multi-stage shear testing of a cohesionless soil

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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

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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




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



25. Relationship Between Void Ratio and Normal Stress 60

26. Mohr Failure Envelopes For 40% Relative Density 61



29. Mohr Failure Envelopes Corrected For Dilatancy For 40% Relative Density 65



32. Summary of Corrected and Uncorrected Mohr Envelopes For 40% 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

(-)


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.


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


Symbol Normal Stress (Psi)

0 15

~ 27 EJ 56

0 112

Test No. 89

0.15 0.20

0.20


FIGURE 17. Typical Test Results Using Procedure D

49

50


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


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


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


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


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


60 80 100

Average Values


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


'-..V /'-...

'-../ /.'-..

20

"-.b '7'-..

'~ ~/

40

Symbol

0 6 0

'-.,/ /'-..

/

Procedure

Conventional A

D E


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------~------~


80

60

40

2J Average Values


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)


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


Average Values

Symbol Procedure

0 Conventional

8 A

0

0 D

E

0 20 40 60 80 100 Normal Stress (psi)


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-----,------.----~


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


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



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


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


Conventional

Proc. B

//~ "'-~"' .___Proc. C

//£/ /.~ '-Proc. A

201 /~/ Uncorrected for Dilatancy

--- Corrected for Dilatancy



100 120

0'1 \0

,....., •r-l til P<

'-..)

Cl)

~ :::l

.-1 •r-l ell ~

+..l CIS

til

100 I ~

80

60


Proc. D

Proc. E Conventional

~ 40 ~ +..l C/)

~ CIS Cl)

..c: r.n 20 Uncorrected for Dilatancy


0 0 20 40 60 80 100 120

Normal Stress (psi)


........ 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.


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


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.


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


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------~,-------.-------~--------~--,


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.


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.

/ ,._,

NUNEZ, E., (1963), "Los Parametros De Corte Obtenidos A Partir De Los Ensayos Triaxiales Excalonados" Second Panamerican Conference on Soil Mechani~s and Foun~ation Engineerinf, Associacao Brasileira de Mecan1ca dos Solos, Vo . 2, Sao Paulo, Brasis, pp. 123-12 9.

,,..., NUNEZ, E., (1970), Personal Communication, April 16, 1970.

PARRY, R. H. G., (1963), "Testing Small Undisturbed Sample", Proceedings of Fourth Australia-New Zealand Conference on Soil Mechanics and Foundation Engineering, University of Adelaide, South Australia, pp. 61~68.

SCHMERTMANN, J. H., (1962), "Comparisons of One and Two-Specimen CFS Tests", Journal of The Soil Mechanics and Foundation D1vision, A.S.C.E., Vol. 88, No. SM6, Proc. Paper 3372.

SCHMERTMANN, J. H., (1963), ''Generalizing and Measuring the Hvorslev Effective Components of Shear Resistance", Laboratory Shear Testing of Soils, ASTM Special Technical Publication No. 361, American Society for Testing and Materials Philadelphia, Pennsylvania, pp. 147-157.

SEED, H.

SKEMPTON,

B. and LEE, K. L., (1967), "Drained Strength Characteristics of Sands", Journal of the Soil Mechanics and Foundations Division, Proceedings of the American Society of Civil Engineers, Vol. 93, No. SM6, November, 1967, pp. 117-141.

A. W., (1953), "The Collodial Activity of Clays", Proceedings of Third Internat~onal C?nfer~nce on Soil Mechanics and Foundat1on Eng1neer1ng, Switzerland, Vol. I, p. 57.

TAYLOR, D. W., (1948), Fundamentals of Soil Mechanics, John Wiley and Sons, Inc., New York, p. 346.

TAYLOR, D. W., (1950), "A Triaxial Shear Investigati?n on a Partially Saturated Soil", A.S.T.M. Spec1al Technical Publication No. 106, pp. 180-191.

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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,

multi-stage shear testing of a cohesionless soil

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