of
oven dry sand is poured through a funnel into the frames it
will be completely inundated. The top stone is then placed
on top of the sand. A steel plate slightly larger than the
porous stone is placed on top of it and vibrated until the
plate rests on the top of the frame and the porous stone is
flush with the frame. For the high relative density samples
the sand is put into the frame in two layer with the first
layer being vibrated before the second layer is added. This
is done to help insure a constant density throughout. By
vibrating the porous stone flush with the top of the frame
the same height of sample is obtained each time. Since the
diameter of the samples is constant and a predetermined
weight of sand is used, a given void ratio can be repro
duced. After vibration, the steel plate is removed and the
reservoir is filled with water, The elevating screws are
then put in place and the sample is ready to be put into the
loading device.
C. Testing Procedure
The first stage of a multi-stage test is the same as
that of the conventional test. The sample is placed in the
machine and consolidated under a predetermined normal load.
After consolidation, the sample is sheared at a constant
rate of 0.01 inches/per minute until failure is reached.
Failure is defined as the point at which no increase in
shear stress takes place with further horizontal deflection.
Documented test procedure for this test is given in
Appendix 1. After completing the first stage, different
procedures were used to complete the multi-stage test.
Idealized representations of the different procedures are
shown in Figures 7, 8, 9, 10 and 11.
1. Procedure "A"
After reaching failure, the shearing is stopped and the
normal force is increased to another predetermined level.
Failure in the multi-stage test is defined as previously
given for the conventional test. The sample is allowed to
consolidate under the new normal pressure. The sample is
then sheared to failure at the same rate of strain. The
process is repeated for each stage. See Figure 7.
2. Procedure "B"
29
After reaching failure, as previously defined, the
shearing force is reversed and the shear plates pushed back
to their original positions, that is, to the point of zero
horizontal deflection. The normal force is then increased
and the sample is allowed to consolidate. The shearing force
is then applied again in the forward direction and the
sample is taken to a second failure. The procedure is
repeated for each stage. See Figure 8.
S t ~g e 1 _ __,.,,..1-EE--1
I
30
Stage 3
Ul Ul Q)
Conso~hear ~Consol~ Shear Consol.~ Shear ~
I
!-< .f-1 C/)
~ ~------------------~ s !-< 0 z 0~------~--------------------------------------------~
Ul Ul Q)
!-< .j...) C/)
!-< cd Q)
..r:l C/)
0~----~~----~----------------~----------------~
Ul Ul Q)
!-< .f-1 C/)
0~----~------~--------------~--------------~
r--lr:::: cd 0
.f-J•r-1 r::::.j...) 0 u N Q)
•r-1 r--i !-<4-i OQ) ::c:~
oiL-----~~----~--------------------------------~
FIGURE 7.
Time
Idealized Representation of Procedure "A"
Stage 2 1 1
I
__,...~ Stage 3 I
31
Reverse Sheqrin~------4-------------
0~------------------------------------------~----------~
....-! cd
!/) !/)
<!) H ~ U)
0
~ •r-i 1=:+-l 0 N <!)
•r-i ....-! H4-i 0 <!) ::r::~
FIGURE 8.
Time
Idealized Representation of Procedure nB"
3. Procedure "C"
This procedure is the same as procedure "B" except at
failure when the shearing is stopped, the normal force is
completely released, The plates are then pushed back to
the zero horizontal deflection. The new normal force is
then applied, the sample allowed to consolidate, and the
shearing repeated. See Figure 9.
4. Procedure "D"
After reaching failure, the normal force is left on
the sample and the shearing force is reversed as in "B".
The plates are pushed back to the point that there is no
shear force on the sample. The normal force is then
increased to a predetermined level and the sample allowed
to consolidate. The shearing is then repeated. See
Figure 10.
5. Procedure "E"
This is the same as procedure "D" except that the
normal force is decreased instead of increased. The first
stage is run at the highest normal force and decreased
with each following stage. See Figure 11.
D. Test Results
32
In order to evaluate the usefulness of the multi-stage
test, test results are compared to results from conventional
tests. The conventional and multi-stage tests were run at
various relative densities (40, 60 and 80 percent) and up
to four different normal stresses (15, 27, 56 and 112 psi).
IJ) IJ)
(1.) (1.)
1--< 1--< ~~ tl) tl)
1--<.-i m m (1.) s
..C:J...< ti)O
z 0
.-il:: m o ~·M ~~ 0 u N (1.)
'M rl 1--<4-1 0 (1.) ::r::Q
0
~oe-- Stage 1
FIGURE 9.
I .,.I .. Stage 2
J
Reverse SheJring I .
I I
Time
Stage 3
Idealized Representation of Procedure nc"
33
-
Stage 1 Stage 2 ·'· Stage 3
I I
I I
Shectri Reve,rse g
I J
I
0~----~------------------------~--------------------~
OL---~~----~------~--------------------------~ Time
FIGURE 10. Idealized Representation of Procedure "D"
34
Stage 2 J~ Revarse Shefri. g
I I I I
I I
Stage 3 I
0~------------~--------------------------~~--------~
Cfl Cfl Cfl Cfl (J) (J) $-.< $-.<~ ~t:J) t:J)
....-1 $-.< Cii C1:l s (J) $-.<
,.J::!O t:J)Z
0
....-11=! Cii 0 ~ ·r-1 !=!~ 0 u N (J)
•r-1 ....-1 l--<4-1 0 (J)
::r::t=l
0
FIGURE 11.
Time
Idealized Representation of Procedure "E"
35
36
A summary of the results for both conventional and
multi-stage direct shear/consolidated drained (DS/CD) tests
are given in Table III.
1. Conventional Tests
Since the first stage of the multi-stage test is the
same as a conventional test, the results of this stage were
used as conventional test results. Figure 12 shows typical
results of the conventional direct shear test, where shear
stress and vertical dial reading are plotted versus
horizontal deflection.
Figure 13 shows the relationship between the angle of
internal friction (¢f) for various normal stresses versus
initial void ratio and void ratio at failure. The curves
show that for an increase in void ratio (decreasing
relative density), there is a decrease in ¢f. Similarly,
for a given void ratio, there is a decrease in ¢f with an
increase in normal force. For high void ratios (low
relative density), there is very little change in ¢f with
change in the normal force. The curves also show a
non-linear relationship between void ratio and ¢f. This
relationship has greater non-linearity with increasing
normal force on the shear plane. The results of the
conventional tests agree with previous work on sands.
(Means and Parcher, 1963).
2. Direct Shear/Consolidated Drained/Multi-Stage Tests
Typical test results for different test procedures are
TABLE III Test Results for Direct Shear Tests
Test MS Void Ratio Test D 9! e.
No. Ro Type (1) Proc. 1
76 40 Con. 0.646
113 40 Con. 0.646
116 40 Con. 0,646
29 40 Con. 0,646
49 40 Con. 0.646
51 40 Con. 0.646
52 40 Con. 0.646
53 40 Con. 0.646
79 40 MS A 0.646
0.630
0.628
0.623
(1) Con. = Conventional, MS = MultF~tage (2) Based on cohesion = 0
ec
0.627
0.627
0.631
0.618
0.627
0.617
0.614
0.614
0.636
0.627
0.623
0.618
ef L\Hor.£ (in.)
0.625 0,07
0.622 0.06
0.631 0.06
0.621 0.11
0.625 0.11
0.610 0.11
0.601 0.13
0.610 0.09
0.630 0.06
0.627 0.10
0.623 0.14
0.617 0.19
crn '[£ (Psi) (Psi)
27 19.2
27 17.8
27 18.6
56 39.2
56 40.1
112 76.6
112 77.3
112 77.5
15 9.9
27 19.8
56 39.4
112 71.9
$£0 (2)
35.5
33.4
34.6
35.0
35.6
34.4
34.6
34.7
33.4
36.4
35.2
32.7
VI -...:!
TABLE III continued
I 61 I 40 MS A 0.646 0.637
I 0.634 0.625
0.627 0,621
127 40 MS D 0,646 0.640
0.631 0,628
0.623 0.619
0.615 0.609
148 40 MS D 0.646 0.633
0.628 0.625
0.624 0.619
0.617 0.610
152 40 MS D 0.646 0.637
0.631 0.629
0.627 0.622 ---
0.633 0.04
0.626 0.11
0,621 0.16
0,635 0.08
0. 630 0.11
0.621 0.14
0.610 0.16
0.633 0.07
0.629 0.10
0.622 0.12
0.612 0.15
0.634 0.04
0.632 0.09
0.626 0.16
15 I 56
112
15
27
56
112
15
27
56
112
15
27
56
9.2
40.2
73.6
11.0
18.8
37.2
69.0
12.4
23.4
44.8
82.5
11.3
19.1
40.1
31.4
35.6
33.3
36.2
34.8
33.6
3~.6
39.6
41.0
38.6
36.4
36. 9 !
35 2 I • I
I
3s. 6 1
V-1 00
TABLE III continued
' 155 40 MS D
40 60 Con.
77 60 Con.
115 60 Con.
27 60 Con.
45 60 Con.
47 60 Con.
26 60 Con.
30 60 Con.
59 60 Con.
65 60 Con. ~-
o.646 I o.633
0.628 0.625
0.623 0.619
0.617 0.610
0.594 0.584
0.594 0.579
0.594 0.576
0.594 0.576
0.594 0.576
0.594 0.579
0.594 0.573
0.594 0.575
0.594 0.572
0.594 0.573
0.632 0.06
0.628 0.09
0.621 0.11
0.613 0.15
0,581 0.08
0.580 0.05
0.577 0.09
0.585 0.09
0.576 0.07
0.584 0.06
0.572 0.07
0.577 0.07
0.573 0.07
0.574 0.08 L__ --- --- -~
15 12.0
27 22.0
56 42.5
112 79.4
15 15.0
27 24.2
27 22.7
56 40.2
56 46.5
56 44.9
112 73.9
112 69.3
112 91.2
112 84.4
38.6 1
39.2
37.2
35.4
45.0
41.7
40.0
35.6
39.7
38.7
33.4
31.7
39.2
37.0
VI 1.0
TABLE III continued
81 60 I MS A 0.594
0.589
0.589
I 0.588
62 60 MS A 0.594
0.587
0.583
33 60 MS A 0.594
0.602
0.596
35 60 MS B 0.594
0.579
0.559
63 60 MS c 0.594
0.591
0.590 ----
0.586 0,586
0.587 0.589
0.586 0.587
0.583 0.583
0.586 0.586
0.580 0.583
0.579 0.579
0.588 0.602
0.594 0.594
0.591 0.589
0.585 0.594
0.568 0.570
0.554 0.554
0.588 0.591
0.576 0.579
0.564 0.567
0.04
0.07
0.09
0.13
0.05
0.09
0.13
0.09
0.12
0.21
0.0~
0.10
0.11
0.04
0.06
0.09 -
15
27
56
112
15
56
112
15
56
112
15
56
112
15
56
112
13.5 42.0
23.2 140.6
42.4 37.1
74.6 33.6
14.7 44.5
46.0 39.4
82.8 36.5
17.9 50.1
40.5 35.8
65.0 30.1
14.3 43.7
40.3 35.8
79.5 35.2
13.2 41.4
39.0 34.8
75.1 33.8
~
0
TABLE III continued
78 80 I Con. 0.541
114 80 Con. 0.541
so 80 Con. 0.541
55 80 Con. 0.541
41 80 Con. 0.541
54 80 Con. 0.541
56 80 Con. 0.541
83 80 Con. 0.541
60 80 MS A 0.541
0.544
0.541
82 80 MS A 0.541
0.544
0.549
0.547 -
0.525 0.539
0.533 0.540
0.529 0.540
0.528 0.533
0.524 0.531
0.522 0.527
0.520 0.522
0.526 0.532
0.537 0.542
0.538 0.540
0.537 0.540
0.536 0.543
0.542 0.547
0.546 0.546
0.542 0.542
0.08 27
0.05 27
0.07 56
0.07 56
0.07 112
0.07 112
0.09 112
0.07 112
0.04 15
0.07 56
0.10 112
0.03 15
0.06 27
0.08 56
0.11 112 -
29.2
28.1
54.3
55.5
89.0
96.4
90.0
101.7
18.5
53.6
96.0
19.2
29.1
48.4
81.4
47.2
46.1
44.2
44.7
38.5
40.7
40.6
41.0
50.9
43.7
40.6
52.0
47.2
40.8
36.0
-!:> ......
TABLE III continued
85 80 MS E 0.541 I I 0.528
I 0.534
0.540
I 89 80 MS D I 0.541
0.537
0.537
I 0.532
0.527 0.531 0.06
0.531 0.537 0.08
0.537 0.541 0.08
0.541 0.551 0.11
0.533 0.540 0.06
0.535 0.541 0.08
0.532 0.538 0.11
0.527 0.532 0.15
112 98.3
56 62.6
27 33.8
15 24.8
15 17.8
27 34.1
56 61.2
112 102.0
41.2
48.2
51.3
58.8
49.9
51.6
47,5 I
I
42.3 1
+:>. N
U} U} U} U} Q)
Q) !--< !--<.j..) .j...)(/)
(/) r-1
!--< cO cO s Q) !--< ...c:o (J)Z
,--..
~ •r-1 '-'
Q)
r-1 p... s cO
(/)
'-H 0
.j..)
...c: b.O
·r-1 Q)
::r:: ~
·r-1
Q)
b.O ~ cO
...c: u
FIGURE
1.2
0. 2
0
.015
.010
.005
(+)
0
(-)
.005
.010
12.
Direct Shear/Consolidated Drained Conventional Tests
DR= 60% ei 0.594
0 Test No. 26, C5 = 112 8
n Test No. 45, C5 = 56
[] n Test No. 40, C5 = 15 n
0.05 0.10 0.15
psi
psi
psi
0.20
Horizontal Deflection (in.)
Typical Results From Conventional Direct Shear Tests
43
44
52 Tests
,--... 0 '---'
Q)
1-< ;::::$
M •r-i
Cl$ J:..I..
.j..)
Cl$
s:: 0
•r-i .j..)
u ·r-i
1-< J:..I..
M Cl$ s:: 1-< Q)
.j..)
s:: H
4-l 0
Q)
M b.O s:: ~
4-l -e-
50
48 Symbol Normal
46 Stress (psi)
0 15 'V 27
44 0 56 0 112
42
40 ~ \.
" 38 ' ' ' 36 '
34
Initial Void Ratio 32 ---- Void Ratio at Failure
30 .soo .520 .540 .560 .580 .600 .620 .640 .660 .680 Void Ratio
I I 80 60 40
Relative Density (%) FIGURE 13. Relationship Between Angle of Internal
Friction and Void Ratio
shown in graphs of normalized shear stress versus
horizontal deflection and change in the height of sample
versus horizontal deflection in Figures 14 through 18.
Since the diameter of the sample is assumed to be constant
throughout the test, the change in height of the sample
is a direct relationship to the change in volume. A
negative change in height is the same as a decrease in
volume and a positive change in height is an increase in
volume. An increase in height or volume during shear is
commonly known as interlocking or dilatancy. Dilatancy
will be discussed in greater detail later. Five different
methods or sequences of applying shear stresses were
investigated. They are procedures A through E.
Procedure A is the simplest test to run. This
procedure is the conventional multi-stage test.
In procedure B (see Figure 15) it can be seen that
fairly large negative shear forces are produced in the
reverse shearing operation. In procedure C (see Figure 16),
which differs from B in that the normal load is relieved
before the reverse shearing, only very small negative shear
forces are produced.
Procedures D and E are similar procedures except that
the sequence of applying normal forces is reversed.
In the direct shear test, the horizontal deflection re
presents the relative movement of the shear rings. Figures
19 to 21 show the relationships at the different relative
45
Direct Shear/Consolidated Drained/Mul ti.,.·Stage
DR~ 60% ei = 0.594
....-1 cO
cO 1:: Q)
~ U)
,..-._ . ~
•r-1 "-'
Q)
....-1 p.., 1:: cO
U)
f.H 0
~ ~ bl)
•r-1 Q)
::r:: ~
•r-i
Q) bl)
~ cO ~ u
8 0. 4 z
0.2 Test No, 81
0.0 0.05 0.10 0.15
0.01
0.01
0.005
( +)
0.0
(-)
Horizontal Deflection (in.)
FIGURE 14. Typical Test Results Using Procedure A
0.20
0.20
46
tJl tJl tJl tJl (l) (l) !--< !--< ~ ~ (/) (/)
,....., !--< 1:'0 1:'0 e (l) !--< ~ 0 (/) z
Direct Shear/Consolidated Drained/Multi-Stage DR = 60% ei = 0.594
o-o Symbol Normal Stress (psi)
0 15
6 56 112 0 112
Test No. 35
0.15
0.15
Horizontal Deflection (in.) FIGURE 15. Typical Test Results Using
Procedure B
0.20
0.20
47
1.
r-:' 0.015 ~
·M '--'
(!)
r--i 0.010 p...
@ U)
~ 0
.f-)
~ b.O
"M (!)
::r:: ~
"M
0.0
(-)
~0.010 ~ cO
,..c:: u
48
Direct Shear/Consolidated Drained/Multi-Stage DR= 60% ei = 0.594
0.15 0.20
FIGURE 16.
Horizontal Deflection (in.)
Typical Test Results Using Procedure C
en en en en (J) (J) 1-1 1-1 ..j-J
..j-J [f.) [f.)
...-l 1-1 ttl ttl ~ (J)
~ 0 [f.) ;z;
,--... . 0.2 ~ •rl '--'
(J) 0.0 ...-l 0.. s ttl
[f.) 0.015 I.H 0
.j...l 0.010 ...c: b(\
•rl (J)
::r:: 0.005 ~
(+) •rl
~ 0. 0 § (-) ~
u 0.005
Direct Shear/Consolidated Drained/Multi-Stage DR = 80% ei = 0.541
Symbol Normal Stress (Psi)
0 15
~ 27 EJ 56
0 112
Test No. 89
0.15 0.20
0.20
Horizontal Deflection (in.)
FIGURE 17. Typical Test Results Using Procedure D
49
50
Direct Shear/Consolidated Drained/Multi-Stage DR = 80% ei = 0.541
en en en en(]) Q) !--l !--l.j....) .j....)U) U)
o-i !--let! ctl ~ Q) !--l
...c1o U):Z:
,.-.., . !=:
•r-t '--'
Q)
o-i p.. ~ ctl
U) 0.015 1+-1 0
.J..J 0.010 ...c1 bO
•r-t (])
::r:: 0.005 !=:
(+) •r-t
~ 0. 0 !=: (-) ctl
...c1 u 0.005
FIGURE 18.
.. D--.. ov
' Symbol
0
~ c:J
0 Test No,
0.10
Normal
15
27
56
112
85
0.15
0.15
Horizontal Deflection (in.)
Typical Test Results Using Procedure E
Stress (Psi)
0.20
0.20
densities of the horizontal deflection at failure to the
change in normal stress. It should be remembered that in
all the procedures except E the first stage (normal force
of 15 psi) is the same as a conventional test. In
analyzing the effect on the horizontal deflection, the last
stage will show the greatest variation.
It can be seen that as the normal force increases, the
horizontal deflection at failure for the conventional test
is lower than for the multi~stage procedures. The
horizontal deflection at failure for procedures A and D
seem to be fairly close. This might be expected in that in
procedure A the horizontal deflection is continuous with no
reverse shearing and only very small decreases in
horizontal deflection (see Figure 17) were needed 1n
procedure D to relieve the shear force. Procedures B and
C tend to be close as might be expected since in both
procedures the horizontal deflection is taken to zero
after each stage. In Figure 20 it can be seen that
procedure A tends to have greater horizontal deflections
at failure than B and C.
The shear strength of a sand is made up of three
components; the internal frictional resistance between
the grains, particle reorientation, and a third factor
commonly known as interlocking or dilatancy (Taylor, 1948).
Dilatancy is a phenomenon which contributes to the shear
strength of dense sands. In order for dense sand to shear,
51
+.J cO
!=: 0
0.1
0.1
0.1
Direct Shear/Consolidated Drained DR = 40% ei = 0.646
•o-1 +.J u (]) 0.08
r-1 ~ (])
~ Average Values 0.06 Symbol Procedure
0 Conventional
8 A
!;!] D
0.02
0 · 00 0~----~2~o------~4~o----~6~0~----~8~0-----1~o~o~--~1~2o Normal Stress (psi)
FIGURE 19. Relationship Between Horizontal Deflection at Failure and Normal Stress
For 40% Relative Density
52
,.-..
s::: ·r-1 "'----'
(!)
!-< ;j
....-f ·r-1 cti ~
-!-)
cti
s::: 0
•r-1 -!-)
u (!)
....-f 4-1 (!)
0
....-f cti
-!-)
s::: 0 N . ...., !-< 0
::r::
0.16r------.-----.------~-----.----~-------
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00 0
Direct Shear/Consolidated Drained DR = 60% ei = 0.594
20
Average Values
Symbol Procedure 0 Conventional
b A
0 B
9 c
40 60 80 100 Normal Stress (psi)
120
FIGURE 20. Relationship Between Horizontal Deflection at Failure and Normal Stress
For 60% Relative Density
53
,.....-.,
~ . ...., '---'
Cl.l !-< ;:j r-i . ...., ttl ~
.j-)
ttl
~ 0 . ...., .j-)
u Cl.l r-i tH
Cl.l r::=i
r-i ttl .j-)
~ 0 N . ...., !-< 0
::r::
0.16r------.------~------r-----~------~------
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00 0
Direct Shear/Consolidated Drained DR= 80% ei = 0.541
'/ /.,
'// f"'-
I~ qf
20
Average Values
Symbol Procedure 0 Conventional
6 A
D
E
40 60 80 Normal Stress (psi)
100
FIGURE 21. Relationship Between
120
Horizontal Deflection at Failure and Normal Stress For 80% Relative Density
54
sand grains must ride up over each other during shearing
which results in an increase in height or expansion of the
55
sample. Energy must be supplied for this expansion to occur.
The amount of energy required is equal to the product of
the thickness increase and the normal force on the sample.
This amount of energy is found by setting an exnression
for energy used equal to the energy that is supplied:
where:
on X A X 6.Ht. = Ed X A X L\.Hor. (V -1)
on = normal stress on the sample, psi
A = cross sectional area of sample, in. 2
6.Ht. = change in height of the sample, in.
= that part of the shearing stress that supplies the energy for expansion (dilatancy), psi
L\.Hor. = change in horizontal deflection, in.
Rearranging and solving for Ed:
6.Ht. L\.Hor. (V- 2)
The relationship between dilatancy and normalized
dilatancy versus normal force for the different procedures
and relative densities are shown in Figures 22, 23 and 24.
At low normal stress, which were the first stages, the
results should be the same. As the normal stress is
increased, greater variations between conventional and
multi-stage tests are found. This can be explained in that
for a given normal stress the effect of dilatancy will vary
as the void ratio varies. For a lower void ratio the
,--.. •r-i
C/1 p...
'--'
>--u ~ ro
.j..J
ro r-1 •r-i ~
,--..
"''"' '--'
0 0 r-1
>< C/1 C/1 Q)
!--< >-- .j..J
u ~ ro
.j..J ro ro s
r-1 !--< •r-i 0 ~z
20r-----~r-----.------~-----r----~~-----
10
5
20
10
0
Direct Shear/Consolidated Drained DR = 40% ei = 0.646
60 80 100
Average Values
Symbol Procedure 0 Conventional
6 A EJ D
8
---------------8
20 40 60 80 100 Normal Stress (psi)
120
56
FIGURE 22. Relationship Between Dilatancy and Normal Stress For 40% Relative Density
57
20r-----~-----.------T-------------------J Direct Shear/Consolidated Drained
DR= 60% ei = 0.594
15
10
5
0 20 40 60 80 100
Symbol Procedure 20 0 Convention
6 A ,-.. c:J o\O B '--' 0 c 0 0 ,.....;
>< U') U') Q) 10 ~
:>-.. .j..)
u ~ ro
.j..) ro ro s
1'"""i ~ •r-1 0 0 z
0 40 60 80 100 20 120
Normal Stress (psi)
FIGURE 23. Relationship Between Dilatancy and Normal Stress For 60% Relative Density
,.--,. .,..., Ul p. ...__,
:>--u ~ ctl
+-l ctl
,....; .,..., ~
,.--,. o\"' ...__,
0 0 ,....;
>< Ul Ul Cl)
~ :>-- +-l u C/)
~ ctl ,....; ~ ctl ctl s
,....; ~ .,..., 0 ~z
FIGURE
20
15
10
5
0
20
10
0
Direct Shear/Consolidated Drained DR = 80% ei = 0.541
'-..V /'-...
'-../ /.'-..
20
"-.b '7'-..
'~ ~/
40
Symbol
0 6 0
'-.,/ /'-..
/
Procedure
Conventional A
D E
40 60 80 Normal Stress (psi)
100
100
58
120
24. Relationship Between Dilatancy and Normal Stress For 80% Relative Density
effect of dilatancy will be greater, It will be seen later
in this discussion that as the stages proceed and the
normal stress is changed, the different procedures have
different void ratios at failure, The more stages the
greater variation in void ratio and thus greater variation
in dilatancy.
59
Figure 25 shows typical results of the change in void
ratio with the change in normal force during the different
stages of shearing. It can be seen that the greatest change
in void ratio during shear is in procedure B, while
procedures D and E have very little change in void ratio
during multi-stage shearing at a relative density of
80 percent.
E. Comparison of Results
The results of the conventional and multi-stage tests
are compared on the basis of Mohr failure envelopes. The
Mohr envelopes are shown in Figures 26, 27 and 28 for the
average values of conventional and multi-stage procedures,
uncorrected for dilatancy, for relative densities of 40,
60 and 80 percent respectively. All the procedures seem
to be in fairly good agreement with the conventional tests.
The test results vary at higher pressures especially as the
relative density increases. The Mohr envelope for
procedure A tends to be slightly below the envelope for
the conventional tests, but it gives the best approximation
to the conventional test envelope. The two envelopes are
.68~------r-----~------~----~~----~----~
Direct Shear/Consolidated Drained/Multi-Stage
.66
40
.64
.62 ·A 61 -------QD 48
0 •r-1 .j..l .60 cd
0:::
"ij •r-1 0 >
60
.540
f'.... .....................
I ..__ -·- """........._ ·A 62 -- ....... -- "· --- r.. ........... ~ ........... (:)
1 '·:Y c 63
a--·-·--,____ . • ..,J ---
L_ ------0B 35
-· ·- ~ ·~-.-...---
~-....-:.=:
A 82
D 89 E 85
· 520 ol------2J0-------4~0------6~0-------8L0------1~0-0-----1~20 Normal Stress (psi)
FIGURE 25. Relationship Between Void Ratio and Normal Stress
80
60
,--..
"''"" '--'
>-.j..l
·r-1 til s:: Q)
0
Q)
> •r-1 .j..l
cd ..-l Q)
~
,....... 'M (/)
p.. '-'
<!) f., ;::$
,....; •.4 (ij
ll-.
.jJ (ij
(/)
(/) <!) f., .jJ tf)
f., (ij <!)
,..c; tf)
100~------~------~------~-------T------~------~
Direct Shear/Consolidated Drained DR= 40% ei = 0.646
80
60
40
2J Average Values
Symbol Procedure 0 Conventional
6 A 0 D
0 0 20 40 60 80 100 120 Normal Stress (psi)
FIGURE 26. Mohr Failure Envelopes For 40% Relative Density
0\ f-l
100 I
Direct Shear/Consolidated Drained D = 60% e. = 0.594 R 1
l 80
r-. •r-i Ill p...
\._.)
Q)
1-< ;j 60
r-1 •rl t\l ~
+-l t\l
Ill Ill Q)
40 1-< +-l (/)
2J ~ Average Values
1-< Symbol Procedure ro
Q)
0 Conventional ~ (/)
6 A [] B
0 c
20 40 60 80 100 t~ormal Stress (psi)
FIGURE 27. Mohr Failure Envelopes For 60% Relative Density
120
0\ N
100~------~------~------.-------,-------~~
,....., 'M (/) 8 0 P< ~
(!)
!--< ;::J rl •r-1 ro ~ 60 .j-J
ro (/) (/) (!)
!--< .j-J
t.f) 4 0 !--< ro (!)
..c: t.f)
20
0
Direct Shear/Consolidated Drained DR = 80% ei = 0.541
Average Values
Symbol Procedure
0 Conventional
8 A
0
0 D
E
0 20 40 60 80 100 Normal Stress (psi)
FIGURE 28. Mohr Failure Envelopes For 80% Relative Density
120
0\ lN
64
well within the expected range of results from the
conventional tests. Procedures D and E show a tendency to
be slightly higher than the conventional test results while '
procedures B and C are lower.
Figures 29, 30 and 31 show these same test results
corrected for the effects of dilatancy using equation V-2.
Summary curves for the corrected and uncorrected
failure envelopes for the three relative densities tested
are given in Figures 32, 33 and 34. The correction for
dilatancy rotates the failure envelopes resulting in a
lower value of ~f· It can be seen that as the relative
density increases the corrected and uncorrected envelopes
move further apart. This is as expected since the effect
of dilatancy increases as the density increases; very
loose sands show no dilatancy. Procedure A tends to give
the best agreement with the conventional test. However,
test results using procedure A result in a lower value of
~f when uncorrected for dilatancy when compared with
conventional tests. When the dilatancy correction is
applied, the reverse is true.
Although procedures B and C are in fairly good
agreement with the conventional tests in the uncorrected
analysis, they fall well below the conventional test results
in the corrected analysis. Procedures D and E tend to have
envelopes at a larger angle ~f than that of the conventional
test. This would tend to make their results unsafe if used
100------~-----.------r-----,------.----~
Direct Shear/Consolidated Drained DR = 40% ei = 0.646
Corrected for Dilatancy 80
,....., •M
Vl p.
"-.)
(!)
1-< 60
;j ,....., •M ro
IJ..<
~ ro 40 Vl Vl (!)
/ Average Values 1-<
~ tl) Symbol Procedure 1-< Conventional ro 0 (!) 20
...!=: #' 8 A tl)
[] D
0 0 20 40 60 80 100 120
Normal Stress (psi)
FIGURE 29. Mohr Failure Envelopes Corrected For Dilatancy For 40% Relative Density 0\
tJ1
100------~-------r------.-------r------.------,
,-.. •.-1 VI p.
\._J
a> 80 ~ ::s
...-1 •.-1 ro ~
+-> ro VI 60 VI a> ~ +-> U)
~ ro a> 40
...c:: U)
20
Direct Shear/Consolidated Drained DR= 60% ei = 0.594
Corrected for Dilatancy
Average Value Symbol Procedure
0 Conventional 8 A 0 B
0 c O V: I I I I I I
0 20 40 60 80 100 120 Normal Stress (psi)
FIGURE 30. Mohr Failure Envelopes Corrected For Dilatancy For 60% Relative Density
0\ 0\
lOOr-------~------r-------~------~------------~
,.-.., •r-1 IJ)
p... '-..J
(!)
h
80
~ 60 ·~
(Tj ~
.j..) (Tj
IJ)
IJ)
(!) 40 h
.j..)
r.J)
h (Tj (!)
..c! r.J)
20
Direct Shear/Consolidated Drained DR = 80% ei = 0.541
Corrected for Dilatancy
Average Values Symbol Procedure
0 Conventional
6 A 0
0 D
E
0
.@ 0
0 ~------L-------~------L-------~------~----~ 0 20 40 60 80 100 120
Normal Stress (psi) FIGURE 31. Mohr Failure Envelopes Corrected For Dilatancy
For 80% Relative Density
0'1 '-.I
100--------------~-------.------,-------~----~
,..-.. ·r-1 Vl
~ 80 (])
~ ~ r-i •r-1 cd u.. .j-) 60 cd
Vl Vl (])
~ .j-) Cl)
~ 40 cd (])
..c: Cl)
20
0
Direct Shear/Consolidated Drained
DR= 40% ei = 0.646
Conventional
Proc. A
D
Uncorrected for Dilatancy ------ Corrected for Dilatancy
20 40 60 80 100 Normal Stress (psi)
120
FIGURE 32. Summary of Corrected and Uncorrected Mohr Failure Envelopes For 40% Relative Density
0\ 00
r-"\
•r-1 Ul p.,
\..-)
Q)
1-4 ::I
...-i •r-1 td ~
+J td
Ul Ul Q)
1-4 .j..) C/)
1-4 td Q)
...c: C/)
80
I 60
I
401
I
Direct Shear/Consolidated Drained DR= 60% ei = 0.594
Conventional
Proc. B
//~ "'-~"' .___Proc. C
//£/ /.~ '-Proc. A
201 /~/ Uncorrected for Dilatancy
--- Corrected for Dilatancy
40 60 80 Normal Stress (psi)
FIGURE 33. Summary of Corrected and Uncorrected Mohr Failure Envelopes For 60% Relative Density
100 120
0'1 \0
,....., •r-l til P<
'-..)
Cl)
~ :::l
.-1 •r-l ell ~
+..l CIS
til
100 I ~
80
60
Direct Shear/Consolidated Drained DR = 80% ei = 0.541
Proc. D
Proc. E Conventional
~ 40 ~ +..l C/)
~ CIS Cl)
..c: r.n 20 Uncorrected for Dilatancy
Corrected for Dilatancy
0 0 20 40 60 80 100 120
Normal Stress (psi)
FIGURE 34. Summary of Corrected and Uncorrected Mohr Failure Envelopes For 80% Relative Density
........ 0
in an engineering analysis.
Seed and Lee (1967) observed that the drained shear
strength is a function not only sliding friction and
dilatancy but also a function of particle crushing and
rearranging. The additional energy required for the
crushing should increase the friction angle to a value
larger than the correction for dilatancy indicates. The
effect of crushing and rearranging increases as the
confining pressure increases. To see if particle
crushing was taking place in the multi-stage test, sieve
analyses were run on the tested material at various times
during the study. No appreciable particle crushing was
found.
71
72
VI. TRIAXIAL COMPRESSION TESTS/CONSOLIDATED DRAINED
A. Equipment
The triaxial cell used for the drained tests was manu
factured by Wykeham Farrance (Model T67). The tests were per
formed on a Geonor triaxial machine developed by the
Norwegian Geotechnical Institute (Anderson and Simons, 1960).
A complete description of the testing apparatus is given in
the Geonor manual St. 22/63-AA/as. Application of the cell
pressure and determination of the volume changes were made
by using the apparatus previously discussed on page 22. The
deviator load and axial deflection were measured respectively
by a Mercer loading ring (No. 63260) and a Lufkin 0.001 inch/
division dial gauge. The equipment set up and ready for test
ing is shown in Figure 35.
B. Sample Preparation
Specimens used in the triaxial test were approximately
3.64 centimeters (1.43 inches) in diameter by approximately
8.40 centimeters (3.31 inches) long. The following procedure
was used to prepare saturated samples of predetermined
densities. This procedure is much like that presented by
Lee (1965). Approximately 150 c.c. of deaired water is placed
in a 500 c.c. volumetric flask. The flask and water is then
heated over a bunsen burner until the neck of the flask be
comes hot to the touch. The flask is then removed from the
heat and to it is added a known weight of oven dry sand. The
flask and contents are then placed under a vacuum and allowed
to boil. The vacuum is left on the sample for at least
FIGURE 35. Triaxial Compression/Consolidated Drained Equipment Ready for Testing
73
thirty minutes with occasional shaking of the sample.
Great care is taken to see that all the lines leading
to the cell base are filled with deaired water. A fully
saturated porous stone is then placed on the specimen base
of the cell and a single thin membrane (0.002 inches thick)
is attached to the base. The membrane is secured to the
base with a rubber 0-Ring. A cylindrical forming jacket is
then fitted around the membrane and specimen base. The
membrane is pulled tight over the former thus making it
conform to the shape of the former as much as possible. The
membrane is then filled with deaired water.
74
At this point the procedure varies according to the
desired density of the specimen. One method was used for
the forty and sixty percent relative density samples and a
slightly different one for the eighty percent relative densi-
ty samples. This difference in procedure is caused by the ex-
tra compactive effort needed for the higher density samples.
For the low density samples, the base of the cell with
membrane and former is submerged in a tank of deaired water.
The flask containing the sand is then completely filled with
deaired water. It is inverted with the neck of the flask
under the water in the tank and over the split mold. The sand
flows completely out under water from the flask into the mold.
Since the dry weight of the sand and the diameter of the
mold are known, it is only necessary to tap or vibrate the
side of the mold until the desired height and thus the desired
density is obtained.
75
For the high density samples the cell with membrane
and former is not submerged in the tank of water until after
the sample is formed. The sand is spooned into the water
filled mold and the mold vibrated until the desired height
obtained. The higher compactive effort needed for the
higher density is much easier to apply with the sample out
side the tank of water. After compacting to the desired
height, the base and sample is submerged very carefully
into the tank of water.
From this point on the procedure is the same for all
samples. The top cap is placed on the specimen and the
membrane pulled up around it and secured to it with a rubber
band. A small negative pressure was then applied to the
drain line and the forming jacket was removed. The use of
the thin membrane has the disadvantage in that it is very
easily punctured and this occurred often during the forming
process. This inside membrane is then deliberately punctured
and two additional thin membranes were then placed on the
sample. Since it is impossible to get all the water from
between the membranes, the deliberate puncturing avoided the
harmful effects which would occur if it were punctured during
the test and the entrapped water allowed to enter the sample
at that time. This additional water would effect the volume
change and pore pressure readings. The membranes are then
secured with the addition of two rubber 0-Rings at the base
and two at the top cap.
76
The cell base with sample is then removed from the water
tank and the dimensions of the sample are taken. Recorded
are the diameter of the sample, measured at the top, middle
and bottom, and the height of the sample. The rest of the
cell is assembled and is ready for filling with deaired water.
C. Testing Procedures
The first stage of the triaxial compression/consolidated
drained/multi-stage (TX/CD/MS) procedure is the same as a
conventional triaxial (TX/CD) test. The soil sample is
placed in a triaxial cell and positioned within the loading
machine. After the sample is consolidated to a predetermined
cell pressure, it is sheared at a constant rate of 0.012
inches per minute until failure. Volume changes are
measured throughout the test. Failure is defined
point at which the maximum principal stress ratio
as the crl
Ccr-)max 3
or the maximum deviator stress (crd = cr 1 - cr 3 )max is reached.
In a drained test, they occur at the same time. Only one
procedure was used in the multi-stage triaxial tests.
After reaching failure in the first stage, the shearing
process is stopped and the vertical load is removed from
the sample. The cell pressure is changed to a second
level and the sample is allowed to consolidate under
isotropic conditions. Different sequences of applying the
cell pressures were used in this study. After consolidation
the sample is again sheared to failure. The procedure is
then repeated for the desired number of stages. Details
for the test procedure are g1ven in Appendix 2.
D. Test Results
Conventional and multi~stage triaxial compression/
consolidated drained tests were run and test results
compared. Conventional tests were run for relative
densities from 40 to 80 percent and with various cell
pressures, 8, 17 and 35 psi, corresponding to those used
in the direct shear tests. Additional conventional test
results are obtained by varying the sequence of applying
cell pressure in the multi~stage test.
The results of the conventional and multi-stage
TX/CD tests are summarized in Table IV.
1. Conventional Tests
Typical test results are shown in Figure 36 for a
relative density of 80 percent, where the deviator stress,
principal stress ratio and volumetric strain are plotted
versus axial strain. It can be seen that failure occurs at
a relatively low axial strain, approximately 3 percent.
From tests at other confining pressures, Mohr circles are
drawn on Figure 37 defining a Mohr failure envelope. It
can be observed that as the confining pressure is increased,
the angle of internal friction ($f) decreases. At low
confining pressures dilatancy causes significant increase
in $f and accounts for the high angle measured in dense
sands (Lee and Seed, 1967).
The relationship between $f and void ratio at failure
77
Test D 9! Type Ro No.
66 68 TX/CD
67 55 TX/CD
68 57 TX/CD
69 49 TX/CD
70 56 TX/CD
71 59 TX/CD
73 43 TX/CD
74 40 TX/CD
75 76 TX/CD
84 80 TX/CD/MS
TABLE IV Test Results for Triaxial Shear Tests
Void Ratio (crl'/cr3')f I 0"3
e· ec ef (Psi) 1
0.572 0.563 0.582 35 4.44
0.605 0.597 0.625 35 4.17
0.601 0.583 0,605 35 4.37
0.622 0.617 0.637 8 4.71
0.603 0.597 0.622 17 4.58
0.594 0.583 0,606 17 4.59
0.637 0.589 0.589 17 4.56
0.646 0.601 0.626 35 4.15
0.551 0.538 0.577 17 5.12
0.541 0.499 0.538 35 4.95
0.536 0.552 17 5.39
0.546 0.562 8 5.43
(J"d e:f% (Psi)
120.4 3.32
111.0 4.70
117.8 3.61
29.7 2.11
60.9 3.02
61.0 3.02
60.6 2.72
110.1 4.24
70.0 2.67
138.2 4.83
74.4 6.04
. 35.4 6.64
<Pf
39.2
37.9
38.6
40.5
40.1
40.1
39.8
37.6
42.3
41.3
43.4
43.5
I
-...]
00
TABLE IV continued
87 I 60 I TX/CD/MS I 0.594 I 0.582 0.612 35 4.81
0.611 0.626 17 5.12
0.623 0.637 8 5.28
88 I 60 I TX/CD/MS I o.594 I o.512 0.613 8 4.85
0.593 0.610 17 4.66
0.595 0.610 35 4.47
91 I 60 I TX/CD/MS I o.596 I o.589 0.610 8 4.88
0.598 0.617 17 4.67
0.601 0.610 35 4.41
92 I 80 I TX/CD/MS I 0.541 I 0.537 0.572 8 5.38
0.553 0.572 17 5.17
0.556 0.571 35 4.84
112 I 80 I TX/CD/MS I o.541 I o.521 0.549 17 5.05
0.533 0.549 35 4.82
0.546 0.559 8 5.78
133.4 3.62
70.0 4.83
34.2 5.43
30.8 4.22
62.2 5.13
121.6 6.34
31.0 2.45
62.3 3.98
119.4 4.60
35.0 3.32
70.8 4.23
134.5 5.14
68.9 3.64
133.7 4.86
38.2 5.16
41.0
42.0
42.9
41.1
40.2
39.4
41.3
40.7
39.0
43.4
42.5
41.0
42.0
42.1
45.0
"' 1.0
!-< 0 +J ctl,-.. ·~·~ !>Vl Q)P, ~ '-'
,....,Vl cOVl P,Q) ·~ !-< U+J ~CJ) ·~ !-<
0..
,...., ctl p. ·~ 0 U·~ 5 ~+J ·~ ctl !-<~
0..
Q) !> ·~ +J 3 u Q)
4-1 4-1 ~
1 ,...., 0
Q)Vl 4 s ~ ;:::.1 0 ,...., u 0 3 > !-<
Q) ~ +J ·~ 2 o::r: Q)
Q) ~ s 1 ctl ;:::.1
,J:! ,...., u 0
0 >
-1
Triaxial Compression/Consolidated Drained
Conventional Test Test No. 75 DR = 80%
o--o--o,----0
2 3 4
0---0---0
4
Strain (%)
5
5
80
5
FIGURE 36. Typical Results From Conventional Triaxial Compression/Consolidated Drained Tests
120
100
r--. 80 •r-l V)
p.. '-'
I V)
V)
~ lo-4 60 .jJ
I r.J)
lo-4 ctl ~
..c: 40 r.J)
20
0 0
Triaxial Compression/Consolidated Drained
Mohr Failure Envelope
20 40
Conventional Tests DR= 80% ei = 0.541
/ Test No. 84
Test No. 112
60 80 100 Confining Pressure (psi)
FIGURE 37. Mohr Circles From Typical Conventional Tests
180
00 f-l.
82
for three confining pressures is shown in Figure 38.
It can be seen for a given void ratio, increasing the
confining pressure results in a decrease in the angle of
internal friction. Similarly, increasing the void ratio
(decreasing relative density) for a given confining pressure
reduces the angle of internal friction.
2. Multi-Stage Tests
Multi-stage tests were performed on samples at relative
densities of 60 and 80 percent, as sample preparation
difficulties were encountered in making samples at 40 percent
relative density. Several sequences of applying the
confining pressure to the sample were used. These
sequences are: 8, 17 and 35 psi; 17, 35 and 8 psi; 35, 17
and 8 psi.
Figure 39 shows typical results of a TX/CD/MS test
with a sequence of confining pressure going from the lowest
to the highest confining pressure. The deviator stress
(cr1 - cr 3 ), principal stress ratio (cr 1 ;cr3) and the volumetric
strain c~v;v ) are plotted versus axial strain for the c
three stages. In drained tests, failure according to
maximum principal stress ratio or maximum deviator stress
occur simultaneously.
E. Comparison of Results
Conventional and multi-stage triaxial compression/
consolidated drained tests results are compared using a
relationship between deviator stress at failure and final
r---. 0
'-----'
(J)
l-< ;:i
...-1 ·..-{
cti [:.I.;
.j...)
cti
I=: 0
·..-{
.j...)
u ·..-{
l-< [:.I.;
...-1 cti I=: l-< (J)
.j...)
I=: H
4-! 0
(J)
...-1 bl)
I=: c::r:
45
40
35
Triaxial Compression/Consolidated Drained Isotropic Consolidation Conventional Tests
·~
Symbol Confining Pressure (psi)
0 8
6 17
0 35
30~----~~----~------~------~------~------~~ .54 .56 .58 .60 .62 .64 . 52
Void Ratio at Failure
I I 80 60 40
Relative Density (%) FIGURE 38. Relationship Between the Angle of Internal
Friction at Failure and Void Ratio at Failure
83
r-.. ·~ ~l6or-------r-------r-------r-------r-----~r-----~ P-1
'-J
~ ~ C])
]:120 U)
~ 0
+-J ro ·~ 80 :> C])
0
0 0 ·~
.j..l
ro 0:::
~ ~ C])
~ 5 .j..l C/)
..--i ro p.. ·~ 3 u ~ ·~ ~
p..,
1
4
3
2
1 (+)
0 (-)
1
FIGURE 39.
Triaxial Compression/Consolidated Drained
D = R
8
1
80% Multi~Stage e. = 0.541
1
Test No. 92
cr3 = 17 psi
2
2
3
Strain (%) Typical Multi-Stage Test
= 35 psi
5
5
o--/ 4 5
Results
84
void ratio and also by the use of p-q diagrams. Figure 40
shows the former relationship for the different confining
pressures used. For a given void ratio, the deviator
stress at failure increases as the cell pressure increases.
Similarly, for a given cell pressure~ the deviator stress
at failure decreases as the void ratio increases. The
85
decrease in deviator stress may be explained by noting that
as the void ratio increases, a decrease in relative density,
the effect of dilatancy decreases and less deviator stress
lS required to fail the sample.
An alternative way to plot the test results of a
triaxial test is by the use of a p-q failure diagram 01 + 03 01 - 03
(where: p = and q = ). The p-q points
represent the failure points of the stress strain curves.
The line which is drawn through these points is called the
Kf-line.
P-q diagrams are shown on Figures 41 and 42 for
conventional and multi-stage TX/CD tests for 60 and 80
percent relative density, respectively. The Kf-line is
also curved at high confining pressures as is the Mohr
failure envelope shown in Figure 37. The relationship
between the angle of internal friction (~f) from the Mohr
d h 1 f th K ll.ne l·s given by: envelope an t e ang e ~f rom e f-
sin ~f = tan ~f (VI-1)
The plots show very good agreement between the
conventional and multi~stage procedure regardless of the
160 Triaxial Compression/Consolidated Drained
,-... •r-i tJ)
p..
140
'-'120 Q)
1-< ;:::s ~
•r-i
~ 100
tJ) tJ)
~ 80 ~ U)
1-< 0 ~ cd
·r-i 6 0 ? Q)
~
40
20
0 .52
(J = 35 3
-------1..:.~ p~
---:.... __ _ 6 'CBr-----o-
.54
0 Conventional Test
6 Multi -Stage Test
.56 .58 .60 Void Ratio at Failure
I I
.62 .64
80 60 40 Relative Density (%)
FIGURE 40. Relationship Between the Deviator Stress at Failure and Void Ratio at Failure
86
100'r-------~--------~--------~------~--------~---
80
II
cr' 4 0
20
0 0
FIGURE
Triaxial Compression/Consolidated Drained
DR = 60% ei = 0.594
sin <Pf = tan cx:f
20
41. p-q
~ Conventional
--6---- Multi-Stage
40 60 80
crl + cr3 p 2 (psi)
Diagram For 60% Relative Density,
100
TX/CD
87
88
lOOr--------r------~,-------.-------~--------~--,
Triaxial Compression/Consolidated Drained
80 DR= 80% ei = 0.541
,--. •r-i Ul 0.. ~ 60
t.t")
b
N
..-I b
II 40 0'
20
0 Conventional
~ Multi-Stage
0 0 20 40 60 80 100
p = (psi)
FIGURE 42. p-q Diagram For 80% Relative Density, TX/CD
multi-stage sequence of applying the cell pressure. The
next chapter presents results from triaxial compression/
consolidated undrained tests.
89
VII. TRIAXIAL COMPRESSION TESTS/CONSOLIDATED UNDRAINED
A. Equipment
The triaxial cell used was a conventional type cell
borrowed from Law Engineering Testing Company. A Farnell
constant-rate-of-feed testing machine was used for applying
the deviator stress. The pore pressures were measured by
a BLH pressure transducer, 0 to 150 psig capacity, in
conjunction with a BLH strain indicator. The deviator
load was measured by a strain gauge load cell, 0 to 500 lb.
capacity, in conjunction with a Budd strain indicator
(Model HW-1) and the deflections were measured by a Lufkin
0.001 inch/division dial gauge. The cell pressure and
back pressure were applied by the apparatus previously
discussed on page 22.
B. Sample Preparation
The sample preparation for the undrained test is
exactly the same as that for the drained test, except that
the dimensions of the sample are 3.56 centimeters (1.40
inches) in diameter by approximately 8.13 centimeters
(3.20 inches) in height.
C. Testing Procedure
As in the TX/CD test, the first stage of the triaxial
compression/consolidated undrained, (TX/CU) multi-stage
90
test is a conventional test. The triaxial chamber with a
saturated sample is placed in the loading machine and a
confining pressure is applied. The drainage valve is opened
and the sample is allowed to consolidate under this
confining pressure. After the sample has consolidated~
the drainage is closed and the sample is sheared at a
constant rate of 0.005 inches per minute to failure.
Failure in the TX/CU is defined as the point at which the
maximum principal stress ratio is reached. Pore water
pressures within the sample are measured throughout the
shearing process and recorded. After reaching failure,
shearing is stopped. The axial load is then completely
released from the sample. The confining pressure is
changed to the desired level for the second stage and the
drainage valve is opened and the sample is allowed to come
to equilibrium under the new confining pressure. When
equilibrium is reached the drainage is once again closed
and the shearing process is repeated. The procedure is
then repeated for the desired number of stages. Details
of the test procedure are given in Appendix 2. This is
the only test procedure used in the multi-stage testing.
D. Test Results
91
As difficulty was encountered in running triaxial
compression/consolidated undrained (TX/CU) tests with pore
pressure measurements, only a limited number was performed.
The multi-stage tests were performed using various sequences
of confining pressures. Conventional and multi-stage
triaxial compression/consolidated undrained tests are
compared in this study for a relative density of 60 percent
r-.. ·o-1 Vl p.
\....!
~l II
0"'
160
120
80
40
Triaxial Compression/Consolidated Undrained
Typical Test - Test No, 108 DR= 60% ei = 0,594
0 11::,
0
Effective Confining Pressure
(psi) 8
17
35
oJ &l& dJo ~o 1~0 1~0 ;oo 1
cr I + cr I
1 3 ( . ) 2 ps1 pI :
FIGURE 43. Stress Path Representation of Triaxial Compression/Consolidated Undrained Test
1.0 t.N
,--.._ •r-1 VI p..
"-'
::~ II
0"'
94
200 r--------.--------,-------~~-------r--------
160
120
80
40
0
Triaxial Compression/Consolidated Undrained DR = 60% ei = 0.594
40 80
/ /
0
8
Conventional
Multi-Stage
120 160
cr ' + cr ' p' = 1 3 (psi) ------
200
FIGURE 44. p-q Diagram For 60% Relative Density, TX/CU
This was further substantiated when photomicrographs were
taken of untested sand and sand tested in a triaxial
compression/consolidated undrained/multi~stage test. These
photomicrographs are shown in Figure 45.
95
a. Untested Sand (Magnified 40 Times)
b. Tested Sand (Magnified 40 Times) TX/CU/MS a 3 = 8, 17 and 35 psi D = 80% r
FIGURE 45. Photomicrographs of Lane Spring Sand
96
VIII. CONCLUSIONS
Three types of shear tests were performed using both
conventional and multi~stage procedures, These tests
were: direct shear/consolidated drained~ triaxial com-
pression/consolidated drained and triaxial compression/
consolidated undrained with pore pressure measurements.
Analysis of the conventional and multi-stage test results
lead to the following conclusions:
1. Multi-stage testing can easily be performed on
cohesionless material. The shear strength parameter, ¢f
obtained from these tests were in good agreement with those
obtained from conventional shear tests.
2. Of the five procedures used in the direct shear/
consolidated drained/multi-stage test, procedure A gives
the best approximation of the conventional test. The shear
strength parameter, ¢f, as determined by the multi-stage
tests, is approximately equal to the conventional test
results at low normal stresses (40 psi). At higher normal
stresses, ¢f determined by the multi-stage procedure is
slightly larger than ¢f determined by the conventional
procedure. However at 40 percent relative density the
multi-stage ¢f was always slightly higher. The agreement
is good for the shear strength and angle of internal
friction, but only fair to poor agreement is found for
dilatancy, void ratio at failure and horizontal deflection
at failure. This would tend to agree with Lumb's (1964)
97
conclusions for the triaxial test.
3. The results from triaxial compression/consolidated
drained/multi-stage testing are in good agreement with
the results from conventional tests, However, it appears
that ~f obtained from multi-stage testing is slightly lower
than ~f obtained from conventional tests, Thus, using
the multi-stage parameter, ~f' would be slightly on the
conservative side.
98
4. For the limited results of the triaxial compression/
consolidated undrained testing, the multi-stage and con-
ventional test results are in good agreement.
5. For the pressures investigated there was no
appreciable particle crushing in either the conventional or
multi-stage tests.
6. Although only one granular material was used in
this study, it is believed that the same conclusion
regarding multi-stage testing should apply to other
granular materials.
7. Valuable time can be saved by using multi-stage
test procedures to evaluate the shear strength parameter,
~f. Within the time of approximately two hours, a
multi-stage test with three to four stages can be
completed, the data plotted and the shear strength
parameters evaluated. The savings to a soil mechanics
laboratory and to a client could be substantial.
99
IX. APPENDICES
APPENDIX 1
DETAILED TEST PROCEDURES ~
DIRECT SHEAR/CONSOLIDATED DRAINED
The first stage of the multi~stage test is the same
procedure as a conventional test. The procedure for this
stage is as follows:
1. The sample is prepared as outlined on page 25
under "Sample Preparation".
100
2. The shearing assembly with sample is placed in the
Karol-Warner machine. The machine with sample in
place ready for shearing is shown in Figure 46.
The shearing device is further broken down in
Figure 47. In this figure the parts are as
follows: A is the water reservoir with lower
ring and porous stone in place, B is the top
porous stone, C is the upper ring stop, D is the
upper ring with elevating screws in place, E is
the loading block, F is the alignment screws and
G is the loading arm.
3. The upper ring stop is seated on the upper sample
ring and the assembly is moved so that the ring
stop lugs bear against the base lugs.
4. The load block is then placed on the top porous
stone and the load arm is adjusted until it barely
touches the load block. A small ''bulls~eye" level
is used to keep the load arm level.
FIGURE 46 . Direct Shear Sample in Place Ready for Testing
101
1 02
FIGURE 47. Direct Shear Device Disassembled
103
5. The vertical strain dial indicator is placed on
top of the pin in the load arm so that approximately
half of its movement is registered~ and then it
is zeroed.
6. The air pressure relief valve is shut and the
toggle valve between the pressure regulator and
loading device is closed. The air regulator is
slowly opened until the desired pressure is
indicated on the gauge. This gauge pressure is
predetermined from the calibration chart for the
desired normal load.
7. The toggle valve is opened and the normal load is
instantaneously applied to the sample. The sample
is then allowed to consolidate under the normal
load for approximately thirty minutes. The
consolidation in all cases was almost instantaneous.
After consolidation, the reading from the vertical
strain dial is recorded.
8. The three alignment screws are carefully removed
from the sample rings. The elevating screws are
then turned 3/4 turn - clockwise - to provide
clearance between the rings. The 3/4 turn
provides a clearance of approximately 0.0375 inches,
which is slightly larger than the largest soil
grain. This was checked to be sure that the
top half would not ride up on a grain which might
9 .
get between the rings,
The play is taken out of the shear drive system
by tightening the nut on the load cell extension
against the reservoir chamber lug. Care must be
taken so that no shear load is applied to the
sample. This can be checked by watching the
strain indicator reading.
10. The vertical strain dial is once again checked
and the reading recorded. There will be some
change because of the spreading of the rings.
11. Both the horizontal and vertical strain dials
are zeroed and the initial reading recorded from
the strain indicator.
12. The motor is then turned on and the variable
speed drive set to a speed from 20 to 25 rpm.
13. At increments of horizontal deflection, readings
are taken of shear force, vertical and horizontal
deflection and time. Readings were usually taken
at increments of 0.01 inches of horizontal
deflection and at 0.005 inches when failure
seemed close.
14. The test stage is continued until 0.1 inch
horizontal deflection or until a constant or
decreasing shear force is obtained. In all cases
in this study, failure occurred before maximum
deflection was reached.
104
105
At this point, different procedures were used for the
additional stages. The procedures were as follows:
Procedure "A"
15. The shearing is stopped by turning off the
variable speed drive, Readings are taken on
horizontal and vertical deflection and shear force.
16. The normal force on the sample is then increased
to a predetermined level. This is done by further
opening the air pressure regulator.
17. The sample is then allowed to consolidate and
readings are taken at the end of the consolidation
period.
18. The procedure is then the same as steps #11
through #14. If more stages are desired the
pressure is further increased and the procedure
repeated.
Procedure "B"
15. The shearing is stopped, horizontal and vertical
deflection and shear force readings are taken.
16. The variable speed drive is then turned to the
reverse position thus causing the motor to turn
in the opposite direction. The force is then
tending to push the bottom ring back to its
original position.
17. Two "C" clamps must be used to hold the ring
stop lugs, which hold the top ring, to the base
106
lugs. If this is not done the top ring will move
with the lower ring,
18. The reversing force is continued until the
horizontal deflection dial reads the same as at
the beginning of the stage and is then stopped.
For this study, the reading was always zero.
Readings were taken at intervals of horizontal
deflection the same as in the forward shearing
process.
19. The normal force is then increased as in
Procedure "A" and the sample allowed to con
solidate.
20. The procedure is then continued the same as steps
#11 through #14. If further stages are desired,
this procedure is repeated.
Procedure "C"
15. The shearing is stopped and readings are taken.
The normal force is then released. This is done
by closing the toggle valve between the bellows
and air regulator and opening the air pressure
relief valve.
16. The procedure is this continued the same as
steps #16 through #20 of Procedure "B".
Procedure "D"
Steps #15 through #17 the same as Procedure "B".
18. The reversing force is continued to the point
107
that there is no shear force on the sample. This
point is found by stopping the motor when the
reading on the Budd indicator is the same as at
the beginning of the stage. Readings were taken
at intervals of horizontal deflection.
19. The procedure is then continued the same as steps
#19 and #20 of Procedure "A".
Procedure "E"
Steps same as #15 through #18 of Procedure "D".
19. The normal force is then decreased to a pre
determined level and the sample allowed to come
to equilibrium.
The procedure is then continued the same as #19 and
#20 of Procedure "A".
APPENDIX 2
DETAILED TEST PROCEDURES ~
TRIAXIAL COMPRESSION/CONSOLIDATED DRAINED
The procedure used in the triaxial compression/
consolidated drained tests is as follows:
1. After preparation of the sample, the top of the
triaxial chamber is put in place and secured.
The chamber is then put into position in the
loading machine. The confining pressure and
volume change leads are already connected to the
chamber and are closed.
108
2. The chamber is filled with deaired water by
gravitational flow. As the water gives support
to the sample, the back vacuum valve to the
sample is closed. The cell is filled until there
is no air in the chamber and water escapes from
a valve at the top of the chamber. The valve
is then closed.
3. The chamber pressure valve is opened to permit
the pressure within the chamber to be
atmospheric. The loading piston is then brought
into contact with the top cap of the sample.
4. The loading ring is put into place and brought
into contact with the loading piston. The
displacement dial is positioned in contact with
the chamber and zeroed in. This is the initial
109
reference for the change in height of the sample.
The loading ring is then raised away from the
loading piston during back pressure and
consolidation phases,
5. The confining pressure is then increased to a
predetermined level by opening the chamber
pressure regulator on the back pressure - volume
change apparatus, The pressure is monitored
by a test gauge of ~ percent full scale
accuracy.
6. Initial readings are taken on the volume change
burette. The valve at the base of the chamber
from the volume change burette is opened and the
sample is allowed to consolidate.
7. After consolidation is completed, the loading
ring is brought into contact with the loading
piston and top cap of the sample. The displace
ment dial is read and recorded. The difference
between the initial reading and the reading
after consolidation gives the change in height
of the sample during consolidation.
8. A reading of the volume change burette is taken
and recorded; the displacement dial and load
ring dial are zeroed.
9. External or chamber volume change readings may
also be taken if desired. These readings are
110
taken during drained tests and are used to detect
leakage in the triaxial membranes.
10. The sample is now ready to be sheared. The
loading machine is turned on and the sample
sheared at a predetermined rate of strain.
11. During shearing, readings are taken from the
loading ring and volume change burette at
predetermined increments of strain. The time
from the beginning of the test is also recorded.
12. When failure is reached, the load machine is
turned off. Failure is defined at the maximum
principal stress ratio or maximum deviator stress.
In the TX/CD, they occur at the same point.
Final readings are recorded. To this point, the
procedure described is a conventional test. The
test is continued using the multi-stage procedure.
13. The sample is then unloaded by turning the
knurled nuts on the loading arm in a counter
clockwise direction. The unloading is continued
until the load ring reads zero. Unloading is
stopped and the readings from the displacement
dial and volume change burette are recorded.
14. The loading arm and loading ring are then raised
during the consolidation phase.
15. The valve connecting the volume change burette to
the chamber is then closed and the chamber
pressure is changed to a predetermined level for
the second stage.
16. The valve to the volume change burette is then
opened and the sample is allowed to consolidate
for the second stage.
The procedure is then repeated for the desired number
of stages.
111
APPENDIX 3
DETAILED TEST PROCEDURES -
TRIAXIAL COMPRESSION/CONSOLIDATED UNDRAINED
The procedure used in the triaxial compression/
consolidated undrained test is as follows:
112
1. After preparation of the sample, the top of the
triaxial chamber is put into place and secured.
The chamber is then positioned in the loading
machine. The confining pressure and volume change
leads are already connected to the chamber and are
closed. The pore pressure transducer is also in
place and great care is taken to see that no air
is in the system.
2. The chamber is filled with deaired water by
gravitational flow. As the water gives support
to the sample, the back vacuum valve to the
sample is closed. The cell is filled until there
is no air in the chamber and water escapes from a
valve at the top of the chamber. The valve is
then closed.
3. The chamber pressure valve is opened to permit
the pressure within the chamber to be atmospheric.
The loading piston is then brought into contact
with the top cap of the sample.
4. The loading ring is put into place and brought
into contact with the loading piston. The
113
displacement dial is positioned in contact with
the chamber and zeroed in. This is the initial
reference for the change in height of the sample.
The loading ring is then raised away from the
loading piston during back pressure saturation
and consolidation phases.
5. Saturation of the sample is then checked. This
is done by back pressure saturation. The
procedure is as follows:
a. Take the initial readings on the volume
change burette and the pore pressure transducer.
b. Raise the confining pressure, by turning
the chamber pressure regulator, to a small
pressure, i.e. cr 3 = 3 psi.
c. Open the volume change valve and allow
drainage (consolidation).
d. Shut the volume change valve; record
reading on volume change burette.
e. Raise the confining pressure by a small
increment, i.e. cr 3 = 5 psi.
f. Raise the back pressure, by turning the
back pressure regulator, to a small pressure,
i.e. aBP = 2 psi. Open the volume change valve
and let the sample come to equilibrium.
g. Close the volume change valve and raise the
confining pressure by a small increment
i.e. cr 3 = 10 psi,
change burette,)
(Record reading on volume
h. Raise the back pressure i.e. crBP = 5 psi
and open the volume change valve allowing the
sample to come to equilibrium.
1. Close volume change valve and record
reading on volume change burette.
j. Raise the confining pressure, i.e. cr 3 =
15 psi, and record the reading on the pore
pressure transducer.
114
The saturation of the sample can then be checked
by calculating the B pore pressure parameter.
It may be calculated by the following relation-
ship:
where:
~u B = (IX-1)
~U = the change in pore pressure
~a 3 = the change in confining pressure
For 100 percent saturation B should be approxi-
mately: 1. The value of B for 100 percent
saturation will vary for different soils. (Lee,
1965). Satisfactory saturation is usually
assumed when it reaches 95 percent. If this
value is not found the saturation procedure
continues.
k. Raise the back pressure, i.e. crBP = 10 psi
and open the drainage allowing the sample to
115
consolidate. Record reading on volume change
burette. Close drainage.
1. Raise the cell pressure, i.e. a = 3 20 psi
and check the B parameter. If it is not to the
desired level continue the process. If it is to
the desired saturation, the back saturation can
be stopped.
m. Assuming the desired B parameter has been
reached, raise the confining pressure and back
pressure so that the back pressure is at its
predetermined level and the difference between
the back pressure and confining pressure is
equal to the desired consolidation pressure.
n. Open the drainage and allow the sample to
consolidate.
6. After consolidation, take readings on the volume
change burette and the pore pressure transducer.
Close volume change valve.
7. The loading ring is brought into contact with the
loading piston and top cap of the sample. The
displacement dial is read and recorded. The
difference between the initial reading and the
reading after consolidation gives the change in
height of the sample during consolidation. The
displacement dial and load ring dial are zeroed.
8. The sample is now ready to be sheared. The
loading machine is turned on and the sample
sheared at a predetermined rate of strain.
9. During shearing, readings are taken from the
loading ring and pore pressure transducer at
predetermined increments of strain.
10. When failure is reached the loading machine is
turned off. Failure is defined at the maximum
effective principal stress ratio. To this
point, the procedure described is a conventional
test. The test is continued using multi-stage
procedure.
11. The sample is then unloaded by turning the
knurled nuts on the loading arm in a counter
clockwise direction. The unloading is continued
until the load ring dial reads zero. Unloading
is stopped and the readings from the displacement
dial and pore pressure transducer are recorded.
12. The loading arm and loading ring are then raised
during the consolidation phase.
13. The confining pressure is then changed to a
predetermined level for the second stage and the
volume change valve is opened allowing the
sample to consolidate.
The procedure is then repeated for the desired number
of stages.
116
APPENDIX 4
BACK PRESSURE - VOLUME CHANGE APPARATUS
The procedure for the usage of the back pressure -
volume change apparatus shown in Figure 4 is as follows:
Air pressure entering the apparatus is regulated by
the back pressure regulator (operating range 0-60 psig,
150 psi maximum) and the chamber pressure regulator
(operating range 0-120 psig, 200 psi maximum). The
117
pressures are monitored by pressure gauges which are located
on the apparatus. The pressure from the chamber pressure
regulator goes to the chamber pressure burette. The
pressure within the burette is transmitted from the air to
the water at the air-water interface. When the connection
is opened between the chamber pressure burette and the
chamber, the pressure is further transmitted within the
chamber. The pressure from the back pressure regulator
goes to both the back pressure burette and the volume
change burette. These two burettes are brought together
to a single connection to the base of the sample.
The volume change burette was calibrated without back
pressure and for the smallest division on the scale (0.1 em.)
a volume change of 0.0079 cc was found. The burette and
tubing leading to the cell were then calibrated for volume
changes due to expansion of the tubing under increasing
pressures. From this calibration, the change in height
of the water column due to the change in pressure was
found to vary according to the equation:
118
~H ~ 0.64 p 0 · 55 (IX-2)
where: ~H = change in height of water in burette
P = the applied back pressure
All volume changes found in this research were corrected
according to this equation.
119
X. BIBLIOGRAPHY
ANDERSEN, A. and SIMONS, N. E., (1960), "Norwegian Triaxial Equipment and Technique", Research Conference On The Shear Strength of Cohesive Soil, A.S.C.E., pp. 695~709.
BISHOP, A. W. and GREEN, G. E., (1965), "The Influence Of End Restraint On The Compression Strength Of A Cohesionless Soil", G~otechnique, Vol. XV No. 3.
DEBEER, E. E., (1950), "The Cell Test", Geotechnique, Vol. II, pp. 162-172.
FLEMING, H. D., (1952), "Undrained Triaxial Compression Tests on a Decomposed Phyllite", First Australia New Zealand Conference on Soil Mechanics and Foundation Engineering, pp. 112-122.
KENNY, T. C. and WATSON, G. H., (1961), "Multi-Stage Triaxial Test for Determining C' and ~· of Saturated Soils", Fifth International Conference on Soil Mechanics, Vol. I, pp. 191-195.
LAMBE, T. W. and WHITMAN, R. V., (1969), Soil Mechanics, John Wiley and Sons, Inc., New York, pg. 448.
LEE, K.
LEE, K.
L., (1965), "Triaxial Compressive Strength of Saturated Sand Under Seismic Loading Conditions", Thesis presented to the University of California, at Berkley, California in 1965 in partial fulfillment of the requirement for the degree of Doctor of Philosophy.
L. and SEED, H. D., (1967), "Drained Strength Characteristics of Sands", Journal of the Soil Mechanics and Foundation Division, Proceedings of the American Society of Civil Engineers, Vol. 93, No. SM6, 1967, pp. 117-141.
LUMB, P., (1964), "Multi-Stage Tr~axial.Test~ On Undisturbed Soils", Civ1l En~1neer1n~ and Public Works Review, May, 19 4, pp. 91-595.
MEANS, R. E. and PARCHER, J. V., (1963), Physical Books Properties of Soils, Charles E. Merrill Inc., Columbus, Ohio, p. 326.
/ ,._,
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120
VITA
Robert Clyde Gullic, the son of Clyde A Gullic and
Anna A. Gullic, was born 2 May, 1946 at McLeansboro,
Illinois.
121
He received his primary and secondary education from
the Eldorado Public School System, Eldorado, Illinois. He
entered the University of Missouri - Rolla in September,
1964, and graduated with a bachelors degree in Civil
Engineering in January, 1969. He received a reserve
commission as a Second Lieutenant in the Army Corps of
Engineers at that time. While pursuing his undergraduate
studies he was the recepient of the Jesse H. Stienmesch
Memorial Scholarship and the General Contractor of Missouri
Scholarship. He takes great pride in having been named
to Who's Who in American Universities and Colleges, 1969.
Since January, 1969 he has pursued studies toward a
Master of Science Degree in Civil Engineering at the
University of Missouri - Rolla.
He married Miss Suzanne Stearns in March, 1969.
He is a member of Chi Epsilon, Tau Beta Pi, Phi Kappa
Phi and Scabbard and Blade, National Honor Fraternities.
He is a member of the American Society of Civil Engineers,
an Engineer in Training in the Missouri Society of
Professional Engineers, and a member of the International
Society of Soil Mechanics and Foundation Engineers,