V1
-——v w

 

I":

v—W vvvv

 

FAELURE MODES IN. «CLAY

Thai: far fhe mtg!“ of M. 5..
MEEHEGAN.$TATE' untVEasm
David L, Waréer
1954

:rHEsxs

 

LIBRARY

Michigan State
University

 

 

ABSTRACT

FAILURE MODES IN CLAY

By David L. Warder

An experimental study was made to evaluate the
deformation conditions that accompany failure in a clay
under axial compression. The type of end restraint and the
strain rate were varied in a series of unconfined compression
and CPS tests in order to study their effect on the type
of failure and on the strength of the clay.

It was found that after the appearance of a single
failure surface, further deformation is limited to rigid
body sliding along the failure surface° The use of friction—
less end plates and shorter samples tend to prevent the
formation of a single failure surface and produce multiple
slip lines. Frictionless end plates and increased strain

rate increase the strength as well as the failure strain.

FAILURE MODES IN CLAY

BY

1/.
L"

‘/
David L. Warder

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Civil Engineering

1964

'1 ‘u’ " “' I

.7-/!» t7

ACKNOWLEDGMENTS

The writer wishes to express his sincere appreciation
to Dr. T. H. Wu, Department of Civil Engineering, under
whose supervision this research was carried out. His
guidance and encouragement in the preparation of this
thesis, as well as throughout the writer's Master's Degree
program, have been invaluable. The writer is also indebted
to Dr. A. K. Loh for his assistance in the laboratory and
for his many worthwhile suggestions.

The writer wishes to thank the National Science
Foundation and the Division of Engineering Research at
Michigan State University for the Graduate Research

Assistantship that made this research possible.

ii

TABLE

Chapter
I° INTRODUCTION . . . . . . . . . . . .
II. THEORETICAL CONSIDERATIONS . . . . .
2.1 Failure surface
2.2 Plasticity solutions for axial symmetry
2.3 Solution for axial symmetry by
kinematics
III. EXPERIMENTAL PROGRAM . . . .
3.1 Soils used
3.2 Preparation of samples
3.3 Unconfined compression tests
3.4 CFS tests
IV. PRESENTATION AND DISCUSSION OF RESULTS
4.1 Failure types
4.2 Effect on strength
V. CONCLUSIONS . . . . . . . . . . . . .

BIBLIOGRAPHY . . . . .

APPENDICES . . . . . .

OF CONTENTS

iii

boo

10
10
ll
11
15
21

21
25

32

34

35

ll.

12.

l3.

14.

15.

16°

17.

18.

19.

20.

21.

LIST OF TABLES

Index properties . . . . . . . . . . . . . . .

Final water content variation for consolidated
samples 0 0 I O 0 O O O 0 O 0 O U 0 0 0 0

Summary of testing program on kaolinite . . .

Summary of unconfined testing program on Sault
clay . . . . . . . . . . . . . . . . . . .

Summary of CFS tests . . . . . . . . . . . . .

Results of unconfined compression tests on
kaolinite . . . . . . . . . . . . . . . .

Results of unconfined compression tests on
saUlt Clay 0 O O O O 0 O O O O O O O O 0 0

Summary of CFS results . . . . . . . . . . . .
Summary of CFS results on ¢ and C . . . . .
Data sheet for W—K-U—l . . . . . . . . . . . .
Daé. sheet for W—K-U—6 . . . . . . . . . . ..
Data sheet for W—S-U—4 . . . . . . . . . . . .
Data sheet for W-C-CU—2 . . . . . . . . . . .
General data sheet for WF-CFS—6 . . . . . .

Consolidation data sheet for WF-CFS—6 . . . .
Typical CFS data sheet from WF—CFS-6 . . . . .
CFS calculation sheet for WF-CFS—6 . . . . .

General data sheet for GF-CFS-Z . . . . . . .
Consolidation data sheet for GF-CFS-2 . . .

Typical CFS data sheet from GF—CFS-Z . . . . .

CFS calculation sheet for GF-CFS-Z . . . . . .

iv

Page

10

12

15

16

20
28

29
3O
31
36
37
38
4O
49
50
51
52
54
55
56

57

Figure

10.
11.
12.
13.
14.
15.
16.
17.
18°
19.
20.
21.
22.
23.

24.

LIST OF FIGURES

Mohr circle . . . . . . . . . . . . . . .
Formation of dead zones . . . . . . . . .
Sketch of deforming region for Eq. (6) .
Sketch of deforming region for Eq. (8)
Sketch of deforming region for Eq. (13) .
Cross section of frictionless end plates
Set-up for instantaneous load application

Sketch of bottom of triaxial sample . . .

Cross section of bottom condition for CFS
Diagram of triaxial set—up . . . . . .
Types of failure . . . . . . . . . . . .

Comparison of deformation modes of W-K—U—3 and 4

Relationship of $6 and CE with strain . . . . .

Stress-strain curves for unconfined tests
Stress—strain curves for unconfined tests
Stress-strain curves for unconfined tests
Stress—strain curves for unconfined tests
Stress-strain curves for unconfined tests

Stress-strain curves for unconfined tests

CFS curves for WF—CFS—Z . . . . . . . . .
CFS curves for WF-CFS-3 . . . . . .

CFS curves for WF-CFS-4 . . . .

CFS curves for WF—CFS-6 . . . . . . . . .
CFS curves for WF-CFS-7 . . . . . . . . .

O

Page

14
14
17
18
19
21
23
27
42
43
44
45
46
47
59
6O
61
62

63

Figure
25.
26.
27.
28.
29.
30.
31.
32.

33.

CFS

CFS

CFS

CFS

CFS

curves

curves

curves

curves

curves

for

for

for

for

for

Photographs of

Photographs of

Photographs of

Photographs of

GF-CFS-l
GF-CFS-Z
GF—CFS-3
GF—CFS-4
GF—CFS-S
deformed
deformed
deformed

deformed

vi

specimens
specimens
specimens

specimens

Page
64
65
66
67
68
74
75
76

77

Appendix

A.

LIST OF APPENDICES

SAMPLE DATA SHEETS AND STRESS-STRAIN
CURVES FOR UNCONFINED COMPRESSION

TESTS . . . . . . . . . . . .

SAMPLE DATA SHEETS AND CURVES FOR CFS TESTS

SAMPLE CALCULATIONS AND INTERPRETATION OF

DATA 0 0 O O O O O O I O O O

PHOTOGRAPHS OF DEFORMED SPECIMENS

vii

Page

35

48

69

73

deviator

Notation

shear strength

normal stress

major principal stress
minor principal stress

maximum compressive stress in unconfined compression
test

shear stress

cohesion

cohesion, as determined from CFS test
angle of internal friction

angle of internal friction. as determined from

CFS test

axial strain

axial strain at failure
strain rate

radial velocity

axial velocity

shear strain rate

angle measured from a horizontal line through the
center of a specimen

tan (45° + #3)

twice the angle between the principal directions of
stress and strain

water content

length of sample at beginning of test

stress, (Cl - O3)

viii

I . INTRODUCTION

The shear strength of a soil as evaluated from a
triaxial shear test is usually based on the Coulomb failure

criterion. The strength is given by,
S = C + J tan ¢ (1)

in which S is the shear strength of the soil, C is a con-
stant termed the cohesion, o is the normal stress on the
slip plane, and ¢ is a constant called the angle of
internal friction.

In many cases, the failure surface is visible at
the conclusion of a triaxial test. In other cases, exami-
nation of a failed sample shows no failure surface but
only a general bulging of the specimen. In still other
samples, a predominant failure plane is absent but many
lesser slip lines are visible. The effect of the type of
failure on the shear strength and on the friction and
cohesion of a soil is not fully understood.

Haythornthwaite (1959, 1963) applied the plasticity
theory to calculate the velocity field inea triaxial
sample and showed that the solution is not unique. He
states that a stress—strain relation in addition to the

failure criterion would be required to establish uniqueness.

The purpose of this study is to evaluate the
deformation conditions that accompany failure and their

effect on the failure criterion.

I I . THEORETICAL CONSIDERATIONS

2.1 Failure surface

The relationship given by the Coulomb equation (1)
produces a straight line when shear stress is plotted
against normal stress. Stresses at failure can be repre-
sented on the same plot by a circle with the center at

. 014-03
(T = 0, o = -——§———) and a diameter of (u

01 and 03 are the major and minor principal stresses

respectively (see Fig. 1).

l - 03), where

T

 

 

 

 

Fig. l. Mohr circle.

The straight line defined by equation (1) is known
as the failure envelope and the circle is known as the Mohr
circle. Failure is represented by the point of tangency,

a, between the circle and the failure envelope.
In a conventional triaxial test, the friction of the

end plates does not permit the soil in contact with the

plates to expand in a radial direction. Rowe (1964)
pointed out that this produces dead zones at the ends of
the sample as shown in Fig. 2. This restricts lateral
strain to the middle portion of the specimen and causes
failure to occur within narrow zones. This often results

in the formation of a single slip surface.

 

 

 

 

 

 

 

 

 

Dilating /z>( g I
zone \ /"\ / --L~ a=45° + 3
> ‘ 2
/ \/
/é\
1 \
Fig. 2. Formation of dead zones.

Rowe (1964) notes that the use of frictionless end
plates would eliminate the dead zones and thus tend to
prevent the formation of a predominant failure surface.

He explains that without the dead zones, uniform lateral
strain results and there is no longer a tendency for one
zone to fail before another. He predicts that this causes
the sample to reach larger strains before failure and that

the failure occurs in the form of multiple failure surfaces.

2.2 Plasticity solutions for axial symmetry

Haythornthwaite (1959) used the theory of plasticity

to calculate the velocity fields during a triaxial test.

In his solution, the soil is assumed to be an isotropic,
ideally plastic material. Due to the assumption of isotropy,
the principal direction of strain coincides with the princi—

pal direction of stress. Thus the shear strain rate in the

r—Z plane, yrz,must be zero. This can be written as,
- Bu 3w
hrs—2+3?“ (2’

where u and w are the radial and axial velocities respective-

ly. The other strain rate components are,

. _ Bu ° _ u ° _ __.
6r — r ' 66 _ r ’ e (3)
According to the plastic potential theory, the strain rate

components must satisfy the relationship,

. . . 2 o .3 _

er + 69 + EZ tan (45 + 2) — 0 (4)
Substituting (3) into (4),

-%% +-% + 3% tan2 (450 + g) = 0 (5)

Equations (2) and (5) are the governing differential
equations.

These equations are first solved using the boundary
conditions shown in Fig. 3. The rigid zones shown at both
ends are the result of the end restraint. Continuity of
velocity is assumed across OB so that u = w = O on OB
except at 0. Using these boundary conditions, the

solution of the differential equation is,

‘VNZ - tanZY
(6)
tan.1 'Vsz cotZY — 1

 

 

=HN =IIN

r
Deforming Deforming
Region Region

 

a

Fig. 3. Sketch of deforming region for Eq. (6).

Deforming
Region

Deforming
Region

 

Fig. 4. Sketch of deforming region for Eq. (8).

where N = tan (450 + g).

The nature of the deformation defined by (6) is shown by
the dotted lines in Fig. 3.

In order to show that the deformation defined by
equations (6) is not the only possible mode of deformation
for the axially symmetric case, Haythornthwaite solves
equations (2) and (5) using the boundary conditions shown

in Fig. 4. In region OAC, the field used is

_ r._ 0 3;

u — 2a tan (45 + 2)
(7)

_.Z 0 .2

w — 2a tan (45 + 2)

Equations (7) satisfy (2) and (5) and also the boundary
condition w = l on AC. The solution for region AOB,

using the boundary conditions of Fig. 4 is,

 

 

 

 

 

 

_ R (NZ cos ‘1’ tan-1 VNZ cotz‘l’ - l - sin ‘1’sz - tanz‘l’
u - ZFaN
H8)
2. l
w = R (cos I _VNZ - tanzY - sin I tan-l-V N coth-lL
WaN

 

The deformation described by equations (8) is shown by the
dotted line in Fig. 4. In equations (6) and (8) Y varies

from O0 to (450 + g).

2.3 Solution for axial symmetry by kinematics

Saint—Venant's Principle states that the principal
direction of strain coincides with the principal direction

of stress. By an analysis of the kinematics along the slip

planes, de Jong (1958) proves that this is true at failure
only for a material with ¢ = O. For a material with ¢ > 0,
the angle between the principal directions of stress and
strain may be anywhere between zero and ¢. Haythornthwaite
(1963) proves the same thing using a different approach.
Haythornthwaite (1963) presents another solution
for axial symmetry in which he assumes an angle of a/2
between the principal directions of stress and strain. From
the geometry of the Mohr circle for strain, the following

relationship holds;

i
tand=7—£Z—,- (9)
er - EZ
With the definitions
E =.5_9_.€ 32.6 __.éiv
r 5r'e r’zaz (3)
. _ Bu SW
and ”Hz-afar (10’
(9) becomes
tan a 3% - §% - g¥ - tan a gg- = O (11)
The zero dilation equation is
Bu u 5w _
E+r+az-0 (12)

Equations (11) and (12) are the governing differential
equations. It can be noted here that if the principal
directions of stress and strain coincide (d = O) as is
assumed in the plasticity solution of Sec. 2.2, equation (11)
degenerates to equation (2) which is one of the governing
differential equations in the plasticity solution. Equations
(11) and (12) are solved using the boundary conditions

shown in Fig. 5.

 

Fig. 5. Sketch of deforming region for Eq. (13).

The solution of (11) and (12) is

 

 

 

 

 

 

 

2 W/N - tan Y W
_ cos a N + tan Y
u — W l
§+Cl+'2—Sin20.
. N13)
.1 —l .1 j’N - tan Y
w _ 2 — sin (tan Y cos a - sin a) + 2 sin 2 a N + tan Y
" 1 .1. -

2 + a + 2 Sln 2 a J

where N = tan (450 +-%)

and Y varies from O0 to (450 + %)° The deformation pattern

described by (13) is shown by the dotted lines in Fig. 5.

III. EXPERIMENTAL PROGRAM

The experimental program is designed to observe the
deformation characteristics of specimens at failure and
their effect on the shear strength parameters. The variables

studied are the strain rate and the end restraint.

3.1 Soils used

There are three different clays used in the testing
program. The first is a glacial lake clay taken from a site
near Sault Ste. Marie, Michigan, at a depth of approximately
5 feet below the ground surface. This is referred to as
Sault clay. The Sault clay contains about 50 percent illite,
25 percent vermiculite, and 15 percent chlorite. The re—
maining 10 percent is a combination of montmorillonite,
quartz, feldspar, and kaolinite according to X—ray diffraction
tests (Dillon, 1963). The other two soils used are com—
mercial grundite and kaolinite. The index properties of

the soils used are given in Table 1.

Table 1. Index properties.

 

 

 

. Plastic Liquid Plasticity Clay
Type 8011 Limit Limit Index Fraction
Sault 23.6% 60.5% 36.9% 0.60
Grundite 25.0% 78.0% 53.0% 0.65
Kaolinite 28.0% 50.0% 22.0%

 

10

11

3.2 Preparation of samples

The Sault clay and grundite samples are compacted
and trimmed as described by Holliday (1963). Due to the
difficulty in trimming, the kaolinite samples are prepared
differently. The dry clay is mixed with enough distilled
water to make a water content of approximately 25 percent.
After the clay and water are thoroughly mixed, the mixture
is compacted in the Harvard Compaction mold in 5 layers.
Each layer is tamped 25 times evenly over the surface.

The force delivered by the tamper is 50 pounds over a cir-
cular area of .15 square inch.

Specimens that are referred to as "compacted" are
those prepared in one of the two ways mentioned above.

The term "remolded" as used in this report means that the

sample is remolded by hand immediately prior to trimming.

3.3 Unconfined compression tests

Haythornthwaite (1963) pointed out that while the
final deformation pattern of a triaxial sample is well
known, it is not clear exactly how the deformation proceeds
during the test. In order to study the deformation patterns
of clay samples, photographs are taken at various strains
throughout a series of tests. The photographs are taken
by a camera that is mounted on a frame in front of the
triaxial cell. Initial plans were to take photographs
during triaxial tests. However, this proved unsuccessful

due to the fact that the lucite of the triaxial cell and

12

the water within the cell prevented accurate focusing.
It was then decided to remove the lucite cell and run un-
confined compression tests.

In the first unconfined compression tests
(W — C - CU - 2 and W - C - CU - 3), the sample was first
consolidated under a hydrostatic pressure of 2.00 kilograms
per square centimeter. The pressure was then relieved,
the water drained out, and the lucite cell removed. The
photographs showed that most of the deformation took place
at the bottom of the sample. Upon checking the final water
content, it was determined that the water content was
higher at the bottom of the sample. Table 2 shows the

moisture content variation within the sample.

Table 2. Final water content variation for consolidated

 

 

 

samples.
Test Initial Final Water Content — %
Designation Water
Content-% Top Huddle Bottom
W—C-CU—2 40.8 30.1 31.8 32.8
W—C-CU—3 41.9 28.8 30.7 32.6

 

The higher water content at the bottom is probably
due to the absorption of water from the porous stone as the
specimen tends to swell upon release of pressure. It seems
reasonable, therefore, that the large deformation at the
bottom is the result of non-homogeneity rather than a
failure characteristic. On the basis of this, it was
determined to run tests on samples immediately after trim-

ming without consolidation.

13

"Frictionless" end plates are used in order to
determine their effect on the mode of failure and on the
shear strength. The end plates are made of lucite and are
approximately 2 inches in diameter. The bottom end plate
is cut out at the bottom so that it fits over the pedestal
of the triaxial cell. Two small holes that line up with
the holes in the pedeStal are drilled through the bottom
end plate. The frictionless condition is obtained by
sprinkling graphite on to the lucite end plates and then
placing a thin rubber membrane over it. The top and bottom
of the sample are then in contact with a rubber membrane
which is free to expand in the radial direction due to the
graphite. This is illustrated in Fig. 6.

Unconfined compression tests are run on both
kaolinite and Sault clay. Most of the tests are run at a
constant strain rate with several different strain rates
being used. In order to obtain an extremely fast strain
rate, an instantaneous load is applied in two of the tests
(W-S-U-lO and W-S-U-ll). This is done by placing an 8
kilogram weight on to a loading yoke as shown in Fig. 7.
Photographs are taken in selected tests. A summary of the
test program on the kaolinite is given in Table 3 and on the
Sault clay in Table 4.

Stress-strain curves are obtained in each test.

The maximum compressive stress (Omax) and the strain at which
the maximum compressive stress occurs (6f) are determined.

The deformation patterns are studied by overlaying the

14

. ' Rubber
% band
Graphite-
==EE”‘“”'”M ”I” 1 Rubber '
membrane

.5 Sample
M.

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

(a) Top (b) Bottom

Fig. 6. Cross section of frictionless end plates.

A AL.

WT

 

PPiston

 

 

 

 

 

 

,‘;=;—‘Loading YOke

Sampleqz;

 

 

 

 

 

 

 

 

 

 

 

 

_f

 

 

 

 

Fig. 7. Set—up for instantaneous load application.

photographs taken at different strains.

failure is noted in each test.

The type of

Table 3. Summary of testing program on kaolinite.

 

 

 

Water Strain Type of Length
Test Designation Content Rate End Plate - in.

w-% -%/Hr. °
W—K-U—l* 24.8 360 Conventional .
W—K—U—2* 25.3 360 Conventional .
W-K-U-3* 26.1 360 Conventional .
WeK-U—4* 23.8 0.23 Conventional .
W-K-U—5* 25.9 360 Frictionless .
W—K-U—6* 26.2 360 Frictionless .
WeK-U—7* 25.9 360 Conventional .
WeK-U-8* 25.2 0.40 Frictionless .
W—K-U—9 26.1 700 Frictionless .
W-K-UelO 26.1 700 Frictionless .
W—K—U-ll 26.1 360 Frictionless 2.

 

*Photographs taken.

3.4 CFS tests

The CFS tests follow the same technique as that

described by Schmertmann and Osterberg (1960).

triaxial test in which the cohesion (Ce) and angle of

It is a

friction (¢€) are determined at various strains throughout

the loading process.

below.

The procedures used are described

After the sample is trimmed and cut to a length of

2.8 inches, three wool yarns are placed lengthwise through

the sample using a needle.

This is essential to quick

response to pore pressure changes and to rapid consolidation.

.cwxmu mammumouoams

 

16

 

¢0.N HmCOHucm>GOO 00m AN manna mmmv Uwumpflaomcoo «MIDUIOIZ
¢0.N Hmcofiucm>cou b.¢ AN manna mmmv pmumnflaomcou *NIDUIUIB
m.m mmmHGOHuoHum 000.0¢ 0.0m pm©H0Emm HHIDImIB
m.m mmmH:0HuoHHm 000.0¢ 0.0m pm0a05mm oalblmlz
m.m mmmHGOHDUHHm 00¢ 0.0m UthOEom mlblmlz
m.~ mmmacoapoflnm 00¢ 0.0m meHOEmm mIDImlz
m.m mmmacoHuUHum 00¢ 0.0m Umoaoamm hunlmlz
m.m mmeGOADUHHm 00¢ 0.0m ©m©HOEwm olblmuz
m.m mmmHCOHuoHum 00¢ ¢.0m ©mUHOEmm mIDImIB
m.m Hmcoflucm>coo 00¢ n.5m UmpHOEmm ¢|D|m|3
m.m Hmcoflucm>coo 00¢ m.mm wmuommsoo mIDImuz
m.m mmmHGOHuUHHm 00¢ 0.0¢ meHOEQm smIDImIB
m.m mmmasofluoflum 00¢ m.0¢ Umpaofimm *HIDImIB
o Sinuw a-..
.CH I q wumam paw mumm Dampsou COHumnmmmum soaumsmflmmn
£u0cmq mo mama cflmnuw kumz umma

 

 

.mmao pasmm so Emumonm msflmumu meHmcoocs mo mumEEsm .¢ maflme

17

With the frictionless bottom end plate, it is necessary
to connect the yarns with the holes in the end plate to
ensure proper drainage. This is done by placing the ends
of two of the yarns so as to line up with one of the holes
in the end plate and the third yarn to line up with the

other hole. This is shown in Fig. 8.

Filter
Paper

 

Fig. 8. Sketch of bottom of triaxial sample.

A l/4 inch wide piece of filter paper is placed on
each side of the sample to further speed up consolidation.
The sample is then weighed and placed between the end
plates. It is covered with two rubber membranes, each of
which is secured at each end by at least two rubber bands.
The sample is then placed in the triaxial cell by fitting
the bottom end plate over the pedestal. A third membrane,
which had been secured to the bottom of the pedestal by
rubber bands, is then stretched over the bottom end plate
and rubber bands are stretched over the outside of this
membrane. This bottom condition is shown in Fig. 9.

All samples are consolidated under a pressure of
2 kilograms per square centimeter for 24 hours. A back
pressure of 2 kilograms per square centimeter is then

applied for 24 hours. A pore pressure change of 0.5

18

kilograms per square centimeter is applied periodically

in order to obtain the two stress—strain curves of the CFS
test. Thus, the effective major principal stress (61)
alternates between 2.0 and 1.5 kilograms per square centi-
meter. For a detailed description of the procedure, see
HOlliday (1963). A diagram of the triaxial set up is

given in Fig.10.

    
  
 
 
 

Bottom End Plate

Rubber Bands Rubber Membrane

Pedestal

Fig. 9. Cross section of bottom condition for CFS test.

CFS tests are run on both grundite and Sault clay
compacted samples. Frictionless end plates are used in
all CFS tests in this study. Due to the uniform deformation
caused by the smooth ends, each CFS test is carried out to
a strain of at least 40 percent. This allows ¢€ and C6
to be calculated at large strains. The pore pressure is
continually adjusted to balance the deviator stress,
with one exception. In the slower strain rate tests, it
is necessary for the test to run overnight. In this case,
valve C (Fig. 10) is closed at night and reopened in the
morning. It should be noted that the pore pressure usually
varies only slightly overnight and is easily readjusted in

the morning.

l9

.0: pom HMmeHHu mo Emummfln .0H .mflm

Hmmnz amass
Honucou HOMDGOU
musmmmhm whom whammwnm Hawu

        
            

@

 

 

   
 

HHmU mHQEmm Hamo
musmmmum musmmmum
ucmumcou pcmumcoo

HHOU
HMHxMHHB
mpumusm
coumHm
kumfiocmz

  
     

   

mmmw
mHSmwmum

00mm
whommmnm

mCHm
0CH>OHm

Emflcmnomz
mCH>HHQ

20

Using the two stress—strain curves from each test,
$6 and C6 are calculated at several strains according to
the method show n in Appendix B. $6 and C6 are plotted
against strain to determine their relationship and the type

of failure is noted in each test. Table 5 gives a summary

of the CFS tests.

Table 5. Summary of CFS tests.

 

 

 

Test Designation Clay Rig: éSEr%;Hr. Waigitgghtent
wi - %
WF—CFS-Z Sault 1.25 42.3
WF—CFS-3 Sault 1.28 40.8
WF—CFS-4 Sault 1.25 42.0
WF-CFS-6 Sault 6.12 42.0
WF-CFS—7 Sault 5.93 40.2
GF-CFS-l Grundite 1.24 40.9
GF—CFS—2 Grundite 1.24 40.8
GF—CFS-B Grundite 7.06 40.9
GF-CFS-4 Grundite 4.94 40.8
GF-CFS—S Grundite 1.26 41.4

 

IV. PRESENTATION AND DISCUSSION OF RESULTS

The results of the unconfined compression tests
on kaolinite and Sault clay are tabulated in Tables 6 and
7 reSpectively. Similarly, Tables 8 and 9 summarize the

CFS test results.

4.1 Failure types

The types of failure encountered in this study can
be classified into three main groups. The three types,
failure plane, bulging, and multiple slip lines are

sketched in Fig. 11.

(a) Failure plane (b) Bulging (c) Multiple slip lines

 

Fig. 11. Types of failure.

In cases where either a failure plane or slip lines
appear, they become visable shortly after the maximum stress
is reached. For kaolinite, the maximum stress usually occurs
at about 15% strain. In all of the kaolinite tests on
standard length (2.8 inches) samples, the photographs
show bulging until shortly after this peak stress is

reached. A single failure plane then develops and further

21

22

motion is limited to rigid body movement along the failure
surface. This is particularly apparent upon comparing the
photographs of W—K—U—3 and W-K-U—4 (see Fig. 12). The
photographs at early strains show the same general bulging
in each test. Later photographs in WeK-U—4 show large
rigid body movement of the right side downward with respect
to the left side. This is readily visible since the move-
ment took place perpendicular to the direction of the
photographs. In W-K-U-3, photographs at later strains show
no change; although, it is obvious that a large amount of
sliding tookplace parallel to the direction of the photo—
graphs. This shows that all of the movement is along the
failure plane, probably because there is a reduction in
area along that section as soon as the failure plane develops.

By using shorter specimens (1.4 inches) in tests
W—K—U—lO and W—K-U—ll, formation of a single failure plane
is prevented. Thus, there is no area reduction and failure
in the form of multiple slip lines occurs at a larger
strain (25% i).

Since a single failure plane develops at such low
strains in the 2.8 inch kaolinite specimens, the type of
end plate does not affect the type of failure. In the
case of the unconfined compression tests on the Sault
clay, however, a failure plane does not develop at low
strains and, therefore, the type of end restraint has a
marked effect_on the failure type. For example, in most

of the tests (W—S-U—3 and 4, W-C-CU—3) with the conventional

23

/o%

 

 

. ‘ O

 

 

 

 

 

(a) W—K-U—3

.z‘0%

 

o I o (‘1‘10.5%

 

.
O
U '

 

O
D 9 .'
N—
O

 

 

 

 

 

(b) W-K-U—4 ' '

Fig. 12. Comparison of deformation modes of WeK-U—B and 4
(taken from photographs).

10.7%
. 410.7% /

 

16.1%

24

end plates, gross distortion was noted in the form of
bulging near the center of the sample. Either a peak
stress is reached at a strain of about 25% or the stress—
strain curve is still rising at the conclusion of the test
(see Table 7). Frictionless ends, however, allow large
strains without too much bulging of the specimen and
multiple slip lines form at strains of 35% i in most

tests. This result, coupled with the results of the kaolinite
tests on short specimens, indicates that if area reduction
due to sliding along a single failure plane or bulging at
the center can be prevented by the use of shorter specimens
and frictionless end plates, failure occurs at greater
strains in the form of multiple slip lines.

The strain at which slip lines develop was found
to be sensitive to strain rate. Slip planes form at
greater strains as the strain rate increases. This is,
particularly apparent from the results of the unconfined
compression tests on the Sault clay. This trend is not as
clear in the tests on kaolinite.

The results of the CFS tests with frictionless end
plates show two trends relating to conditions affecting the
type of failure. First, single failure planes appear only
in those tests in which the top end plate tilted. This
is believed to be due to the fact that the tilted end plates
produce non uniform stress distribution thus causing failure
along the failure surface. Hence, this is not considered

to be representative of the soil behavior. Multiple slip

25

lines occur in each test on the Sault clay (even though the
top end plate tilted in WF-CFS-Z). Most of the failures
on the grundite involve tilting of the top end plate and
are combinations of A and C types. This indicates that
had tilting not occurred, multiple slip lines might have
developed at larger strains.

While the photographs help to gain insight into
the deformation conditions that accompany failure, it is
difficult to measure the exact magnitude of the bulging
from the photographs since the bulging takes place only at
small strains in most tests. Therefore, it is difficult to
confirm or reject any of the solutions given in Chapter II.
In cases where the bulging continues to large strains,
the change in stress distribution due to the bulge would
make the solutions of questionable value. It can be noted,
however, that bulging occurs throughout the entire length
of the sample and is not confined to the zones predicted

by Haythornthwaite's solutions (in the rough end tests).

4.2 Effect on strength

The strength depends on the strain rate and the
type of end restraint. The strain rate effect is parti—
cularly apparent in the CFS tests and unconfined compression
tests W—C—CU—Z and W-C-CU-3. Comparison of these tests,
in which other variables are held constant, clearly shows
that the strength increases as the strain rate increases.
Further examination of the CFS test results shows that as

the strain rate increases, the cohesion (Ce) increases while

26

the angle of friction ($6) decreases. More tests at dif-
ferent strain rates would be necessary to determine the
relationship between the shear strength parameters and
strain rate.

The strength is greater in the tests in which
frictionless end plates are used. This is best exemplified
by comparing tests W—S-U-l and 2 with W-S-U—3 and 4. The
former pair of tests with frictionless end plates, shows
greater strength even though the tests are similar in all
other respects. Comparison of the CFS test results with
those obtained by A. K. Loh at Michigan State University
using conventional end plates show the same trend. This
is believed to be due to the fact that the frictionless
ends produce a more uniform stress distribution and de-
formation mode, thus preventing a premature failure caused
by stress concentrations in certain portions of the specimen.

Since the frictionless end plates produce fairly
uniform deformation even at large strains, it is possible
to measure the shear strength parameters to a strain of
40%. These relationships are shown in Fig. 13 (for
results of specific tests, see Appendix B). The angle of
friction increases with strain as shown in Fig. 13(a).

Most of the friction is developed before the strain reaches
10 percent but in most cases it continues to rise at

larger strains. The cohesion reaches a peak between 5 and
13 percent strain and then decreases to a constant value

at large strains. The strain at which the peak cohesion

27

occurs increases as the strain rate increases. This differs
significantly from tests with conventional end plates in
which the maximum cohesion is developed at a strain of

1 percent or less (see Loh, 1964).

 

 

 

 

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V. CONCLUSIONS

The following conclusions may be drawn from the

test results.

a.

further

a.

After a single failure plane develops, further
deformation is limited to rigid body sliding along
the failure surface since that section experiences
an area reduction.

If gross distortion of the specimen can be pre—
vented by using frictionless end plates and shorter
samples, failure occurs at a greater strain in

the form of multiple slip lines.

The strain at which slip lines appear increases

as the strain rate increases.

The strength increases with strain rate.

The unconfined compressive strength, cohesion and
friction are all higher when frictionless end plates
are used.

The strain at which the peak cohesion occurs in-
creases as the strain rate increases.

On the basis of this study, it is suggested that
investigations be carried out on these subjects.
The use of frictionless end plates and shorter
samples should be investigated further to determine

their general usefulness.

32

33

Tests should be run at different strain rates so
that the relationship between the appearance
of slip lines and strain rate can be established.
Tests similar to those used in this study should
be conducted on other soils to determine the

general application of the findings of this report.

BIBLIOGRAPHY

de Jong, G. "The Undefiniteness in Kinematics for Friction
Materials," pp. 55—70. Brussels Conference 58
on Earth Pressure Problems, vol. 1. Brussels: 1958.

Dillon, H. B. "Structure and Identification of Clay Soils,"
Laboratory report for Soil Science 945, Michigan
State University, East Lansing, Michigan, 1963.

Haythornthwaite, R. M. "The Kinematics of Soils," pp. 235-250.
Progress in Applied Mechanics, The Prager Anniversary
V01ume. U.S.A.: 1963.

Haythornthwaite, R. M. "The Mechanics of the Triaxial
Test for Soils." U.S. Army Ordnance Corps Tech.
Rept. No. l: 1959

.Holliday, Frank J. "Stress Transfer Due to Creep in a
Saturated Clay." Master's thesis, Michigan State
University, East Lansing, Michigan, 1963.

Loh, A. K. “Mechanism of Friction and Cohesion in Clay."
Ph.D. thesis, Michigan State University, East
Lansing, Michigan, 1964.

Rowe, P. W. "Importance of Free Ends in Triaxial Testing,"
pp. 1-27. Journal of the Soil Mechanics and
Foundations Division, A.S.C.E., vol. 90. Ann
Arbor: 1964.

 

Schmertmann, John H. and JoerL Osterberg. "An Experimental
Study of the Development of Cohesion and Friction
with Axial Strain in Saturated Cohesive Soils,"
pp. 643-694. Research Conference on Shear Strength
of Cohesive Soils, A.S.C.E. Ann Arbor: 1960.

34

APPENDIX A

SAMPLE DATA SHEETS AND STRESS-STRAIN

CURVES FOR UNCONFINED COMPRESSION TESTS

Table 10.

Data sheet for W—K-U—l.

 

 

a.

General Data

Water Content Data:

 

 

 

Date - April 20, 1964 Container No. 319
Operator - Warder Wt. of cont 26.97 9
Test - W—K—U—l Wt. wet soil +
Call - #3 cont. 63.73 g
Proving Ring ~ #3141 Wt. dry soil +
Proving Ring Constant — cont. 56.43 9
0.0382 kg/div Wt. water 7.30 9

Length - 2.80 in I 7.11 cm Dry wt. 29.46 9
Diameter = 3.33 cm w 24.8 %
Area - 8.71 cm
V01. - 62.0 cm3
Weight of Sample - 120.00 g
Strain Rate — 360 %/hr
End Plates - conventional

b. Stress-Strain Data

Load Axial Strain Photograph

Dial N Pressure Dial % Strain Taken

KG/cm2

0500 0 0 000 0 1

0643 143 0.619 050 1.79

0795 295 1.25 100 3.57 2

0990 490 2.04 150 5.26

1200 700 2.86 200 7.15 3

1425 925 3.71 250 8.93

1604 1104 4.35 300 10.71 4

1800 1300 5.00 350 12.50

1820 1320 4.98 400 14.38 5

1450 950 3.50 450 16.07

1180 680 2.46 500 17.85 6

 

36

37

Table 11. Data sheet for W-K-U—6.

 

 

a. General Data Wt. of sample 119.85
Date - May 3, 1964 Dry wt. 94.97
Operator - Warder Wt. water 24.88
Test — W-K-U-6 w 26.2 %
Cell - #3

Proving Ring - #684
Proving Ring Const. -
.147 kg/div.
Length - 2.80 in = 7.11 cm
Diameter - 3.33 cm
Area - 8.71 cm2
Vol. - 62.0 cm3
Strain rate — 360 %/hr
End Plates — frictionless

b. Stress—Strain Data

 

 

Load Axial Strain Photograph

Dial N Pressure Dial % Strain Taken
KG/cm2

0000 0 0 000 0 6

0009 9 0.149 050 1.79

0014 14 0.228 100 3.57

0027 27 0.431 150 5.36 7

0047 47 0.737 200 7.15

0077 77 1.185 250 8.94

0112 112 1.69 300 10.71 8

0155 155 2.29 350 12.5

0190 190 2.75 400 14.3

0226 226 3.20 450 16.1 9

0259 259 3.59 500 17.9

0280 280 3.81 550 19.6

0293 293 3.90 600 21.4 10

0271 271 3.52 650 23.2

0216 216 2.74 700 25.0

0215 215 2.66 750 26.8 11

 

Table

38

12. Data sheet for W—S—U—4.

 

 

a. General Data

Water

Date — May 23, 1964
Operator — Warder

Test - W-S-U—4

Cell - #3

Proving ring — #314A
Proving ring constant = 0.00455 kg/div.
Length — 2.80 in = 7.11 cm
Area - 10 cm

Vol. - 71.1

Strain Rate — 400 %/hr

End Plates - Conventional

Content Data:

Container no. 7

Container wt. 16.32 g
Cont. wt. + wet wt. 30.00 g
Cont. wt. + dry wt. 26.26 g
Water wt. 3.74 9
Dry wt. 9.94 9
w 37.7 %

 

 

39

 

 

Table 12. Continued.
33:? N -233; 85:21“ %
KG/cm
0500 0 0 000 0
0522 22 .098 050 1.79
0526 26 .114 100 3.57
0533 33 .142 150 5.36
0536—1/2 36-1/2 .154 200 7.15
0540 40 .166 250 8.94
0546 46 .187 300 10.71
0550 50 .199 350 12.50
0556 56 .218 400 14.3
0558—1/2 58-1/2 .223 450 16.1
0562 62 .232 500 17.9
-- -- —— 550 19.6
0569 69 .247 600 21.4
0571-1/2 71-1/2 .250 650 23.2
0571 71 .242 700 25.0
0572-1/2 72—1/2 .242 750 g 26.8
0574 74 .240 800 28.6
0574 74 .234 850 30.4
0574 74 .228 900 32.1

 

40

Table 13. Data sheet for W-C-CU—Z.

 

 

a. General Data
Date - March 20, 1964
Operator — Warder
Test - W-C-CU—2
Cell - #2
Proving Ring — #3141
Proving Ring Constant
Strain Rate - 4.7 %/hr
End Plates - Conventio

Length - 2.64 in.

Area - 8.88 cm2

Volume - 59.5 cm3
Initial wt. - 123.17 9
Final wt. - 113.70 g

Initial Water Content Da

Container no.
Container wt.
Cont. wt. + wet wt.
Cont. wt. + dry wt.
Water wt.
Dry wt.
w
Final Water Content Data:
Top
Container no. 3
Wet wt. 33.99 9
Dry wt. 26.10 9
Water wt. 7.89 g

- .0382 kg/div

nal

ta:
2
15.74
51.56
41.17
10.39
25.43
40.8 %
Middle
4
38.61 g
29.41 g
9.20 9

w 30.1 % 31.3 %

Bottom
10
40.97
30.87
10.10
32.8

9
9

9
%

 

41

Table 13. Continued.

 

 

b. Consolidation Data

 

 

 

 

Elapsed Chamber Burette Drainage
Date Time Time Pressur cc cc
-Min. — KG/cm
3—21—64 8:53 2.00 0 0
.25 2.00 1.5 1.5
2.00 1.7 1.7
8:54 2.00 2.0 2.0
8:55 2.00 2.45 2.45
8:58 2.00 3.40 3.40
9:03 10 2.00 4.50 4.50
9:08 15 2.00 5.50 5.50
9:23 30 2.00 7.50—a-0 7.50
9:53 60 2.00 2.30 9.80
10.53 120 2.00 3.90 11.40
12:53 240 2.00 4.45—4-0 11.95
16:53 480 2.00 .35 12.30
3—22-64 08:53 1440 2.00 .60 12.55
c. Stress-Strain Data
Time 3:2? N .3:::i.. Saizi“ % ...... Phazizzaph
KG/cm2
11:00 0500 0 0 000 0 9
11:15 0702 202 0.85 050 1.89 10
11:31 0743 243 1.01 100 3.79 11
11:59 0762-1/2 262—1/2 1.06 150 5.68 12
12:26 0774-1/2 274-1/2 1.09 200 7.58 13
12:54 0781 281 1.09 250 9.47 14
13:21 0784—1/2 284—1/2 1.07 300 11.38 15
14:15 0791 291 1.06 400 15.15 16

 

42

 

 

 

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47

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APPENDIX B

SAMPLE DATA SHEETS AND CURVES
FOR CFS TESTS

Table 14. General data sheet for WF—CFS-6.

 

 

1

Date - July 13, 1964

Operator — Warder

Test - WF-CFS-6 2
Chamber Pressure - 2.00 kg/cm

Cell ~ #4

Proving Ring - #3141

Proving Ring Const. - .0382 kg/div.
Strain Rate - 6.12 %/hr.

End Plates — Frictionless

Initial wt. - 127.01 9

Initial Measurements:
Length - 2.80 in.
Area - 10 cm2
V01. - 71.1 cm3

After Consolidation:
Length - 2.64 in
Area - 8.93 cm3
Vol. — 59.8 cm

Initial Water Content Data:

Container no. 2
Container wt. 15.74 g
Cont. wt. + wet wt. 49.07 g
Cont. wt. + dry wt. 39.06 9
Water wt. 10.01 9
Dry wt. 24.32 9
w 42.0 %
Final Water Content Data:
Final wet wt. 118.18 9
Final dry wt. 89.42 g
Water wt. 28.76 9
w 32.2 %

 

49

50

 

 

 

Table 15. Consolidation data sheet for WF—CFS-6.
Elapsed Chamber Burette Drainage Pore
Date Time Time Pressure (cc) (cc) Pressu e
(min.) (KG/cmz) (KG/cm )
7—14—64 07:58 0 2.00 0 0 --
.25 2.00 1.70 1.70
.5 2.00 1.80 1.80
07:59 1 2.00 1.90 1.90
08:00 2 2.00 2.15 2.15
08:03 5 2.00 2.60 2.60
08:08 10 2.00 3.15 3.15
08:13 15 2.00 3.65 3.65
08:28 30 2.00 4.95 4.95
08:58 60 2.00 .75—"0 6.75
09:58 120 2.00 2.25 9.00
10:58 180 2.00 3.40 10.15
11:58 240 2.00 .95-¢~0 10.70
19:58 720 2.00 1.30 12.00
7-15—64 08:06 1448 2.00 2.00 12.70 --
08:15 -- 4.00 Back Pressure Applied 2.00

 

51

 

 

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52

 

 

 

Table 17. CFS calculation sheet for WF-CFS-6.
Upper Curve Lower Curve
'31 2.00 '01 = 1.50
3(31" 3‘31" %(El— 3(3 "’
Strain U 47 a, U3) 03 3 _6, 3 C’3) G3)
% 1 3 3 Y2 X2 1 3 3 Y1 X
2.5 1.120 0.880 0.5600 1.4400 1.068 0.432 0.5340 0.9660
5.0 1.276 0.724 0.6380 1.3620 1.192 0.308 0.5960 0.9040
7.5 1.378 0.622 0.6890 1.3110 1.280 0.220 0.6400 0.8600
10.0 1.433 0.567 0.7165 1.2835 1.330 0.170 0.6650 0.8350
12.5 1.463 0.547 0.7265 1.2735 1.348 0.152 0.6740 0.8260
15.0 1.440 0.560 0.7200 1.2800 1.329 0.171 0.6645 0.8356
17.5 1.387 0.613 0.6935 1.3065 1.258 0.242 0.6290 0.8710
20.0 1.338 0.662 0.6690 1.3310 1.207 0.293 0.6035 0.8965
22.5 1.301 0.699 0.6505 1.3495 1.777 0.323 0.5885 0.9115
25.0 1.280 0.720 0.6400 1.3600 1.155 0.345 0.5775 0.9225
27.5 1.268 0.732 0.6340 1.3660 1.143 0.351 0.5715 0.9285
30.0 1.261 0.739 0.6305 1.3695 1.140 0.360 0.5700 0.9300
32.5 1.259 0.741 0.6295 1.3705 1.137 0.363 0.5685 0.9315
35.0 1.256 0.744 0.6280 1.3720 1.133 0.367 0.5665 0.9335
37.5 1.254 0.746 0.6270 1.3730 1.132 0.368 0.5660 0.9340
40.0 1.255 0.745 0.6275 1.3725 1.131 0.369 0.5655 0.9345

 

53

 

 

Test No.

WF-CFS-6

Computed by Warder

Sample No. WC-l6

Date 7—17-64

 

.4380

Tan 0 Y;-:1Tana
YZ-Yl XZ-X1 =Sin 9e ¢€ XlTana = Cecos 06 Ce
.0260 .474 .055 3.15° 00531 .4809 .482
.0420 .458 .0917 5.260 .0829 .5131 .515
.0490 .451 .1087 6.240 .0935 .4565 .551
.0515 .4485 .115 6.600 .0960 .5690 .572
10525 .4475 .1172 6.730 .0968 .5772 .582
.0555 .4445 .125 7.180 .1044 .5601 .565
.0645 .4355 .148 8.500 .1289 .5001 .505
.0655 .4345 .151 8.680 .1354 .4681 .473
.0620 .438 .1418 8.150 .1293 .4592 .464
.0625 .4375 .143 8.220 .1319 .4456 .451
.0625 .4375 .141 8.220 .1328 .4387 .444
.0605 .4395 .1377 7.900 .1281 .4419 .447
.0610 .4390 .139 8.000 .1295 .4390 .444
.0615 .4385 .1403 8.070 .1310 .4355 .441
.0610 .4390 .139 8.000 .1298 .4362 .441
.0620 .1417 8.140 .1324 .4331 .438

 

54'

Table 18. General data sheet for GF-CFS-Z

 

 

Date - August 10, 1964

Operator - Warder

Test - GF—CFS-2 2
Chamber Pressure — 2.00 kg/cm

Cell - #4

Proving Ring — #3141

Proving Ring Const. — .0382 kg/div.
Strain Rate - 1.24 %/hr.

End Plates - Frictionless

Initial wt. — 126.03

Initial Measurements:

Length 2.80 in
Area 10 cm
V01. 71.1 cm3

After Consolidation:
Length 2.66 in.
Area 9.09 cm2
vo1. 61.4 cm3

Initial Water Content Data:
Container no. 3
Container wt. 15.76 g
Cont. wt. + wet wt. 47.00 g
Cont. wt. + dry wt. 37.95 9
Water wt. 9.05 g
Dry wt. 22.19 9
w 40.8 %

Final Water Content Data:
Final wet wt. 116.95
Final dry wt. 88.29
Water wt. 28.66
w 32.5

Bat-GOLD

 

55

 

 

 

Table 19. Consolidation data sheet for GF-CFS-Z.
Elapsed Chamber Pore
Date Time Time Pressure Burette Drainage Pressure
(min.) (KG/cmz) (cc) (cc) (KG/cmz)
8-11-64 07:52 0 2.00 0 0 —-
.25 2.00 1.50 1.50
.5 2.00 1.90 1.90
07:53 1 2.00 2.05 2.05
07:54 2 2.00 2.30 2.30
07:57 5 2.00 2.80 2.80
08:02 10 2.00 3.30 3.30
08:07 15 2.00 3.70 3.70
08:22 30 2.00 4.70 4.70
08:52 60 2.00 6.10 6.10
09:52 120 2.00 7.80—->0 7.85
10:52 180 2.00 .95 8.80
12:02 250 2.00 1.60 9.45
14:00 368 2.00 2.35 10.20
15:52 480 2.00 2.80 '10.65
19:52 720 2100 3.25 11.10
8-12-64 07:52 1440 2.00 3.75 11.60 ——
08:00 —— 4.00 Back Pressure Applied 2.00

 

56

 

 

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57

 

 

 

Table 21. CFS calculation sheet for GF—CFS—Z.
Upper Curve Lower Curve
'51 = 2.00 '81 = 1.50
_ _ _ 30.1 3*; ' _ _ _ 3%1) 3(g1)
Stgain 01—03 03 YV3) X 3) 01-33 33 Y3 X 3
° 2 2 1 1
2.50 1.051 .949 .5255 1.4745 1.032 .468 .5160 .9840
3.75 1.139 .861 .5695 1.4305 1.109 .391 .5545 .9455
5.00 1.197 .803 .5985 1.4015 1.159 .341 .5795 .9205
6.25 1.238 .762 .6190 1.3810 1.193 .307 .5965 .9035
7.50 1.267 .733 .6335 1.3665 1.217 .283 .6085 .8915
8.75 1.283 .717 .6415 1.3585 1.228 .272 .6140 .8860
10.00 1.292 .708 .6460 1.3540 1.231 .269 .6155 .8845
12.50 1.289 .711 .6445 1.3555 1.219 .281 .6095 .8205
15.00 1.263 .737 .6315 1.3685 1.180 .320 .5900 .9100
17.50 1.230 .770 .6150 1.3850 1.142 .358 .5710 .9290
20.00 1.201 .799 .6005 1.3995 1.112 .388 .5560 .9440
25 1.160 .840 .5800 1.4200 1.069 .431 .5345 .9655
30 1.132 .868 .5660 1.4340 1.039 .461 .5195 .9805
35 1.111 .889 .5555 1.4445 1.017 .483 .5085 .9915
40 1.094 .906 .4570 1.4530 1.000 .500 .5000 1.000

 

58

 

 

 

Test No. GF-CFS-Z Sample No. G—16
Computed by Warder Date 9-9—64
Yl-XlTand
Tan 0 = a

Yz-Yl xz—xl =Sin 4E 4E XlTan 0 -C€cos 46 C6
.0095 .4905 .0194 1.110 .0191 .4969 .497
.0150 .4850 .0309 1.770 .0292 .5253 .526
.0190 .4810 00395 2.260 .0364 .5431 .544
.0225 .4775 .0471 2.700 .0426 .5539 .555
.0250 .4750 .0526 3.020 .0469 .5616 .563
.0275 .4725 .0582 3.340 .0516 .5624 .564
.0305 .4695 .0650 3.730 .0575 .5580 .559
.0350 .4650 °0753 4.320 .0671 .5424 .544
.0415 .4585 .0905 5.200 .0824 .5076 .509
.0440 .4560 .0965 5.540 .0896 .4814 .483
.0445 .4555 .0977 5.620 .0922 .4638 .466
.0455 .4545 .1001 5.75 .0966 .4379 .440
.0465 .4535 .1025 5.880 .1005 .4190 .421
.0470 °4530 .1038 5.950 .1029 .4056 .408
.0470 .4530 .1038 5.950 .1038 .3962 .399

 

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APPENDIX C

SAMPLE CALCULATIONS AND INTERPRETATION

OF DATA

1. Sample Calculations
(a) Calculation of stress
The stress is calculated on the assumption that
the area increases as the inverse of one minus the axial
strain. The load is determined from a linearly elastic
proving ring which is calibrated and the constant slope
of the load-deflection curve is known. An example is
given from WF-CFS-6.
Given:
No. of divisions on load dial = N = 345 div.
Proving ring constant = C = 0.0382 kg/div.
Strain = e = 7.58% = .0758 in/in.
Area of start of test = A0 = 8.93 cm2

Stress calculation:

CNgl-e)

A
O

(.0382L(345)(l-.0758)
8.93

Deviation Stress = Aa

1.363 kg/cm2

(b) Corrected dimensions after consolidation
If the sample is consolidated before the test is
run, it is necessary to correct the dimension of the sample
to account for changes due to consolidation. This is done
on the assumption that the area changes as the two—thirds

power of the ratio of the volume at the end of consolidation

7O

71

to the original volume and the length varies as the one—
third power of this ratio. The volume change is measured
by means of a burette during consolidation. An example
from test WF-CFS-6 is given below.

Given:
3

Original volume V = 71.1 cm
Original area = A = 10 cm2
Original length = L - 2.80 in

Volume change during consolidation = AV = 11.1 cm

Calculation of corrected dimensions:

Corrected volume = Vb = VOAV = 71.1 - 11.1 = 60.0 cm3

V

o _ 60.0 _

V — 7ITI'_ 0.844 V

Corrected area = A0 = A (3302/3= 10(.844)2/3= 8.93 cm2
VO 1/3 1/3 .

Corrected length = L = L 0-) = 2.80(.844) = 2.64in

0 V

(c) CFS calculations

Examples of calculating Ce and $6 from a CFS test
are given in Tables 17 and 21. These calculations are
based on the geometry of two Mohr circles, one representing
the upper curve and one representing the lower curve. For
a detailed explanation see Holliday (1963).

6i is constant for each curve throughout the test
since the porewater pressure is continuously adjusted to
balance the increase in axial pressure. (61433) is the
deviation stress and is calculated as shown in part (a)

of this appendix. The remaining calculations in Tables 17

and 21 are self—explanatory.

72

2. Interpretation of Data

The failure stress and strain correspond to the
peak on the stress-strain curve. In cases where the stress-
strain curve did not reach a peak, the values of stress
and strain at the end of the test were recorded. In the
two unconfined compression tests in which the instantaneous
load was applied, the failure strain was estimated on the
basis of the final deformation. The peak deviator stress
referred to in Tables 8 and 9 refers to the upper curve in

the CFS test.

APPENDIX D

PHOTOGRAPHS OF DEFORMED SPECIMENS

Fig.

4 A. h-._J..

30.

 

 

 

Photographs of deformed specimens.

74

75

 

(a) W—K-U-7 (Front view)

 

(b) W—K-U-7 (Side View)

Fig. 31. Photographs of deformed specimens.

 

(a) W-K-U-4

 

(b) W-K-U-lO

Fig. 32. Photographs of deformed specimens.

77

 

(a) w—s-U-2

(b) W—S-U—ll

Fig. 33. Photographs of deformed specimens.

 

ROOM 05E UHLI'