ANALYSiS 6F CLAY fiEFGRMATEGN E‘t’ RATE
FRQCESfi THEQR‘!’

Thesis for the Degree of Ph. D.

MICHEGAN STATE UNIVERSETY

Richard W. Chrisi'ensen
1964

TH [SIS

This is to certify that the

thesis entitled

ANALYSIS OF CLAY DEFORMATION BY

RATE PROCESS THEORY

presented by

RICHARD W. CHRISTENSEN

has been accepted towards fulfillment
of the requirements for

BILL—degree in Qiyil Engineering

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Major professor

 

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Date g/Lg ’4 1' 4’ I' a“ (7/

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Michigan State
' University

 

ABSTRACT

ANALYSIS OF CLAY DEFORMATION BY
RATE PROCESS THEORY

by Richard W. Christensen

The deformational characteristics of clays are
analyzed from the point-of—view of the particle structure,
utilizing rates process theory. The deformations at the
particle level are treated as the breaking and reforming of
interparticle bonds as a rate process. Theoretical consid-
erations concerning the nature of the particle structure,
and the physical aSpects of deformation processes are
presented. A schematic model is used to represent the
behavior of the particle structure under load.

Creep and relaxation data obtained from Specimens
prepared in the laboratory and undisturbed specimens are
presented. The echrimental results agree well with the
4 behavior predicted by the model.

The variation of the model parameters in cyclic creep
loading is shown to be related to particle level phenomena
taking place during deformation. The calculated values of

CK , a rate theory paramgter associated with the geometry
of the flowing unit, are found to be consistent with known
geometrical prOperties of the particle structure. The
activation energy,.4 F, is calculated from the rate theory
parameter /57 and also from temperature-creep-rate data; the

two methods give nearly the same value of 11 F.

ANALYSIS OF CLAY DEFORMATION BY

RATE PROCESS THEORY

By

(/1
(‘f‘
(D
13
U)
(D
.3

Richard WK Chri

A THESIE

U

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

DOCTOR OF PHILOSOPHY

Department of Civil Engineering

lQCA

ACKNOWLEDGMENTS

The writer is indebted to his major professor,
Dr. T. H. Wu, Professor of Civil Engineering, for his aid
and encouragement throughout the writer's doctoral studies,
and for his many helpful suggestions during the preparation
of the thesis. Thanks are also due the other members of
the writer's doctoral committee: Dr. 0. B. Andersland,
Associate Professor of Civil Engineering, Dr. T. T. Triffet,
Professor of Applied Mechanics, Dr. L. E. Malvern, Professor
of Applied Mechanics, and Dr. A. E. Erickson, Professor of
Soil Science, for their guidance throughout the doctoral
program. The writer is grateful to A. K. Loh and F. K.
Holliday for their assistance in the laboratory.

Thanks go to Consumers Power Company, Jackson,
Michigan, and to the National Science Foundation for the
financial assistance that made the writer's doctoral studies

possible.

CHAPTER
I.
II.

III.

IV.

V.

TABLE OF CONTENTS

INTRODUCTION . . . . . . . . .
THEORETICAL CONSIDERATIONS . . .. .

2.1 Nature of the Clay-Water System .

2.2 Clay Structure. .

2.3 Physical ASpects of Deformation .

2.“ Deformation of Clays as a Rate
Process . . .

2.5 A Model for Clay Structure.

EXPERIMENTAL PROGRAM . . . . . . . .

3.1 Objectives . . . . . . . . .
3.2 Clays Used . . . . . . .
3.3 Sample Preparation . . . .~
3.4 Triaxial Tests. . .

EXPERIMENTAL RESULTS . . . . . .. . .

4.1 Presentation of Data and Evaluation
of Model Parameters .

4. 2 Validity of the Structural Model.

A. 3 Interpretation of Results . .
4.3.1 The Spring "Constants"

The Parametercx . _.

The Parameterxé’ .

Creep Test on Dry Clay.

Relaxation Tests. .

Temperature Effects.

421:4:th
wwwww:
O‘iU'l tum)

CONCLUSION. . . . . . .

BIBLIOGRAPHY .

APPENDIX

PAGE

l2
16

28
28
28
29
32

37

TABLE
3.1
3.2
14.1
4.2

LIST OF TABLES

Index PrOperties of Clays Tested . . . ,
Summary of Triaxial Tests . . . . . .
Summary of Results.

Variation of Model Parameters During Cyclic
Creep Loading. . . _. . . . . .

\j‘i
O\

FIGURE
2.1

2.3

2.6
4.1

4.3

4.4

4.5

4.6

LIST OF FIGURES

Schematic picture of clay (after
RosenquiSt, 1959) . . . . . . .

Potential surface for interparticle bond:
(a) without external stresses, (b) energy
gradient due to external Stress, (c) with
external stresses applied . . . . .

Flow curves for non~newtonian viscous flow
showing apparent yield limits for the case
7’: A sinh BO; B177 A . . . .

Flow curve for interparticle bond having
yield strength Dy . . . . , . . .

Hypothetical distribution of bond yield
strengths with respect to: (a) unstressed
particle structure, (b) second load incre~
ment, (c) first unloading increment . .

Schematic model for clay particle structure

Dimensionless creep and stress relaxation
curves for structural model . . . .

Typical creep curves (Test No. C-C~l-5). .

Calculation of model parameters from
creep test° . . . . . . .

Typical stress relaxation curves (Test No.
F‘R-S-l) o o a o 2 o o o o 9 0

Calculation of model parameters from stress
relaxation test . , . . . . . . .

K£—— with deviator
K1+k2
stress, D, in cyclic creep loading of

f"

SpeClmen C‘K/‘l o o o a o o o 7 0

Variation in the ratio.

 

14

24

4O
46

47

\n
(I)

FIGURE

4.7

4.8

4.9

4.10

4.11

Distribution of bond yield strengths with
reSpect to the various phases of cyclic
creep loading-~constructed from observed
trends of Kl . ,, .

kl+k2

Variation of the flow parameter, O< , with
deviator stress, D, in cyclic creep
loading of Specimen C-C—l.

Variation in rate parameter ,8 with
deviator stress, D, in cyclic creep.load-
ing of Specimen C-C-l . . . . . . .

Deformation-and tem erature-time curves for
creep test D-c-9— , D=o.67-o.87ks/cm2.

Rate of deformation~deformation relation-
ships for two different temperatures in
creep test D-C—9-4; D=O.67-O.87kg/cm2.

vi

‘PAGE

.60

62

67

73

75

>0

Cir—Iicrmtd

U*

NOTATION

angstroms
actual contact area between two plane surfaces

<61 - (53) = principal stress difference or
'deviator stress

dimensionless stress relaxation function
void ratio

maximum shearing force in friction

flow force on interparticle bonds
activation energy

Planck's constant

Boltzmann‘s constant

spring "constants" of the structural model
normal force

universal gas constant

time

absolute temperature

axial deformation

dimensionless creep function

volume of solids in a clay mass

distance measured along the plane of flow

rate theory parameter associated with the geometry
of the flowing unit

rate theory parameter associated with the activation
energy of flow

i ,

viii

shear strain

octahedral Shear strain
shear strain rate
principal strains

number of non-flowing bonds per unit area in the
plane of flow

distance between equilibrium points in the plane
of flow

distance between points of flow in the direction
perpendicular to the plane of flow

total number of interparticle bonds per unit area
in the plane of flow

coefficient of friction

number of flowing interparticle bonds per unit
area in the plane of flow

principal stresses

= yield strength in comparison

shear stress

= octahedral shear stress

yield stress in shear
shear force on an interparticle bond
yield strength of an interparticle bond in shear

distribution of bond yield strengths

CHAPTER I
INTRODUCTION

The stress—deformation-time behavior of clays is not
well understood. The principal reason for the lack of
knowledge is that clays are extremely complex in their
physical makeup. They consist of solid material (the in-
dividual clay particles), water, and sometimes air; and the
manner in which these components are combined in nature is
highly variable.

The individual particles, by themselves, comprise a
class of substances with a wide range of physical preper-
ties (Grim, 1953). Furthermore, the geometry of the particle
structure has a profound influence on clay preperties and,
depending upon the environment at the time of formation, the
particle geometry can be quite different. A.clear picture
of the particle geometry in various types of clays was only
recently obtained through the use of the electron microsc0pe
(Rosenquist, 1959).

The presence of water in the voids of the particle
network further complicates clay behavior. It has long been
recognized that the water nearest the clay particles is
strongly attracted by the surfaces forces of the particles
(see, for instance, Houwink, 1937) and has been arbitrarily

designated as the adsorbed water layer. However, the nature

of the adsorbed water and its influence on clay preperties

is still not resolved (Lambe, 1960). Furthermore, the
electrolyic content of the pore water influences the inter—
particle force fields and, consequently, affects the particle
geometry, water prOpertieS, and shearing strength of the

clay (Moum and Rosenquist, 1960).

If air is present in the clay pores in addition to
water, the Situation is even more complicated. However,
this investigation deals only with saturated clays.

Recently much interest has been focused on the prOper-
ties of the clay-water system; i.e., the interaction of the
solid and fluid phases in a clay mass. As a result, con-
siderable knowledge has been gained in this area within the
past few years. These recent develOpmentS are utilized
herein in attempting to formulate a working hypothesis for
particle behavior during deformation.

The approach to be adOpted in this study is to treat
the flow between individual clay particles as a rate process.
Using the equation of flow from the rate theory, a model is
devised to simulate the behavior of the particle structure
under external loads. The rate process approach to material
deformations is due to Eyring (Glasstone, Laidler, and
Eyring, 1941) and has been extensively used in studying the
mechanical properties of polymers (Tobolsky and Andrews,
1944), textiles (Eyring and Halsey, 1948), and colloidal

suSpenSions (Tobolsky, Powell, and Eyring, 1943). Murayama

and Shibata (1958) recently applied the methods of rate
theory to the flow properties of a Japanese Alluvial clay.

Results of triaxial Shear tests for creep and stress
relaxation loadings on two glacial lake clays are presented.
The experimental results are compared with the behavior
predicted by the model and the values of the model para-
meters calculated for each test.

Good agreement is found between the behavior predicted
by the model and the experimental results. The values for
the model parameters calculated by comparison of the theore—
tical and experimental curves are interpreted in terms of
the particle structure.

It is hOped that this study will help to clarify the

role of the particle structure in deformation of clays.

CHAPTER II

THEORETICAL CONSIDERATIONS

2.1 Nature of the Clay-Water System

 

It is well known that individual clay particles are
thin, plate-like structures of a Size less than 2 microns.
Because of their size and geometry, these particles possess
a very high surface area-to—mass ratio and are strongly
.influenced by surface forces.

In a clay-water system, the water in close proximity
to the particle is attracted to the particle surface and
forms what is called the adsorbed water film. The preper-
ties of the adsorbed water and its effect on the mechanical
prOpertieS of clay masses are still uncertain.

It was thought for some time that the adsorbed water
layers were rather thick--up to 0.1 microns according to
Terzaghi and Peck (l948)--and quite viscous. The conclusion
was drawn from this concept that the viscous nature of clays
resulted from the presence of the viscous water layers sur-
rrounding each particle. Recent research indicates, however,
that the thickness of water affected by the clay particles
is n0 more than about 25 angstroms (see, for instance,
Rosenquist, 1959).

It is generally agreed that the water immediately next

to the clay particle is different from ordinary water. On

the basis of heat of swelling and vapor pressure-temperature
data, Rosenquist (1959) calculated that a lO-angstrom layer of
crystalline (ice-like) water surrounded the particles in the
particular clay tested. Furthermore, Anderson and Low (1958)
found that the Specific volume of water near clay surfaces
is greater than normal water. This data was cited by Low
(1960) as evidence that the adsorbed water has a structure
that is more ordered than that of normal water. Martin
(1959), on the other hand, presented data that indicates
that the water next to the particles is more disordered than
normal water. The question of the structure of the water
near the particle surfaces must, therefore, be considered
unresolved.

Low (1960) found that the activation energy of the
flow of water through Na-bentonite increases with time after
wetting and concluded that the adsorbed water is more viscous
than normal water. Rosenquist (1959) also found from
deuteron—diffusion measurements that the adsorbed water on
clay particles is more viscous than normal water. However,
Michaels (1959) pointed out some of the Shortcomings in
assessing the properties of the adsorbed water from such
indirect evidence. Michaels also suggested that the adsorbed
water may be not only different from normal water but aniso-
trOpic; i.e., ”the resistance offered by a water molecule
being slid along the surface may be considerably less than
that offered by a water molecule being elevated from or

lowered toward the surface.”

Leonards and Girault (1961) showed that the phenomenon
of secondary compression in the consolidation test cannot be
attributed to adsorbed water films alone. They found that
clays in which the water had been replaced by carbon tetrach-
loride, a non-polar fluid, still exhibit secondary compression.
Similarly, Norton (1952) described a Simple experiment in
which dry, powdered clay when placed in a elastic membrane
and subjected to a vacuum behaves plastically in the same
manner as a moist clay. These findings suggest that the
adsorbed water on clay particles may be of relatively minor

importance in the deformational properties of clays.

2.2 Clay Structure

 

A comprehensive description of clay structure was
first presented by Tan (1953). The individual particles are
assumed to form edge-to-face contacts with one another,
resulting in a continuous solid skeleton in a ”card-house"
arrangement. Tan's concept was later verified by Rosenquist
(1959) by means of electron microscopy. Figure 2.1 is a
schematic drawing of a clay particle network according to
Tan and is in remarkable agreement with Rosenquist's findings
for undisturbed marine clays. Remolded clay structures are
believed to be similar except that the network may consist
of small "packets" of parallel particles rather than individ—
ual particles (Lambe, 1960; Mitchell, 1956).

Rosenquist (1959) also established that the individual

particles are actually in mutual contact by quick freezing

In.

Figure 2.1. Schematic picture of clay (After Tan)

 

‘1...

 

undisturbed clay Specimens in liquid air and sublimating
off the ice. Little or no Shrinkage was observed upon
removal of the frozen pore water and the dried specimen had
considerable strength, indicating the presence of a contin-
uous particle network.

Several mechanisms of bonding between clay particles
have been suggested: (1) Coulomb attractive forces, (2)
van-der-Waals-London forces, (3) cation bonding, (4) hydrOgen
bonding, (5) ionic bonding, and (6) covalent
bonding.

Direct methods for determining the relative magnitudes
of the various bonding types is lacking but the Coulombic
and van-der-Waals-London forces are generally thought to be
the most predominant (see, for instance, Van Olphen, 1951;
Rosenquist, 1959; Tan, 1959; and Lambe, 1953). In particular,
Iler (1955) presented strong evidence for the existence of

the Coulombic attraction between.negatively charged flat

particle surfaces with positively charged edges by showing
electron micrographs of negatively charged silica particles
attracted to the edges of hectorite particles. It is likely
that all the bond types mentioned are present in clays to
some degree, but no reliable method for distinguishing their
relative contribution to the interparticle bond is presently
available.

According to the evidence currently available, the
nature of clay particle structure may be summarized as
follows:

1. The individual particles in a clay mass form a
continuous solid skeleton in which edge -to-face
contacts predominate.

2. At the contact points between particles, bonds
are formed as a result of microsc0pic force
fields in the clay-water system. These forces
consist mainly of Coulomb attractive and repul-
sive forces and van-der-Waals-London forces.

The combined effect of the microsc0pic force
fields determines the strength of the inter-
particle bonds. These force fields are influ-
enced by many factors; e.g., the Size, shape and
mineral composition of the particles, the electro—
lytes in the pore fluid, adsorbed cations,
geometry of the structural network, void ratio,

and perhaps others.

3. .The adsorbed. water films on the particle surfaces
‘play a minor role in determining deformational A
behavior-sit may affect the viscous,flow of clays
under-stress.but is probably not the prime cause

of viscous flow.

2.3 Physical Aspectsgor Deformation

Since deformationsirlclays-involve the interaction of
discrete solid particles, a useful analogy can-be drawn
from the phenomenon of sliding friction between solid sur-
faces. According to modern concepts, friction is envisioned
as being the shearing resistance deve10ped by the inter-
locking asperities of two surfaces brought together under
the action Of a normal force (Bowden and Tabor, 1954). Even
in the case-of highly polished.surfaces, actual contact
occurs oVer a very small area so that the local stresses at
the contact points are sufficient to produce yielding.

Therefore, the total normal force

P = (7"

. w “0 .
where CIyp is the yield stress incompressioneandAc is the

actual area of contact. The maximum Shearing force that
can be applied before failure occurs is
F = z:yp

where'Eyp is the yield stress in shear. -Since the coeffici-

Ac

ent of friction [If is defined as far =§ , it can-be seen

that )if = Ogfl .
YP

lO

Burwell and Rabinowicz (1953) have shown that’uf is
not a constant, but depends upon the speed of sliding. For
a given normal stress, they found that sliding occurs for a
wide range of shearingforces--the coefficient of friction
increases with the speed of sliding up to the point of
failure. Horn and Deere (1962) found that the coefficient of
friction of phlogopite mica also increases with the speed of
sliding. It is probable that this relationship also applies
to clay particles since clay particles have crystal struc-
tures similar to those of the micas.

Burwell and Rabinowicz described the frictional
deformation process as the successive breaking of bonds
formed by the interlocking asperities and subsequent forma-
tion of new bonds as the two surfaces move relative to one
another producing new contacts. A similar process may be
applicable to the phenomenon of sliding between clay parti-
cles. This application does not require that the clay
particles are in direct contact,although this appears to be
the case.

The deformational resistance of the clay structure
rests in the bonds formed between particles at the points
of contact. The strength of these bonds may vary widely in
any given clay so that when external stresses are applied,
some of these bonds will fail in shear while others remain
intact. The particle movements which follow breakage of

the bonds will tend to bring the displaced particles

ll

into contact at other points as the deformation proceeds.
The bonds which are broken may also be expected to reform
in other positions due to attractive forces which exist
between particles at close range. The resistance of clays
to deformation is thus seen to depend upon the strength of
the interparticle bonds and the number of these bonds per
unit volume--a situation which is quite similar to the
deve10pment of sliding resistance between solid surfaces.

In solids, the yield strength in shear, Z is

YP’
usually assumed to be constant. However, in clays, the
strength of reformed bonds may differ from the strength of
the original bonds if the particle geometry is substantially
altered during shear.

It was noted that the contact area in the case of
sliding friction between solids is directly proportional
to the normal force. In clays, on the other hand, the num—
ber of bonds per unit volume is primarily dependent upon
the preconsolidation pressure and particle geometry. The
consolidation process forces some of the water from the
pore spaces, thus bringing the particles closer together
and creating more interparticle contacts. Even after un-
-loading, most of the bonds formed during consolidation
remain intact because of the close range attractive forces.
The particle geometry has considerable effect on the number
of bonds in that more interparticle contacts are possible
in a random arrangement than one in which the particles are

aligned parallel to one another.

12

The number of bonds may, also, be considerably affected by
shear stresses since the resulting shear strains tend to
disrupt the particle structure.

The ability of clays to retain interparticle bonds
upon unloading provides an explanation for the experimentally
observed fact that preconsolidated clays possess a cohesion
intercept on the Mohr-Coulomb diagram while nOrmally con-
solidated clays do not (Rosenquist, 1959). Under the
present hypothesis, therefore, the necessity of explaining
friction and cohesion as two intrinsically different compon-
ents of shearing resistance is eliminated since they are
only different macroscopic manifestations of the same micro-
sc0pic process.

The conClusion may be drawn from this brief discussion
that deformation in.clays under externally applied loads
involves a continuous process of breaking and reforming
interparticle bonds. Processes of this type are well suited
to theoretical treatment by the theory of absolute reaction
rates (Glasstone, Laidler, and Eyring, lghl). In the section
which follows, this theory is adapted to clay particle

structures.

2.4 Deformation of Clays as a Rate Process

 

The deformation of clays under applied stresses is
assumed to be the result of the breaking and reforming of
interparticle bonds which arise at the contact points between

particles as the result of the microscopic force fields that

l3

exist in the particle structure. The use of the term con-
tact points is not intended to imply that the mineral
surfaces of the particles are necessarily in actual contact,
although such may be the case. A contact point, as the term
is applied here, merely refers to the point at which a bond
is formed between particles. Actual contact between the
mineral surfaces is not required. Since the interparticle
bond is the net result of the force fields of the "contact,"
the nature of the "contact" need not be Specified here.

The interparticle bond is assumed to present an
energy barrier to relative motion between particles. This
energy barrier will be represented by the symmetrical
potential surface shown in Figure 2.2a in which .1 is the
distance between the adjacent minimum positions A and B.
In order to break the bond between particle surfaces, an
amount of energy at least equal to the activation energy,.A F,
must be supplied to surmount the potential barrier. The
energy required to raise the bond to its activated (loosened)
state may result from thermal oscillation of the atoms and
molecules making up the bond, applied stresses, or both.
Even if no external stresses are acting, the bond is pre-
sumed to pass through the activated state with a frequency

of

= 52_e’
h

where k is Boltzmann's constant, h is Planck's constant, T is

k' ZiiF/RT times per second

the absolute temperature, and R is the universal gas

14

constant in accordance with the theory of absolute reaction
rates (Glasstone, Laidler, and Eyring, 1941). In this case
there is no net movement, however, since the frequency is
the same in both directions.

It was noted earlier that clays possess a wide range
of bond strengths due to the heterogeneous nature of the
material. Therefore, in dealing with the breaking and re-
forming of bonds as a rate process, a broad spectrum of
activation energies may be anticipated instead of a single
value. In the develOpment which follows, the value of A F
is taken to represent the average of all bonds under con-

sideration.

//:>
K

 

 

AF (c)

l

Figure 2.2. Potential surface for interparticle bond:
(a) without external stresses, (b2 energy
gradient due to external stress, 0) with
external stresses applied.

 

 

 

 

 

15

Consider now a certain plane in the material over
which a shear stress Z'acts. Let the average shear force
exerted on a bond along the plane be d. The effect of this
force is to add to the potential surface, a potential
gradient -¢x, where x is the distance measured in the
direction of the stress (Figure 2.2b). The new potential
surface takes the form of Figure 2.20. The force ¢ will do
work ¢H§L» in moving from A to B in the forward direction.
If the movement is backward, or against the stress, the
work done is -¢.€;__. According to rate process theory (see,
for instance, Tobolsky, Powell, and Eyring, 1943), the not

rate of place change in the forward direction is, then,

¢.R

k, awn/2w]? _ e-fM/ekr] = 2 k, sinh
2kT

times

 

per second (2.1)
If the distance moved in each Jump is A and the average
distance between points of flow in a direction perpendicular
to the plane of flow is ill, the rate of shear strain is

given by

 

7;: 2 i :T e -AF/RT sinhéfi—Ta- (2.2)
I

Since the average force localized on the individual bonds is
¢, thus ‘5': w b’, where.V is the number of bonds per unit
area over the plane of shear.

The equation for shear deformation of the clay particle

structure then becomes

16

'_ .2. kT -4F/RT 733 . .
7” 2 WT e sinh 2am {2.3)

which is the general equation for non-newtonian viscous flow
(Eyring and Halsey, 1943).

Having established the flow relationship of Equation
2.3, the total deformational behavior of clays is now con-

sidered.

2.5 A Model for Clay Structure

 

The flow relationship of Equation 2.3 is, by itself,
inadequate to fully describe shear deformation in clays.

The major characteristics of clay deformation in addition
to viscous flow that must be taken into account in the
theory are as follows.

Creep tests on clays show that an instantaneous de-
formation takes place immediately after the load is applied.
This deformation is largely recoverable and has been attri-
buted to bending in the clay plates and the rotation of the
flat particle surfaces toward one another against the action
of Coulomb repulsive forces (Tan, 1959).

Secondly, at stresses below the failure stress, the
creep curves tend asymptotically toward some final deforma-
tion (Lo, 1961; Casagrande and Wilson, 1950). If the flow
process comes to a halt, then the stress must be carried by
intact bonds which do not flow. Hence, it may be assumed
that a yield value exists, below which no movement occurs.

Alternatively it may be said that when the force on a cord

is very small compared to 13F the flow rate is not measurable.

An explanation for the existence of a threshold stress is

found in the hyperbolic character of the flow equation

derived from rate theory (Eq. 2.3).
Equation 2.3 is of the form

7‘: A sinh B C
where
~ kT -AF/RT
A = 2 44—- ———-e =
A: h and B

2
2kT

 

Now if B >> A and B remains constant the flow curves will each

have an apparent yield limit below which the flow rate is too

small to be measured. This yield limit increases for de-

creasing values of A as shown in Figure 2.3.

7": A sinh so

B:n>A J J
B = constant
A17A2>A37Au

  
  
 
 

A3 A4

Strain rate 7’

ap arent y old 1 ts

 

 

Force C

Figure 2.3. Flow curves for non-newtonian viscous flow showing
apparent yield limits for the caseyV-A sinh Bf;

B=” A.

18

Such flow curves have been observed on the macroscopic
scale in creep tests on clays (Houwink, 1937; Geuze and Tan,
1953). Since A.is inversely prOportional to the exponential
of the activation energy 15F, the apparent yield limit Cy in-
creases with ziF. If the force on a bond is below the appar—
ent yield limit, the rate of flow is extremely small and may
not be detected by laboratory measurements. If the rate of
flow below the apparent yield point is taken as zero, the

flow curve takes the form shown in Figure 2.4.

7’: A sinh BC

 

 

 

l
.p |
a» |
.p
m
s I
s
'3 ' o-a
4% gy _L. g'y—f
(0 fi‘

|

I

I

l

Force C

Figure 2.4. Flow curve for interparticle bond having;yield
strength.Cy.

19

According to this flow curve, the bond possesses a yield
strength Cy beyond which flow proceeds according to the

relationship

7”: A sinh B Cf

where Cf = C - Cy is the force on the bond in excess of the
yield strength. No flow occurs at stresses below Cy.

In a clay mass, a Spectrum of yield strengths may be
anticipated due to the wide range of activation energies.

The solid curve in Figure2.5a shows a hypothetical distribu-
tion of bonds with respect to yield strength for an unstressed
particle structure. .The area under the curve is equal to the
total number of stress-carrying bonds’p per unit area in the
plane of flow. Stress—carrying bonds are all those that will
be stressed when external loads are applied. Thus p =.J +~q
in which V is the number of bonds which flow and q is the
number of bonds which do not flow.

Consider now the effect of external stresses on the
particle structure. Under a given sequence of loading, the
bond forces may be divided into the following categories.

Cy = total yield strength of the bond

ziCyn = additional force that a bond can carry in
the nth increment before flowing OP

Adyn = yield strength of a bond for the nth increment
th

liCn = initial force exerted on a bond due to the n
increment

lACfn = flow force on a bond due to the nth increment

an = non-flow force on a bond during the nth

increment

2O

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“0p pooomop Spas mnpwcoppm oaofim pcon mo soapsnfihpmao Hmoaponpoahm m.m opswfim

ma camcoppm Uaofiz

whaq camcoppm UH mg.

 

H>E< npmcmapm baa?»

 

 

 

 

 

_ p _ p
T T
S S
1. 1.
J J
_ W pquvocH fl
m. omoa new on .n.
I moo oopom econ nm&< I
pddEdhocH m m
wcaomoacs
ma op mop
woaom ocon ”H&<_ .Am 1m pzoEonoda
. ooofi onH on
L moo oopom UQOQ "Haq

 

 

E A5 A3

,3 uomnqwasrp

 

21

Additional designations are defined where needed.

If a system of stresses is applied to the mass, the
bond whose flow curve is given in Figure 2.4 is subjected
to a force, say AC. If AC is smaller than the yield stress
Cy, the bond reacts elastically and does not flow. However,
if.AC is larger than Cy, the bond flows,immediately after the

stresses are applied,under the force
(Mao =A¢ - 25,

Unless all the bonds are stressed beyond their yield point,
the force Z3Cf is gradually transferred to the stronger

bonds as flow proceeds. Thus,.ACf steadily decreases to

zero and the bond ceases to flow. At this point, the flowing
bond carries a force Cy.

As a first approximation, it may be assumed that all
the bonds initially carry an equal share of the applied
stress. At the instant the first stress increment is
applied, each bond then carries a force ASCl. As Figure 2.5a
shows, the force .ACi exceeds the yield strength of some of
the bonds; these bonds flow until the flow force :ACfl on
each flowing bond is diminished to zero by transfer to
stronger bonds. The initial total force per unit area of

particles tending to cause flow is

J. \)o
(Ff1)0 = §:(13¢f1)0 = E:(A¢1 - ACyl)

0 O

22

where ./o is the number of initially flowing bonds per unit
area.

After deformations have ceased, the total flow force
Ffl has been transferred to the initially non-flowing bonds

so that they then carry the force

(Ff1)o
r2”

where VFD is the number of bonds that did not flow during

the first load increment.
At the end of deformation, the bonds which flowed are
stressed to their yield strength, while those which did not

flow have a yield strength

A gy2 = Agyl " (ggl)°o

with respect to additional stress. The distribution of bonds

with respect to [SCyg before application of a second load

increment is as shown in Figure 2.5b. It will be noted that the

number of bonds with any remaining yield strength is consid-

erably reduced by the first load increment. The same processes

take place during the second and all succeeding increments

until all yield strength has been exhausted and failure occurs.
The application of the nth load increment causes all

the stressed bonds to be subjected to a force increment ACn.

The initial flow force on any bond in the nth increment is

{ACW if ACyn = o

(Agfn)o = {Agn "Agyn’ if A¢H>A¢Yn ’0

0, if ACyn> ACn

 

F0
U)

while the initial non-flow force on any bond in the nth

increment is

dy, if A Cn> My,

gg (fl-l) = Afln, if ACyn > ACn

(dgn)

At the end of the nth increment, the force carried by a

given bond is

Cy if ACn > ACyn
gg(n_l) + Aon+E££lEL , if ACyn> ACn

00

(anlc,

If the clay mass is unloaded after the nth increment—-
provided failure has not occurred—-the yield strength of a

bond in the first unloading increment is
, I _

Therefore, the initial bond distribution with respect to
unloading takes the form of Figure 2.50. This curve is
elongated in the horizontal direction compared to that in
Figure 2.5a due to the addition of the term (an)“3 to the
yield strength of each bond. For unloading the flow process
proceeds in the same manner as described for loading. How-
ever, it may be noted that the initial unloading force tfiCi
produces fewer flowing bonds than the first loading force
ZiCl. Therefore, the flow in the particle structure is
considerably less during unloading. Inherent in this behavior
is the experimentally observed fact that recovery is incom-

plete.

24

The deformational prOperties of the particle structure
just described may be illustrated schematically by the model
shown in Figure 2.6. )L

 

 

U'Hfl

 

 

l

1t

Figure 2.6. Schematic model for clay particle structure.

The Spring k2 represents the effect of bond stresses
below the yield point--the stress on the non-flowing bonds
plus the stress on the flowing bonds at or below the yield
point. In this stress range the bonds are assumed to behave
elastically. The right—hand side of the model represents
the effects of the bond stresses which cause flow. The flow
in the dashpot then represents the rate process.

Thus,when a shear stress Z? is applied, elastic defor-
mations occur in accordance with the combined resistance of
kl + k2 which indicates the elastic reSponse of the particle
structure as a unit. As the deformation proceeds, the
stresses tending to cause flow are transferred to stronger

bonds until all flow stOps. The average flow prOperties of

25

all the flowing bonds under a given stress increment.are
represented by the dashpot/3 and, at any time, the stress
in the right-hand side of the model is the stress producing
flow.

It is readily seen that the model possesses the major
deformational characteristics observed in clays. For
example, if a constant load is applied, the Springs k1 and
k2 deform elastically, followed by viscous flow inthe dash—
pot/9 until all the load is finally carried by the Spring k2
and the deformation ceases; it will be noted that this
behavior agrees with that reported earlier for clays.

The shear stress in the left-hand side of the model is
Z - Z = key (2.“)

where 371 is the shear stress in the viscous element and ’7’
is the total shear strain. In the right-hand Side, the shear

stress is
2:1 = k]_ (7'77): (205)

and according to Equation 2.3,

O

 

77: fl sinh 0(3) (2,6)
where AF/RT
; A kT ’ 3 .A
/9 .— 22 A, h e and o( ETU—ETI°

From Equation 2.4

-° 1 ‘ ‘
r: E (z -z:,) (2.7)

26

Combining Equations 2.5, 2.6, and 2.7,

k -+k e _; -
__L_§_ z; = _L z, - l3 sinho‘Z:

0

But for creep loading, Z: = 0, so

 

k1+k2 Z', = — [3 sinh «x13.
R142
01"
d(°‘ Lg) _ - 'L'
klkg — sinh<x (2.8)

WW *5)

Upon integrating Equation 2.8,

a __ l 1 klkg
t, = _oL' 1n tanh [—2 «I5 ———-———k1+k2 (t.- 0)] (2,9)

At the instant the load is applied,
k1

 

‘t= O and Z,==—-———— Z
kl+k2
so that
2(1414442) 1 0< R1 1:
C = .. - - "——
096 k1k2 tanh exp ( k1+k2 )
from which
k kg
1 l __1____-
2:, = - “OT—ln tanh [ '2‘ “/9 k1+k2 1’ + tanh'l exp
(.“k.___1 I )1 (2.10)
kl+k2

From Equation 2.4,
_1_
T: k2 (2-2:!)

The creep equation thus becomes

27

l 1 l kika
T=E§—E +3‘f'k—2—ln tanh ['2'0‘13 k1+k2
-1 0‘le
+ tanh - __....... 2.11
exp ( kl+ k2 >] ( >

In a similar manner, the differential equation for

stress relaxation is found to be

d(cx'51)
d(cx/6 klt)

= - SinhCX-Cl (2-12)

 

Integrating and applying the boundary condition,
at t :0, 31:30 -'C°°

the stress relaxation equation becomes
' l l
I = Lag - 5(- ln tanh [5 086 kit
-1 .
+ tanh exp (-oc [T’o - L...) ) (2.13)

Equations 2.11 and 2.13 describe the stress-strain-
time behavior predicted by the model for creep loading and
stress relaxation, respectively. The validity of the struc-
tural hypothesis developed in this chapter will depend upon
the agreement between the experimental and theoretical

behavior. The experimental program of this study is now

presented.

CHAPTER III

EXPERIMENTAL PROGRAM

3.1 Objectives

 

The first purpose of the experimental program is to
determine whether or not the proposed model reproduces ade-
quately the actual deformational behavior of clays. Secondly,
if the theoretical and experimental behavior show reasonable
agreement, the experimental results may be used to evaluate
the model.parameters which would provide some insight into
the particle nature of the deformation.

In order to achieve these objectives, creep and stress
relaxation tests were performed on a number of specially

prepared clay samples using a triaxial loading apparatus.

3.2 Clays Used

 

The majority of tests reported in this study were
performed on Specimens of a glacial lake clay obtained from
a site approximately 15 miles south of Sault Ste. Marie,
Michigan. The raw clay was obtained from a pit at a
depth of about 15 inches. A series of diagnostic tests,
including x-ray diffraction studies (Christensen, 1963)
shows that this clay contains approximately 50% illite, 20%

vermiculite, 20% chlorite, and some kaolinite and feldSpars.

29

A few creep tests were also performed on an undisturbed
glacial lake clay from Marine City, Michigan. Although
identification tests have not been performed on this clay,
it is presumed to be primarily an illite clay. The index
properties for both the Sault Ste. Marie and Marine City

clays are listed in Table 3.1.

TABLE 3.1. Index PrOperties of Clays Tested

 

Cla

 

Clay L.L. P.L. P.I. Fract on
Sault Ste. Marie 60.5% 23.6% 36.2% 0.60
Marine City 41.4% 21.7% 19.7% 0.73

 

3.3 Sample Preparation

 

The Sault Ste. Marie clay was air dried in the labora-
tory prior to preparation of the test Specimens. The
various methods of sample preparation are described below.

a. Laboratory Consolidated Samples. The air dried

 

clay was soaked in distilled water and remolded at a water
content near the liquid limit. The remolded clay was placed
in a 6 inch diameter lucite cylinder and left to stand for
three weeks. An initial consolidation pressure of .003
kg/cm2 was then placed on the clay. After at least 90%
consolidation was reached, the pressure was doubled and
maintained until 90% consolidation was again achieved. This

procedure was repeated until the clay was consolidated under

30

a pressure of 0.36 kg/cme. The load was then removed and

the clay allowed to rebound. Several weeks later, the clay
was extruded from the cylinder and cut into six sections,
each approximately 2 inches square in cross-section and 3.5
inches in height. These sections were then waxed, wrapped in
aluminum foil, waxed again and stored in a moist room until
required for testing. Immediately before testing, the waxed
sections were trimmed into triaxial Specimens 1.40 inches

in diameter and 2.8 to 3.0 inches in length.

b. Remolded-Compacted Samples. The air dried clay

 

was placed in a muller and reduced to a size less than 2 mm
in diameter (No. 10 U. S. Standard Sieve). Distilled water
was added until a water content of approximately 40% was
achieved. The clay was then placed in an earthen crock,
covered with a rubberized cloth and stored in a moist room
to ensure an even water content distribution. After about
two weeks, the clay was removed from the moist room and
placed in a static compaction ring, 11.25 inches in diameter
and 6.5 inches in height. The clay was placed in the com-
paction ring by hand, with a kneading action to remove as
much of the air as possible. A pressure of l kg/cm2 was
applied to the clay by the loading ram of a hydraulic testing
machine. The pressure was maintained for one hour, after
which the load was released and the compacted cake removed
from the ring. The cake was sliced into 21 sections, each

approximately 2 inches square in cross-section and 4 inches

31

in height. The sections were then waxed, wrapped in
aluminum foil, waxed again and stored in a moist room for

at least two weeks prior to testing to allow equalization

of moisture distribution and to minimize thixotrOpic effects.
Immediately before testing, the sections were removed from
the moist room and trimmed to a diameter of 1.40 inches

and a height of 3.0 inches for triaxial testing.

c. Dry Clay Sample. The air dried clay was pulverized

 

“Ultimortarand pestle until it would pass a No. 100 (U. S.
Standard) sieve. The pulverized clay was placed in a drying
oven at 105°C and left for twenty-four hours. After removal
from the drying oven, the clay was formed into a cylindrical
specimen and placed inside a rubber membrane fitted to a
cylindrical specimen mold. The clay powder was compacted
with a rod to densify the mass. After filling the mold,

the sample was fitted at the tOp with a lucite loading cap
and sealed. A vacuum was then applied to the sample through
the pore pressure line in the pedestal base. All water had
previously been removed from this line so that no moisture
could reach the dry sample. With the dry sample being sup-
ported by the vacuum, the sample mold was removed, the
detachable cylinder and cap of the triaxial cell secured

in place, and the chamber filled with water. Prior to
applying the chamber pressure, the sample dimensions were
taken. The weight of dry clay in the sample was determined
by weighing the supply of dried clay before and after form-
ing the sample.

32

d. Undisturbed Marine City Sample: The undisturbed

 

Marine City clay was obtained by means of thin-walled
piston samplers with an inner diameter of 3 inches. Tri-
axial Specimens were trimmed from the tube samples to the
same dimensions as the remolded-compacted samples. Data
pertaining to each of the individual test samples may be
found in Table 3.2.

3.4 Triaxial Tests

 

All test specimens were subjected to a hydrostatic

2

consolidation pressure of 2.0 kg/cm which remained until

at least 90% consolidation was reached. Except for the dry

2

clay, a back pressure of 1.5 kg/cm was applied after con-

solidation by raising the chamber pressure and pore pressure
simultaneously in increments of 0.1 kg/cm2. The back pres-
sure was maintained for at least twelve hours before testing.

a. Creep Tests. The creep loads were applied by means

 

of a yoke resting on the loading piston. The yoke was fitted
with a hanger from which the weights, required to produce a
certain stress, could be suSpended. These weights were
placed on the hanger with great care to avoid subjecting
the sample to shock loading.

A dial gage, of sensitivity 0.001 inches or 0.0001
inches, was attached to a mount on the triaxial cell with
the stem resting on the loading yoke so that the vertical

(axial) deformation of the Specimen could be measured.

Throughout the test, the chamber pressure was maintained
constant by means of a constant pressure cell.

From the instant the creep load was applied, the axial
deformation and pore pressure were recorded at thirty
seconds, one minute, two minutes, five minutes, and so on
with the time interval between readingsbeing approximately
doubled after each reading. These data, along with the
constant volume conditions permit the calculation of the
effective principal stresses and principal strains.

Each creep load was maintained until the deformation
had practically ceased and the pore pressure had reached
equilibrium. The length of time required to achieve this
condition varied from about one hour to more than one week
depending on the stress level and the stress history of the
specimen.

The loading program was varied considerably for dif-
ferent test Specimens. Some Specimens received only one
large creep load, while others were loaded in small incre—
ments. Still others were cyclically loaded; i. e., the load
was increased in small increments and then unloaded in
similar increments until all the axial stress had been re—
moved. The results of the cyclic loading tests are particu-
larly interesting because they permit a comparison of the
behavior of the material in loading and unloading.

b. Relaxation Tests: The Specimens were subjected to

 

a constant rate of deformation by means of a constant Speed

34

drive mechanism. At a predetermined deformation, the drive
mechanism was disengaged and the deformation maintained
constant.

From the instant the deformation was stOpped, the axial
stress, pore pressure and time were recorded at time intervals
which were approximately doubled after each reading. The
axial stress was measured by means of a proving ring in the
earlier tests and later by means of a load cell. The load
cell, the design of which is described by Schmertmann (1960),
was employed in order to minimize creep in the specimen
during stress relaxation. Since the relaxation of stress in
the proving ring produces substantial deformation in the
Specimen, it was thought that the measured decay of axial
stress might not represent true stress relaxation. After
checking the proving ring results with those from the load
cell which deforms very little with relaxation of stress, it
was found that the creep induced by the proving ring had
little or no effect on the measured stresses.

The room temperature was recorded during all tests by
means of a continuously recording temperature gage. During
the winter months, when most of the tests were performed,
the temperature control was very good--variations greater
than 2°C were rare. During the summer months, however, the
room temperature varied as much as 10°C during the testing
of a single Specimen. The temperature effects were most

pronounced on the stress relaxation testS—-in several cases,

35

rendering the data useless. The effect on the creep tests,
althOugh less severe, could also be seen in changes in slope
in the deformation—time curves. Where temperature fluctua—
tions became appreciable, this fact is noted in the data
which is presented in the Appendix.

A complete listing of the Specimens tested and the type
of test performed on each is provided in Table 3.2. The
results obtained from the experimental program are now
presented and analyzed in terms of the theory develOped in

Chapter II.

36

 

 

 

 

 

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mam. wom.a e eotnoaaoneoo ofisnm e-g-g
coapmxwfiom mmoppm

mom. mam.a cognates: sooneaaoneoo oflsnm m-m-m
HmpCoanocH

wow. wow. ..oooso cognates: consonants: spam ocean: m-o-o
econ oaweam

mmH.H msm.H -aoooo oodanhosp and oasmm H-o-mo
pmoq ofimcam

cow. mos.H -oooso oceansoe: sonnoaaoneoo hasnm m-o-m
oaaoxoufiwpcoanocH

Hmw. mmm.H -eooso accesses: cooneafionsoo hasnm m-o-m
OHHomounpcmanocH

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HmpcoanOzH

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soon oaweam

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oaaomouawpcoEmpocH

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oHpmm pHo> oapmm pHo> once cofipwawgmam maze soQEsz

Hasfia HnHoasH snag canonm

 

 

mpmoa Hmfixmflpe do mamEEsm

.m.m mqmdb

CHAPTER IV

EXPERIMENTAL RESULTS

4.1 Presentation of Data and Evaluation
of Model Parameters

 

 

.In this chapter, the experimental results of this
investigation are analyzed in terms of the structural model
described in Chapter II. The first problem to be considered
is that of devising a consistent method of data representa-
tion which will enable the model parameters to be determined
quickly and consistently. In the following discussion, such
a method is presented.

Consider the theoretical creep equation derived for

the structural model in Chapter II,

 

. k k
‘7": .____t + __1 1n tanh[—21— «,5 l 2
k2 k2“ kl+k2t
- k
-l _ _____.L_
+ tanh exp ( o<C kl+k2 )1 (2.11)

In a three-dimensional stress system, the shear stresses
and strains on the octahedral plane give a good representa-
tion of the shear distortion in the Specimen. The octahedral

shear stress is given by

 

I:oct =7:- ‘\/ (61 "0/2)2 + (62 ‘63)2 + ((3 -J1)2

and the octahedral shear strain is

38

 

2
7”; sl/M‘i- €2>2+ <62— €3>2+ <63— 61>?

oc

In the triaxial test, the principal stress difference
(Cfl -Cf3) and the major principal (axial) strain 6‘1 are
conveniently measured. Under constant volume conditions,

the stress and strain conditions imposed on the Specimen are

and

€1,362 =63;€1+€2 +73 = 0

assuming that the strains are uniform.
With these conditions imposed, the octahedral shear stress

is given by

'C =

oct

(61 ’63) = ’3‘ D

WK?!

H

in which D is the principal stress difference or the "deviator

stress as it is frequently called in the nomenclature of soil

mechanics. The octahedral shear strain is

“

:Vbct : f; c°l

in terms of the axial strain 61
Equation 2.11 can now be rewritten in terms of the measured

quantities D and 6‘1 as

k k2
C _ D l 1
x. l — W + __ 1n tanh “/8 kl+k2t

 

 

Immediately after application of the load (t = O), the

instantaneous strain is

S D
(t I)0 = 3(k1 + k2) ’

 

II
t
\‘l
H
U)

while the ultimate strain under a given load (at t

These relations can be combined with Equation 4.1 to obtain

a dimensionless creep function of the form

-,

1
11* = 1 + A in tanh [z(t) + tanh’l exp (—A) (4.2)

 

 

;‘ _ (V ) _
where U* - } 1 O = E___E2 , U = axial deformation,
2 k k k
A=go<D ___1 ;z(t)=lo<fl 13
kl+k2 2 kl+k2

The dimensionless creep function U* is seen to be de-
pendent upon the parameter A and the time function Z(t) and

varies between the limits of zero and one. By varying the

parameter A, and plotting U* versus log Z(t), the family of
curves shown in Figure 4.1 is obtained.
To determine the parameters o( and {9, the eXperimental

U-UO

Ug- UO
containing these points is then placed over the theoretical

data is plotted as = U* versus log t. The sheet
curves and adjusted horizontally until the points coincide
with one of the theoretical curves, as nearly as possible.

The choice of the best theoretical curve to fit the data

40

OH

.HoooE Handposapm hoe no>a:o coapwxmaoa mmonpm cam goose mmoficoamcofiam

onz .Anvw

HIOH OH mIOH

NI-

 

 

 

q _

    
      

Am-v axe H-ecno + on3 recs 2H

A<-v sxo H-nsoo + AoVN some on

is

H|< Hlm

.H.: madman

*D

mica

 

o

H.O

N.o

m.o

:.0

41

determines the value of the parameter A for that test. With
kl and k2 known from separate considerations, the parameter
(x may be calculated from the relation

Kl+ k2
k1

Cfl>

(4.3)

R
I
filed

The parameterff is found by noting the value of time t,
on the experimental curve,which coincides with some arbitrary

value of Z(t) on the theoretical curve sheet, since,

/5 _ 2Z(t)(k1+k2) (A A)
klk20< t

 

With kl and k2 calculated from the instantaneous and ultimate
creep strains and 0< and/6 evaluated by the curve fitting
technique, all of the model parameters are determined.

In the relaxation test,
I: = Ca, - (2; ln tanh [—2- 076 klt

+ tanh’l exp -o<(Lo -L,c )§ (2-13)

or, in terms of the principal stress difference, D,

D = D — -§- 1n tanh [% «)3 klt
°° o<2 1
+ tanh"1 exp -/§ cx (DO - D,)] (4.5)

In the same manner as described for the case of creep loading,
a dimensionless stress relaxation function is obtained in the

form

42

D*=1+

In tanh [W(t) + tanh’l eXp (-B )] (4.6)

uflh'

2
where s = -3- “(Do-D0,) , W(t) =33“? klt .
Do - D

13*:
. D-Doo

o
The dimensionless stress relaxation function D* depends
upon the parameter B and the time function W(t) and varies
between zero and one. D* is seen to be of the same form as
U* and so the same theoretical curves can be utilized for
both creep and stress relaxation. The determination of

and/6 for the relaxation test is carried out in the manner

as described for the creep test, where, now

 

3B
o<= J? (120- D..-) (4.7)
and
= 2W(t) (4.8)

arklt

It was found during the course of the experimental
investigations, that the ultimate values of strain and
deviator stress for creep and relaxation respectively were
rarely reached within reasonable testing times. The time
intervals required were normally greater than one week and
in some cases more than a month. During that time the test
samples were often subjected to accidental shocks or vibra-
tions on the loading frame and/or temperature fluctuations.
Efforts to eliminate these environmental factors were unsuc-
cessful, so a method was sought by which these ultimate

values could be determined by the Shape of the curves within

43

shorter time intervals. For the case of creep, such a
method was developed by considering the variation of strain
rate with strain.

Consider again the theoretical creep equation in the

form
6,: F +Gln'tanh[Ht + J] (4.9)
_P__ l 1 &
where F = 3kg , G = {gr—“"k'é'“ , H = ‘2’ (X /3 kl+k2 ,
2 k
J ‘= .tanh'l exp - (\f5— o< D --—-—l———- )

The variation of strain rate with strain is given by

dé = d6 dt = 6

d5 dt ' d6 6
Taking the first two derivatives of equation (4.4) yields

é: 2GH csch 2 (Ht + J)

 

and 2
.. -4GH csch 2 (Ht + J)
€= tanh 2 (HT + J)
from which
dé _ d1} _ __ 4 10
Id? _ dU _. 2H coth 2 (Ht + J) ( - )
dU
For (Ht + J) =- 1, EU. 2: -2H 2= a constant. Hence, a

simple arithmetic plot of U versus U should produce a curve
which, after sufficient time has elapsed, will have a constant
lepe of -2H. Extrapolating the straight portion of this
curve to U = 0 will then yield the required value of'Uw ,

the ultimate strain. This technique proved to be a very con-

venient means of determining Up, and also provided a valuable

44

check on the value ofcxf3 Obtained from-the curve fitting
technique.
An analogous procedure can be applied to the stress

relaxation data. In this case the required expressions are

D = Doc - L Meant. [Mt + N] (4.11)
dB
~and 55- = +-2M coth (Mt + N) (4.12)
3 l

where L=\/_20< , M_= '2-CXIB kl,

VG; (Do ‘ D)

N=tanh‘1 exp - 3

dD
. dD
Dd, , is obtained by extrapolating the curve D versus Dyto

for(Mt + N) a- 1, :z +2M. The ultimate deviator stress,
D = 0 and the value of<x;3. can be compared to that obtained
by the separate determination of o( and/6 described earlier.
The complete procedure used in analyzing the experi-
.mental data for determination of the model parameters is now

summarized.

green
1. Plot observed deformation-time readings as U
versus t. The initial portion of the U-t curve
is plotted on an exaggerated time scale and extra-
polated to t = O to find U0. Calculate k1 +.k2 = 3%:‘
2. From U-t curve, calculate the deformation rate U

at several points along the curve and plot U versus

0 and find

U. .Extrapolate the U-U curve to U

 

U10. Calculate k2 = and k1 (k1 + k2) - k2.

D
3(3“,

45

From the final straight portion of the U-U curve

 

k
evaluate 2H=nuiig— and calculate a}? = 2H.El:__3,
Plot deformation-time data as U- a = U* versus log t

00- O

andu find the theoretical curve which best fits
the data points. Calculate cx and/6 from Equations

4.3 and 4.4. Compare “/5. with the value found
in 2.

Stress Relaxation

 

l.
2.

From deviator stress-time data, plot D versus t.
From D—t curve, calculate D at several points
along the curve and plot D versus D. Extrapolate

the final straight portion of the D-D curve to

° 1 (if) 1
D = ODand gind D00 . Calculate «,6 = 2M El=+(.aU—)wpl.
O -
= -x-
Plot W D versus log t and find the

theoretical curve which best fits the data points.
Calculate cx and/5 from Equations 4.7 and 4.8 and

compare «)6 with the value obtained in 2.

Figures 4.2, 4.3, 4.4, and 4.5 illustrate the determin-

ation of the model parameters for typical creep and stress

relaxation tests. Supplementary data are given in the

Appendix.

4.2 Validity of the Structural Model

 

The stress-strain-time behavior predicted by the

structural model is represented by the dimensionless creep

and relaxation functions U* and D* as shown in Figure 4.1,

46

 

 

 

  

 
 

 

 

 

 

 

I I I I I I I I I 50 I l .T I I I l I I
- :5 EH) =_2.085x10'lI -
H dU °° in’l
_ E L10 _ m _
\ I
.. C1 _ _
H ’ .

_ [T 30 _ . _
_ O _ _
r—I
" .p 20 - _

UO=O.OOO4 in 10 —
(see note) _ Ufl=0.0316 in
l l l l l I I I I I O I l I l I l l I I I
o l 2 3 4 5 5 10 15 2o 25 30
Time (103 min) U(10‘3 in)

Note: UO determined from separate U—t plot with exaggerated time

U-X-

scale (not shown).

 

lo 1 1 10 105
Time (min)

Figure 4.2. Typical creep curves (Test No. C-C—l-5).

.onoo

 

K
see me\m5o mIonm.mmufla oonooevnyo

 

L
Tenssbfixmsdfi u .9

 

 

goons ane mhmmemme Hobos mo Soapwasoawo

.m.: mazmflm

uAana a ma.aaVAem.mav I m\xo

m KH.OHVAaw.mHVAoooVAaa.aV .. m\
AmHmVAHoo.ovm I

o to we;
Amx+HxVAoVNm

 

 

 

 

 

 

 

 

 

 

. m an n M\/I
w . o H m pom. E HII\/ H I II I v0
X\NEO Qmw MH v0 AMHQVA Hm HVAM v NVIHX < m
CHE wX\ OHK o NIAN COflflmgv n” «A JJoNKQOQV mmwoom IIIva a OOADUV IH mm a E: mm H Rd
NEO mI : w . Mam DU mx+Hx
mg+ax mam n mx+ax
mmm.o u as mom fix
mEo\mx now u an ssmfim n we I Amx+axv u He
«320.0.on ism on 9. cum
I. III . o . . H O I. H m M III. N m I III N
NEU\W& 3; N. NE Ammw NV OmmtO H X Q X D IW Q X
o
. I m
I a A . Aqooo ovm I 0 03m I I ..ww I o A “V n
mEo\wx mam I me: x .Amw NV Hmm.o I H x Q I dx+Hx . OD I ,w . Q mx+fix
mQOprHSOHmo
Hoo.o I fleas H.0HV N
Hm.a u a
ICHE Iofixmwo.m I HQNWWV mEo\wx omm.o n pdoEmmcCH mmonpm 90pma>op Hmcflm
H J De mEo\wx me.o H peoanocw mmoapm poema>op HmeHCH
ea memo.o ”.3: ea mw.m I H .nnmsoa menace HaanHeH
an aooo.o u o: mIHIOIo .oz once

 

when shoe

BIKE/cm?)

48

 

 

 

 

 

 

 

 

 

 

 

I I I I I | I I I -50 I' l I I l I I l l
_. A ._ db _ —l
e (——) =3.84x10 3 min
Do=l.490 ks/CmE _ g _40_ dDIw _
CU
5 ‘ “‘5 ‘
Q -30 \. “
:4 go _
“D E?
o -20 H ~
r—I .
.2: 71' “
-10 mg ‘
I I L L I I l I I I I I 1 I
2 4 6 8 10 gilg 1.17 1.15 1.13 1.11 1.09
Time (102 min) D(kg/cm2)

 

10
Time (min)

Figure 4.4. Typical stress relaxation curves (Test No5
F-R-S-l .

49

.pmmp COmememp mmoapm ane mpmpoEmamQ HmpoE mo SoameSUHmo .m.: opswam

\
cHs me\Eo mIonos.mHuHH ooeroevmmo
m

II
3%

HsIonmo.aVAm.mmv

 

 

 

 

 

 

- . I II. . E oH Hm.mmv I oHeyo I
Q E X I . . I I I I
HI H mIoH mo 3 m\ /Hoo.oMm Hpvzm QH
. I . AmsoH.HIoms.Hv m\,I qtoIomV m\, I
me\mso m mm I.yo . Hoo.mum I pm I x0
x N \
CHE MX\NE0 QIOmeINNHAN UOLPTEV QCIO mAIHImIHIV rmIOqu®.mV Hm\vo

qmcoEHoon oHpmpdeOU no manor goose ane mEc\wx mod n Hg mESmmm

\& DC I Hx
.I II. I 2 x0
:Iv OOAAMUV m “m\

 

mcoHpmHSOHmo

HIeHs mIonmw.m I Jmmv

mso\me meoH H Axe
3 meo\me ems. H on
m HI m m m .oz once

 

mama pmoB

50

and the ability of the model to predict the behavior of
clays depends upon the agreement of the experimental data
points with these theoretical curves.

The data collected from each test performed in con-
nection with this study are presented in the Appendix. From
inspection of these data, it can be seen that the agreement
between theory and experiment is quite good in most cases.
It would appear from the experimental evidence that the
structural model used herein to describe the deformational
prOperties of clays is a close approximation to the real
behavior. The evidence is, of course, indirect since only
the large-scale behavior of the clays can be observed and
compared with the theory. However, this is the plight of
most microscopic theories of material behavior, and their
validity can only be tested by such comparisons.

For some increments of creep loading, the deformations
were very small, and the dial readings from these tests were
somewhat approximate since it was necessary to interpolate
between the smallest dial divisions. Therefore, each set
of test data contains a note as to the accuracy of the data
points obtainable from the dial readings, assuming that
readings can be accurately interpolated to one-half of the
smallest division. In those tests for which the scatter of.
the experimental data seems to be excessive at first glance,
much of this scatter can be attributed to the limitations of

the dial readings.

51

In some of the creep tests, particularly the first stages
of unloading and reloading, reliable readings could not be ob-
tained at all because the deformations were too small or took
place too rapidly to be recorded with reasonable accuracy.
Consequently, no creep curves are shown for these tests.

The question may be raised whether or not the actual
creep and relaxation curves tend asymptotically to some ulti-
mate value as predicted by the theoretical curves, since the
final portion of the curves is missing in most cases. As
mentioned in the previous section, the eXperimental data often
became erratic in this region due to uncontrollable environ-
mental factors. Consequently, it cannot be stated with
absolute certainty that all the experimental curves approach
an ultimate value. There is considerable evidence in support
of this assumption, however.

In several tests, the ultimate strain appears to have
been achieved (see for instance, Figure A.33). Moreover, the
ultimate strain was frequently as difficult to record for
unloading increments as for loading and it is quite obvious
that recovery strains cannot continue indefinitely. In order
to establish this point conclusively, however, it would be
necessary to perform creep and relaxation tests in an environ-
ment free from temperature fluctuations and external distur-
bances. Such facilities were unavailable to the writer, so
this point remains unproven.

In some of the creep tests-—for example test number

C—C-l-7 in Figure A.7-—the data points for the earlier part

52

of the tests do not fit the theoretical curve that describes
the latter part of the test. Although these points are very
sensitive to the value chosen for U0, this factor alone can-
not account for the magnitude of the deviation in every case.
It appears that, in some cases, the sample behaved differently

during the earlier stages of creep.

4.3 Interpretation of Results

 

As is expected, the parameters are not constant for a
.single test Specimen, but vary with the stress level. A close
examination of the variation of the parameters reveals sig-
nificant information about the behavior of the clay particle
structure under load. Certain combinations of these parameters
have particular physical significance and are compiled in
Table 4.1 for all tests.

The cyclic creep test illustrate,.especially well, the
changes take place in the particle network during deformation.

Table 4.2 summarizes the trends observed in the quantities

k1 ‘
k1+ k2

tions in the model parameters are now considered in detail.

I <1. and /5? during two loading cycles. The varia—

4.3.1 The Spring, ”Constants"
The absolute values of the Spring constants k1 and k2
have little physical significance because there is no way of

knowing how the resistance of these elements is develOped in

___.lf._1___is of
kl+ k2
interest, however, since it represents the portion of the

terms of the particle structure. The quantity

53

 

wH.< No.3 om.m «No.0 o.sm mom.o H.mm mHm.oI HIOIo
sH.a o.sm e.gm mH.m o.m: mom.o mmH HH:.oI e
mH.< IIII m.mm om.m m.mmH mom.o mom SH:.oI e
IIII IIII IIIII IIII IIII 000.0 00.0 «Ha.oI e
mH.a m.mH Hm.m ow.m o.mm mms.o m.mm oHa.o+ 2
3H.« 0.0m s.om mm.m .o.Hm ops.o moH mH:.o+ e
mH.a m.mm m.mm oo.s m.mm som.o smH HHa.o+ e
IIII IIII IIIII IIII IIII mmm.o omm mHm.o+ e
mH.< H.mH Ho.oH ms.m s.m:. omm.o H.:m mHm.oI e
HH.¢ m.mm H.mm mm.s m.ms mmm.o m.ms oam.oI e
oH.< s.mm m.mm mm.m m.mm mow.o s.ms mam.o-. e
m.¢ H.mm s.sm Hm.HH s.w: Hmm.o :mH mHa.oI e
m.<. IIIII s.mm mo.m m.om mmm.o mom HHs.oI m e
III IIIIIIIIIIIIIII IIII mam.o Hm: smm.oI m e
s.< o.omH mHm m.Hs m.om mmm.o mo.H me.o+ s a
w.< m.mm w.mm mm.mH m.mm mmm.o os.m me.o+ m a
m.< s.mm m.mm ms.mH sm.mH. www.o m:.s omm.o+ m e
s.< m.mm m.sm am.MH m.om mam.o m.0H Ham.o+ : e
m.< om.m om.m mm.m m.Hm mmm.o mH.mH amm.o+ m e
m.< so.w mm.: mom.H m.mm mmm.o m.mo mom.o+ m e
H.< mH.m wo.s mam.H m.Hm mmm.o smH oom.o+ H HIoIo

H ASHE wx\NEooIoC \T/. I; \1 )V x) G 1 Im. S
I. I O O X. N. G XI. 0 u 9
a m m be was no a a m an m an a
I i In I / I m m mm am a

.e mwdd “WAV mm %m 70 .6 .6 rue k“ a

p p _ /l\ ( ( (TI. 0 u

I I n+

8 I (\ .IaI

 

 

mpHSmmm mo hamEESm

 

 

r?
00.4 0.00 00.0H 00.0 0.00 000.0 00.0 0.0: 00H.H+ 00H.H 000.0 H H 0 0-0
00.< 0.00 0.00 00.0 0.Hs 0H0.0 0.H0 0:0 000.0+ 000.H 000.0 0 0 0I0I0
00.0 0.00 00.0H 00.0 01H: 000.0 0.00 00H 000.0+ 000.0 0H0.0 0 0 e
:0.< H0.0H 0H.0 000.H 0.0: 000.0 0.0H 000 000.0+ 000.0 000.0 H 0 =
00.0 0.0: 0.00 0:.sH 0.00 H00.0 0.00 000 00s.0+ 000.0 000.0 H H 0I0I0
00.0. 0H0 000 00H 0.00 000.0 00.0 00H 000.0+ 00H.H 000.0 s 00 0I0Im
H0.< 0.0H 00.0 000.0 0.00 000.0 0.0H 00H 0:0 0I 000.0 000.0 0 00 =
00.0 0.00 0.0: 00.0 0.00 000.0 0.0: .00H 0:0.0I 040.0 000.0 = 0H e
00.< H.00HV 0.H0 H0.0H H.00 0H0.0 00.0 0.00 so0.0+ 000.0 000.0 = 0H e
00.< 0.00H 0.00 00.0H 0.00 0H0.0 0.00 00H 0:0.0+ 040.0 000.0 : 0H e
00.< 0.0: 0.00 0H.0 0.0: 000.0 0.00 00H 0e0.0+ 000.0 000.0 0 0H =
00.< 0.00 0.0: 0H.0 0.00 000.0 0.00 0.00 000.0I 000.0 000.0 0 0H =
00.< 0.00 s.H0 00.: 0.00 000.0 .s.H: 00H 0:0.0+ 000.0 000.0 = 0 e
:0.< 0.H0 H.00H 00.HH 0.00 H00.0 0.H0 0.00 0s0.0+ 004.0 000.0 e 0 =
00.0 0H0 0.00H 00.0H 0.00 000.0 00H 00H 000.0+ 000.0 000.0 0 0 =
00.< 0.00 0.0: 00.0 0.00 000.0 0.00 00H 0:0.0+ 000.0 000.0 H 0 e
H0.< H.0H 00.0H 00.0 H.00 000.0 0.00 HHO 000.0+ 000.0 000.0 = 0 0 0I0
00.0 e.H0 0H.0H 00.: 0.00 HH0.0 0.0H 000 0a0.0+ 400.0 000.0 e 0 H 0Ia
0H.< H.00 0.00 0.H0 00.0H 000.0 0.00 0H0 000.0+ 000.0 000.0 H H 0 0I0
Add:
0x\ so 03 I I, I )V I d )0 III S
a 0 m I x) X
t. . O o I. x. YI X0 X3 MI... W mm 8
e 0.. a r... was no so an a 0... Wm pm... 0
a .4da nun m ,WV 20 m m m m mm m t. .0 w a
a w mu/Oa I. 00 8 8 8 {W0 (HwopTo. Mm”
D. D. U (\ /\ (\ (\ I3
8 T. NW 3

 

 

 

 

 

 

AposcHoeo0V H.s mHmae

55

.mcoefloogm amfiHsflm :0 hence moose anm 0&0\mx 00H

.HH.s 0:0 0H.: nosstm oomrs

ax mCHESmm<*

 

000.0

 

 

0s.<r00.sH *00.0 0.00 IIIIIIIIII -- 000.0- 000.0 000.H - 0 0-0-0
s:.<*00.0 000.0 000.0 0.00 IIIIIIIIIII --I 000.0- 000.0 000.H II H 0-0-0
0s.<*00.0H a0H.:H $00.0 0.00 II--- --- II-I 000.0I 00H H 000.H II H 0Im-m
0a.< *0.00 #0:.0H *00.0 0.00 IIIIIIIIII II- 000.0- 000H.H 00H.H II H 0-0-0
Hs.< 0.0HH 0.0HH 00.0H 0.00 000.0 000.0 0.00 0000 0+ 0000.0 00.0 H H H-0-00
03.4 H0.0 000.H 000.0 0.H0 000.0 0.HH 0.00 00.0+ 00.H 00.0 H 0 0-0-0
*a I IIIIIIIIIIIIII 0.0.: eoHnoom oom IIIIIIIIIIIIIIII 00 0+ 00.0 00.0 e s a
00.0 00.0 00.0 000.0 0.3: 000.0 0.H0 0.HOH 00.0+ 00.0 00.0 e 0 a
00.< 00.: 00.0 000.0 0.H0 000.0 0HH s00 00.0+ 00.0 00.0 H 0 0-0-0
0 1.0.0. 0 I n I n- 0. ITV 0...... nm a .00 .0
E IOH TL n
a .30 no. I. no no We. 0.. 0.. mm 0 m0 0.
w mm mm )2 WM 4% m mm m w T. mmT- no w a
new can w an 8 8 .0 L% me. .M m
0d. we .0 I < < I T. I
D. D. _ a
TI.
8 I /\

 

 

 

HooseHosoov H.s Mnge

56

 

000000 00 200000000 00 000
I500020Q00Q 3000 00 002000
2003009 00200000 on 002000

 

00000000 00000000 00000000 00000020 I0oQo0Q 000000>20 0000020 mx
200p0>0p00 00 0000202omx0
00 002O0p0omo00 000000>20
A0020 3000
020500020 00 02000 20 0000 0025 000
0000 0000V 00209 0203000 mo 00QES2 X0
00000000 00000000 00000000 00000020 on 002000000000 000000>20
00209
0050000v 0000000000020 00 3O00 mx + 0&
00000020 00000020 00000020 00000020 00500 on 020000 000000 .i-0x.
0000020 00 20000000 000500
02000002: 0200000 02000002: 0200000 002000002000 00000050 000020000
0 00000 N 00000 0 00000 0 00000

 

02005 00030002

 

0200000 00000 000000 020050 00000E000m 00002 00 20000000>

.m.: m0m<8

57

total shear stress that initially tends to produce flow.
Figure 4.6 shows the variation of RE":;K§' with deviator
stress level over two complete cycles of loading and unload-
ing. .The data from the compacted Specimen C-C-l is chosen
for this illustration because of the completeness of the
data, but the other Specimens show similar trends. Figure
4.6a shows that, throughout first loading on Specimen C-C-l,
nearly all of the applied stress causes flow at the bonds.
According to this trend, the initial bond strength distribu-
tien curve must be skewed toward the direction of lower yield
strengths, which agrees with the curve shown in Figure 2.5a.

The unloading branch of cycle 1 shows that less than
half of the first unloading increment produces flow. For
subsequent unloading increments in the first cycle, EE_:lE§
steadily increases until, for the last increment, nearly all
of the stress causes flow. It was also noted that the creep
reSponse becomes progressively Slower with unloading. These
observations indicate that the distribution of yield strengths
is more uniform for unloading than for loading in the first
cycle. Reference to Figure 2.5c shows that such behavior
is predicted by the theory.

Theoretically, if no changes in the pr0perties of the
‘particle structure take place, the distribution of bond
yield strengths for reloading should be the same as for first

loading. However, according to Figure 4.6c, the behavior of
k1

izf0x—EE during reloading is intermediate between the cases

58

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1'0 1—_j.—F———l— 1‘0
.8 _. Li
g.“ (a) Cycle 1: loading
H + 6 — 6
.2 go go "—
0L:
.0 0
.24 _ - , L
A (b) Cycle 1: L—_—‘
unloading
2 - 2—
O l J l l I O I l I I J
O 0.4 0.8 1.2 1.6 2.0 O 0.4 0.8 1.2 1.6 2.0
D(k%/cm2) D(k%/cm2)
1.0 f 1.0 —
8 — F—'—— .8 —
.6 - .6 0
m
x
EL 01
004 — (c) Cycle 2: loading 002,4 — (d) Cycle 2:
,3 t4 nnloading
.0
2 - .2 0
O 1 1 l l J O J 1 J L .0
O .O.4 0.8 1.2 1.6 2.0 O 0.4 0.8 1.2 1.6 2.0
D(kg/cm2) D(kg/Cm2)

k1
Figure 4.6. Variation in the ratio EE;E:" with deviator

stress, D, in cyclic creep loading of
specimen C-C-l.

59

of loading and unloading in the first cycle, which means
that the yield strength distribution curve for reloading
must be flatter than for first loading.

A possible explanation for the change in the distribu-
tion of yield strengths after a loading cycle is that Some
of the particles, in the process of flow, become aligned
along potential failure planes; thus reducing the number of
bonds in the planes of flow and weakening resistance to de-
formation along these planes. Wu, Douglas, and Goughnour
(1962) observed such particle alignment by means of diffrac—
tion studies on thin sections taken from the failure planes
of triaxial Specimens. Hvorslev (1960) also detected
preferred particle orientation by drying triaxial Specimens
and noting the development of shrinkage cracks.

Furthermore, it is quite likely that some bonds with
greater yield strengths could be created as a result of
particle interference during the flow process. Lambe (1960),
explained that interference can occur when particles become
wedged together during deformation. Additional energy is
then required to lift the particles over one another so that
flow can continue. This would result in a shift in the dis-
tribution of yield strengths toward greater strength and
tend to flatten the curve.

k1
The increase in gkl + kg for the second unloading is

 

basically the same as that for the first unloading. From the
k1
consideration of the variation in k1 + k2 over two cycles

 

60

of loading, it is possible to sketch, qualitatively, the
distribution of bond yield strengths at the beginning of
each phase of loading. Figure 4.7 shows distribution
curves for the beginning of each loading and unloading

which are based on the observed phenomena.

  
   
  
 

lSt loading

//,,\\<:/,,2nd loading (reloading)
I

lSt and 2nd unloading
___ _V_.______.J{___\

Distribution‘ql

 

 

Yield strength Cy

Figure 4.7. Distribution of bond yield strengths with
reSpect to the various phases of cyclic
creep loadin --constructed from observed
trends of l

m

k1+k2

_5»3.2 The Parameter o<

 

According to Equation 2.7,

_ A
°<_ 2010:

'where ,A is the distance between equilibrium points on the

potential surface in the direction of flow and O is the

61

number of flowing interparticle bonds per unit area in the
plane of flow.

It may be assumed for simplicity that .1 , which is a
property of the close range interparticle forces and, perhaps,
the lattice structure near the particle surface does not
change appreciably. Then the factor which controls the
value of 0< , for constant temperature, is \) . Therefore,
the variation of ac for a given sequence of loading gives
some indication of the shape of the yield strength distribu-

tion curve and provides a check on the trends observed in
kl
k1 + k2 '

Figure 4.8 shows that CK changes but little during
the first loading of Specimen C-C-l until the last increment
of deviator stress. Since the fraction of the stress carried'

k
initially by the flowing bonds ("El—117k? )

is near unity for
all increments, large changes in \) are not expected. Under
the last load increment the value of o< is approximately
doubled, indicating a sudden reduction in the number of
flowing bonds in the plane of flow. ‘The axial strain pro—
duced by the last increment is more than twice the total
strain prior to that increment. Consequently, it is reason-
able to assume that the structural changes in the sample
during the last increment are substantially greater than for
any preceding increment.

It was noted earlier that large strains can produce

preferred particle orientation along potential failure planes.

 

 

 

 

 

 

 

 

 

 

 

 

 

62

 

 

 

 

 

 

 

 

 

 

 

 

 

 

604- (a) Cycle lz-loading 120 - (b) Cycle 1: unloading
500 T" 100 -
. fi’
\ O
(\J V 0
X
lo— 20 0
O I. ll. 1 -1. J 1 L. l I .lJ
o 0.4 0.8 1.2 1.6 2.0 0o 0.4 0.8 1.2 1.6 2.0
D(k3/cm2) D(k3/cm2)
60r— 120 _
' (d) Cycle 2:
500. 100 +- unloading
25° 1’1 tel
00.40" 0% EN) —
E L__|__J—— o
3030- V L
‘6 . ‘6 60
20__ (C) Cycle 2: loading 40 __
lOr- 2o _.
O 1 1 1 All I O L ,1 I ’1 J
o 0.4 0.8 1.2 1.6 2.0 o 0.4 .08 1.2 1.6 2.0
D(k3/cm2) MKS/6192)

Figure 4.8. Variation of the flow parameter, c0 , with
deviator stress, D, in cyclic creep loading

.of Specimen C-C-l.

63

As the flat particle surfaces become parallel to one another,
fewer interparticle bonds can develop per unit area and, con-
sequently, some of the bonds that are broken cannot reform.
If particle reorientation takes place during the last load
increment-~which seems reasonable in view of the large
strains observed--then the increase in 0( can be attributed
to a reduction in the number of bonds in the plane of flow.
During the unloading phase of the first cycle, CK
decreases so \) must be increasing which agrees with the

k
trends observed in ’kl ikg . The second loading cycle

 

shows that 0 increases with progressive loading and unload-
ing which also corroborates the evidence from Rigérpfi'. In
general, the variation in 0< substantiates the yield strength
distribution curves shown in Figure 4.7.

It may be noted in Table 4.1 that the consolidated
Specimens, which have larger final void ratios than the com-
pacted Specimens, give larger values of 6X. , indicating that
less bonds flow when the void ratio is larger. The dry
creep Specimen DP-C—l, which has the highest void ratio of
all specimens tested, also gives the largest 0< value for
comparable stages of loading. The implication of this trend
is that the number of bonds per unit volume is inversely
pr0portional to the void ratio which verifies the theoretical
prediction of Section 2.2.

The calculated values of CK provide an excellent

Opportunity to check the reliability of the hypotheses which

64

led to the structural model. Recalling that

 

A
0<
2 J kT
and taking 0( = 30 as a representative value, then
2‘ - 2o<kT - 2 (30) (140 ‘22 8
7 _ _ . 7 x 10 ) (29)
3— = 2.52 x 10’18 cm3

In Specimen C-C-l, the solid weight is 97.5 grams and the
Specific gravity of the solids, GS, is 2.70. Therefore the

solid volume

Vs = 27%0 = 36.1 cm3
An average illite particle is approximately 0.5 microns in
diameter and 100 angstroms in thickness (Scott, 1963),
giving an average volume of approximately 2 x 10"15 cm3.
.Since the Sault Ste. Marie clay has a clay fraction of

0.60, the total number of clay particles is then,

_j§6.1) (0.602 = 1.09 x 1016 particles.
2 x 10 '

 

.The total volume of Specimen C-C-l after consolidation is
63.65 cm3, so the number of particles per unit volume
becomes,

1.09 x 1015
63.65

If it is assumed that each particle forms six contacts as

 

= 1.70 x 101“ particles/cm3

suggested by Rosenquist (1960), then the number of bonds per
unit area in the plane of flow,’p, is approximately

)1 (6)(l.70 x 1014)(%—)(0.5 x 10‘4)(0.707)

’p = 1.20 x 1010 bonds/ Cm2

where p is equal to the number of bonds per unit volume
times the distance between points of flow perpendicular to
the direction of flow and the particles are assumed to be
inclined to the plane of flow at an average angle of 45

degrees. Assuming that 75 per cent of the bonds flow,
A: (2.52 x 10‘18)(l.20 x 1010)(0.75)
A== 2.27 x 10’8 cm = 2.27 angstroms

where Q = 0.750. It is of interest to note that the dis—
tance between adjacent silica tetrahedra in an illite
particle is 2.55 anstroms (Grim, 1953). In view of the
calculated value of A = 2.27 angstroms, it seems reasonable
that the interparticle bonds are associated with the lattice

structure of the particles.

_§.3.3 The Parameteryfi

The concept that the particle structure possesses a
spectrum of yield strengths in its interparticle bonds
suggests that as stresses are applied to the structure in
increments, the activation energy of flow should increase
as stronger bonds are brought into the flow process. From
IEquation 2.7,

- AF/RT

= 2 .X kT
fl ,7 he

 

66

so that/9 should decrease, exponentially, as ALF increases
if A, is constant. Although )0 may not be constant, the
activiation energy is assumed to dominate changes in/g be-
cause of the exponential effect of AtF.

Figure 4.9 shows the variation of/B in Specimen C-C-l
over two loading cycles. For all except the first loading,
/3 generally follows the expected trend--decreasing as the
load is increased for reloading (Figure 4.9c) and decreasing
again as the load is removed (Figures 4.9b and 4.9d). Thus,
the average yield strength of the bonds that flow increases
as loading progresses as a predicted by the yield strength
distribution curves in Figure 4.7.

However, for the first loading/5 increases which is
contrary to the expected behavior. This would seem to indi-
cate that the bonds that reform in the flow process are
weaker than the original bonds. Such a phenomenon is
plausible in light of the evidence of structural changes
detected earlier by the consideration of EEEé—ké'and o<

For example, consider an interparticle bond between
two particles meeting at a large angle and forming an edge—
to—face contact. The attractive forces between these two
particles are large due to the Opposite charges of the edge
and face, while the repulsive forces are small Since the
flat surfaces of the two particles are far apart. This type
of contact, predominant in a random particle structure,

forms a strong bond. 0n the other hand, two particles

29.4

 

 

 

 

 

 

 

 

 

 

 

 

 

Cycle 1:
loading
15 ‘
'3‘ 10 r
'2
.0
E
‘T
25-—
(L
L—__——L__J
0 II I I I
O 0.4 0.8 1.2 1.6 290
D(kg/cm2)
/\ 15"' Cycle 2: loading
H
I
.5
E 7
[0101
lo r
S. l
“l
5—
O 1 1 1 11 1
O 0.4 0.8 1.2 1.6 2.0
D(kg/cm2)
Figure 4.9.

stress, D,
Specimen C-C-l.

 

 

 

 

 

 

67

 

 

 

 

 

15__ Cycle 1: unloading
" ?
[—3 u
q I
«'1
E107
[T
a +0— |
Il_5L- l
L____
O I I I I J
O 0.4 0.8 1.2 1.6 2,0
D(kg/cm2)
15" Cycle 2: unloading
$7
I
2
[T __ .__
<3
r-I
Q50
0 1 I I 1 1
O 0.4 0.8 1.2 1.6 2.
D(kg/cm2)

Variation in rate parameterfé
in cyclic creep o

with deviator
ading of

O

68

meeting at a low angle form a much weaker bond because of
the repulsion develOped between the flat surfaces as they
approach one another.

As the particles become aligned in the planes of flow,
the angles between particles forming bonds becomes progres-
sively smaller and thus the bonds may become weaker as
described above. AxF, therefore, decreases and #3 increases
with strain. Experimental evidence for such particle align-
ment during the first loading has already been cited. The
strains produced by subsequent loadings were much smaller so
structural changes probably had little effect on A F after
the first loading.

As seen from Table 4.1, nearly all of the calculated

values for/5 fall within the range 5 - 15 x 10'7 min.‘1
Using k = 10‘6 as a representative value, .A = 2.27 A and

u x .707 = 1.178 x 10‘5 cm. as

l -
letting Al: g‘x 0.5 x 10
before, the activation energy, ALF, may now be determined.

Noting that

and substituting the values from above, the activation energy

is

(2.27 x 10‘8)(1.407x10‘22)g2981l
(.001987)(298) in [2 Tl.l78x 10-5)(1o-b)(1.125x10-34)

I
.J

AI‘1

AI!1 24.8 k cal mole‘l

'Phis value represents the mean strength of the interparticle

69

bonds broken during the shearing process. Since the bond
strengths are comprised of a complicated interaction of
attractive and repulsive forces between the clay particles,
the contribution of the individual bonding and anti-bonding
force systems is impossible to assess with the knowledge of

the clay-water system presently available.

4.4.4 Creep Test on Dry Clay

It was stated, in connection with the discussion of
the clay-water system in Chapter II, that the role of the
adsorbed water films in determining the deformational charac—
teristics of clays is of minor importance. This view is
based, in part, on an experiment performed by Norton (1952)
in which it was shown that a dry clay, when placed in an
elastic membrane and the air withdrawn, behaves exactly like
a wet plastic clay. Itvwxsbelieved that the conditions of
this experiment could be duplicated in the triaxial cell,
thus producing a dry clay Specimen that could be tested under
creep loading.

A Specimen of oven-dry powdered clay was obtained using
the same technique used in preparing triaxial Specimens of
dry sand. .The details of this technique are described in
Chapter III. No moisture was permitted to enter the sample
during testing.

Because of the fluffy nature of the dry, powdered clay,
compaction in the sample mold was difficult and the resulting

Srmcimen has a rather high final void ratio (e = 1.132) and,

7O

consequently, is quite weak. It was, however, possible to
perform one loading increment on the Specimen using a small
deviator stress. The results of this test are shown in
Figure A.42. It can be seen that the curves for the dry
clay take the same form as the saturated clays for creep
loading. The calculated values of cx and f6 for the dry clay
are also consistent with those obtained for the saturated
clays.

The findings of this test indicate that the behavior
of the clay particle structure is not affected to any impor-
tant degree by the presence of adsorbed water films. Norton
(1952) suggests that the role of water in causing plasticity
in clays consists of forming an air-water boundary around the
surface of the wet clay mass, producing surface tension which
acts to press the particles together. The plasticity of a
wet clay mass is, thus, believed to be a prOperty of the

clay particles and not of the water.

4.3.5 Relaxation Tests

 

It has been demonstrated that the structural model for
clays developed in Chapter II provides a good representation
of creep behavior. The results of the stress relaxation
tests provide an opportunity to check the generality of the
model with another type of loading. The agreement between
the theoretical and experimental relaxation curves is quite
good. The calculated values of/B also agree with those

obtained in the creep tests (see Table 4.1). It will be

71

rioted in Table 4.1 that the value of k1 is estimated from
czreep tests performed on a similar Specimen in order to
czalculate‘fl. This is necessary because the relaxation tests
Iorovided no independent means of evaluating the Spring
"constants."

The values obtained for cx in specimen F-R-8 are some-
xnhat smaller than the correSponding values in creep loading
(on Similar Specimens. Since the results are obtained from
different samples, this discrepancy may simply be due to
‘the unavoidable variation between samples; even though the
Inethod of preparation is identical. The other relaxation
tests yielded values of O< which agree with those obtained
in creep loading on similar Specimens. In general, the
agreement between the results of the relaxation tests and

the creep tests seems to support the validity of the struct-

ural model.

4.3.6 Temperature Effects

The room temperature was measured by means of a
continuously recording temperature gage during the progress
of the loading tests. During the winter months, when most
of the tests were performed, the room temperature was very
well controlled--a maximum temperature variation of about
2°C was average for most tests. During the summer, however,
the temperature varied as much as 10°C during a single test.
These fluctuations were, for the most part, erratic and of

short duration and often produced unreliable results in the

72

tests. In one instance, however, the room temperature was
Inaintained at a abnormally high level for four days, during
‘which time creep test D—9-4 was in progress.

The creep curve from this test is of interest because
it provides an Opportunity to calculate a value for the
activation energy based on temperature variations. Figure
4.10 shows the creep curve from test no. D-9-4 along with
the room temperatures recorded during the test.

Referring to Equation 4.8, it is seen that, for large

values of time,

dfi klkg _ klke 2 - F/RT
--—=::- 2H = -O( — - _._.___.. A c
U fl EEK—2 k1+k2 3‘51”
Taking logarithms of both sides,
at AI?
1 _..._ = .. .. .—
n (dU) 1n S RT (4.12)
where
S _ .515§_. JLE_Q
k1+k2 ,Aluh
Differentiating with respect to temperature,
d 1n ( dU ) = AF (4.13)

dT dU RT?

Upon integrating Equation 4.13 between the limits T1 to T2,

the activation energy becomes

 

(422.)
M = R (T1T2 ) ln __9}L_2_ (4.14)
Tl‘Ta ( dfi )
dU l

(4.11)

73

.mEo\wx ww.o:>©.oum .qumsona pmop

Qmmho pom mm>s50 mEHpaoLSpmmeEmp psorQOflmesOQmm .OH.:

mm

Amhmovoefle

mpswfim

 

mm

mm.:

mm.:

mm.:

0
m
I

(00) aanqeaadwa;

Hm.|

 

——1
-——1

we 0H 3H NH 0H m m a
i _ _ i a i

 

whopmpoQEop

coapmemoemc Hmflxm

oom.amn« mpsumpmmfiop mwwpm><

A
A

"—4

+

oowmnuoLSpmmeEmp owmpm><

V
V

 

O
H

(\l
H

a.
H

\O
H

(I)
H

O
(\J

(u? E_OI)n ‘uotqemaogap TPIXV

74

It may be seen from Equation 4.14 that the calculation

of the activiation energy, A F, by this method requires the

 

evaluation of 33 from the creep curve for the temperatures
T1 and T2. In Figure 4.11, —§%— is determined for the temper-
atures T1 = 26°C and T2 = 31.5°C. The segments of the creep
curve used in this determination are shown in Figure 4.10.

Substituting the apprOpriate values into Equation 4.14,
the activation energy, 15F, becomes

-3

F l
A 5.5 .663 x 10"5

AF‘ 23.5 k cal mole‘l

THliS value of A F agrees quite well with that found by
aanother method in section 4.3.3 and adds further evidence

111 support of the rate theory approach.

.Jse\ms Sm.o-ko.ouo
”2-9-0-9 pmmp Qmmho Ca mmLsmmLmoEmp pCmsmgdao

v; 03p so; mofismcoapmaos coHmeLoewo.e:oaomELommo mo mpmx .HH.¢ mesmflm

Ase m-oHV: sofiemesocme Heexa

om 0H ma SH me me as me me He OH 0 m S
_ _ all _ _ _ a, _ «a _ i n _ o

 

    

8.375
e-gmem-oflxmmm.o u

    

Aoom.Hm.«ev
H-seem-oaxomm.fl n

 

(Rap/u19_07)g ‘uotqewJOJap Ierxe JO aqeg

CHAPTER V
CONCLUSION

The deformation of clays is studied from the point-of-
view of the particle structure. This consideration leads to
the conclusion that processes taking place at the particle
level during deformation can be treated by the methods of
rate theory. Using the flow relationship derived from the
rate theory treatment, the concept of a Spectrum of bond
yield strengths is develOped. According to this concept,
some of the bonds in the particle structure flow under a
given stress increment while others remain intact by virtue
of their greater yield strength. It is shown that the
theoretical concepts presented could be simulated ‘by a
simple structural model which agrees with the observed defor-
mational prOpertieS of clays.

The results of the experimental program Show that the
behavior of the clays tested agrees well with that predicted
by the model for the test conditions employed. The loading
conditions are quite varied with Specimens being tested
tinder single creep loads, incremental creep loads, cyclic
<3reep loading and stress relaxation. In nearly every case,
egood agreement is found between the theoretical and experi-
Inental results. The quality of agreement achieved tends to

snubstantiate the validity of the rate process approach to

77

deformations at the particle level. For further investiga—
tions along these lines, other loading conditions should be
employed; e.g., constant strain rate tests at different rates
of strain would be useful, as would experiments with con-
trolled temperature variations.

The creep test performed on a dry powdered clay sample
shows that the behavior of the dry clay, in creep, is
essentially the same as the saturated clays. This result
lends support to the suggestion by Tan (1959) and others
(Leonards and Girault, 1961; and Norton, 1952) that the
adsorbed water films on the particles are not the prime
cause of viscous flow in clays. Additional tests on dry
clays under various loading conditions are needed; such
tests could provide valuable information on the nature of
the interparticle bonds.

The calculated values of the model parameters Show
considerable variation. In Figures 4.6, 4.8, and 4.9,
attention is focused on the variation of these parameters
through two complete loading-unloading cycles. From the
trends observed in the quantity __E%Ei., it is possible to
sketch, qualitatively, the distributign of bond yield
strengths for the various stages of loading. The variations
in o< and/5 agree well with the distribution curves shown in
ZFigure 4.7 with the exception of’fl during the first loading
stage.

During the first loading, it is believed that the yield

EStrength distribution is affected by the breakdown of the

78

original particle network as the particles become aligned
along potential failure surfaces. The increased alignment
along the slip plane is known to be accompanied by a tendency
toward volume reduction in the potential failure zones. The
calculated variation in the model.parameterscorroborates
this view and agrees with the experimental findings of other
workers (Wu, Douglas, and Goughnour, 1962; and Whitman, 1960).
The increase in the parameter/fl during first loading also
indicates that the interparticle bonds become weaker as
deformation proceeds. This phenomenon is explained in terms
of the changing particle geometry from a random arrangement
toward parallelism. It is noted that the bonds should
become weaker due to the build—up of Coulomb repulsive
forces, as the flat particle surfaces come closer together.

Subsequent loading cycles show less structural change
'than first loading as would be eXpected. The problem of
sstructural changes accompanying deformation needs further
investigation. With the recent develOpment of the electron
rnicroscope, such studies are now feasible and would contribute
rnuch to the understanding of clay deformations at the particle
level.

The measured parameter<x provides a means to check
1:he values of V and A. for the clay particle network. The
EEXperimental values of 0< are found to be entirely consistent

Vvith the dimensions of the clay particles and particle

geometry.

79

From the measured values of the parameter/5, a repre—
sentative value for the activation energy, 13F, is calcu-
lated. The value is in agreement with AiF calculated from
temperature effects. It is noted that present knowledge of
the clay—water system is insufficient to enable 13F to be
interpreted in terms of interparticle forces. The theoret—
ical consideration of the bonding forces between particles

provides a promising area for further investigations.

BIBLIOGRAPHY

Anderson, D. M. and Low, P. F. "The Density of Water
Adsorbed by Lithium-, Sodium-, and Potassium-Bentonite,"
Soil Science Society ganmerica Proceedings, vol. 22,

1958: pp- 99-103.

Bowden, F. P. and Tabor, D. Friction and Lubrication of
Solids, Clarendon Press, Oxford, 1954.

 

Burwell, J. T. and Rabinowicz, E. "The Nature of the Coef-
ficient of Friction," Journal_of Applied Physics, vol.
24, no. 2, 1953, pp, 135—139.

Casagrande, A. and Wilson, S. D. "Effect of Rate of Loading
on the Strength of Clays and Shales at Constant Water
Content,“ Geotechnique, vol. 2, 1950, pp. 251-203.

 

Christensen, R, W. "Structure and Identification of Clay
Soils.“ Unpublished laboratory report, Soil Science
945, Michigan State University, 1963.

Eyring, H. and Halsey, G. "The Mechanical Properties of
Textiles-eThe Simple Non—Newtonian Model," high
Polymer Physics-jg Symposium, 1948, pp. 61_II6T

 

 

Geuze, E. C. W. A. and Tan, T. K. ”The Mechanical Behavior
of Clays," Proceedings gf_the Second International
Congress on Rheology, 1953, pp. 247-259.

 

Glasstone, S., Laidler, K. J., and Eyring, H. The Theory 2:
Rate Processes, McGraw-Hill Book Company, Inc., New
York, 1941.

 

(Grim, R. E. Clay Mineralogy, McGrawefiill Book Company, Inc.,
New York, 1953.

 

Iiorn, H. M. and Deere, D. U. ”Frictional Characteristics
of Minerals," Geotechniqug, vol. 12, no. 4, December,

1952, pp. 319~335.

flouwink, R. Elasticity, Plasticity and Structure of Matter,
Cambridge University Press, Cambridge, England, 1937.

 

fivorslev, M. J. "Physical Components of the Shear Strength
of Saturated Clays," American Society of Civil En ineers
Research Conference pp Shear Strength 6: Cohesive Soils,
June, 1960, pp. 169-273.

 

 

 

Iler, R. K. The Colloid Chemistry of Silica a;rd Silica tes,
Cornell University Press, Ithaca, New York, 1955.

 

 

Lambe, T. W. 3A Mechanist.c Picture of Shear Strength
in Clay, American Sggiety of Civil Engineers Researr-
Conference on Shear SLTe_'Lgth_ of Jo-es1ve Soils, 19 C,

 

 

 

pp° 555 580“

Leonards, c. A. and Girault, P. "A Study of the One-Dimen-
sional Consolidation Test," Proceedings of tte Fifth

International Conference 22 Soil Mechanics and Foun-d-
ation Engineering, vol. 1, 1961, pp, 2134218.

 

 

 

 

Lo, K. Y. "StresseStrain Relationship and Pore Water Pres~
sure Characteristics of a Normally Consolidated Clay,"
Proceedings of the Fifth International Conference on
Soil Mechanics and Foundation Engineering, vol 1,
1961, pp. 219 224.

 

 

 

 

 

 

Low, P. F. "fiscosity of Wa er in Clay Sys stems," Proceedings
of the Eightn National OConference on Clays and Clay_
Minerals, 1960, pp. 182

Martin, R. T. ”Water Vapor Sorption on Kaolinite: EntrOpy

of Adsorption," Proceedings_g§ the Eighth National
Conference 9n Clays and Clay Minerals, 1960, pp, gag-
114.

 

 

 

 

Michaels, A. S. "Discussion: Physico-Chemical Properties
of Soils: Soil Water Systems,” Proceedings of Aflggi-

can Society of Civil Engineers Soil Mecrafils ard

Foundations Division, vol ’85, SM 2, April, 1959, pp.

91-102.

 

 

 

IWitchell, J. K. "The Fabric of Natural Clays and Its
Relation to Engineering PrOperties,” Proceedirzgs,
Highway Research Board, vol. 35, 1956, pp. 693—713.

 

 

Ddoum, J. and Rosenquist, I. T. The Mechanical Properties of_
Montmorillonitic and lllitic Clays Related to 3:3_

Electrolytes 9f_the Pore Water, Norwegian Geotechnical
Institute Publication, No. 37, Oslo, 1960.

 

 

 

 

 

 

Pdurayama, S. and Shibata, T. Qg_the Rheologicai Characters
.9: Clay, Diaster Prevention Research Institute, Bulletin
No. 26, Kyoto, Japan, October, 1958.

 

 

qurton, F. H. Elements of Ceramics, Addison-Wesley Press,
Inc., Cambridge, Massachusetts, 1952.

 

IRosenquist, I. T. "Physico-Chemical PrOperties of Soils:
Soil Water Systemsf'Proceedings 9£_American Society 9i

 

 

Civil Engineers, Soil Mechanics and Foundations
Division, April, 1959, pp. 31—53.

 

Schmertmann, J. H., and Osterberg, J. 0. "An Experimental
Study of the Development of Cohesion and Friction with
Axial Strain in Saturated Cohesive Soils," Ameri-
can Societ of Civil Engineers Research Confer Ef’c or
Shear Strength of Cohesive Soils, 1960, pp. 6434694.

 

Scott, R. F. Principles 23 Soil Mechanics, Addison-Wesley.
PubliShing Company, Inc., Reading, Massachusetts, 1963.

 

 

Tan, T. K. (Discussion), Proceedings of the Ihird ILtere
national Conference on Soil Mechanics and Foqu daF ion
Ergineering, vol. 3, 1953, p. 129.

 

 

 

 

 

H

Tan, T. K. HStructure Mechanics of Clays,

ScientialSigiga,
vol. 8, no. 1, 1959, pp. 83-97.

 

Terzaghi, K., and Peck, R. B. Soil Mechan as in Ergireerirg

 

 

Practice, John Wiley and Sons, Inc., New York, 1948'.

Tobolsky, A. V. and Andrews, R. D. ”Systems Manifesting
Superposed Elastic and Viscous Behavior," Jourral of
Chemical Physics, vol. 13, no. 1, January, 1 9 5, pp

 

3—27
Tobolsky, A. V., Powell, R. E. , and Eyring, H. ”Elastic-
Viscous Properties of Matter," ”The (hemistry L£_Iarge

 

Molecules, 1943, pp. 125— 190.

 

Whitman, R. V. ”Some Considerations and Data Regarding the
Shear Strength of Clays,’ American Societv of Civ11
Engineers Research Conference on Shear Strength of
Conesive Soils, June, 1960, pp. _581 614

 

 

 

 

wu, T. H., Douglas, A. G., and Goughnour, R. D. "Friction
and Cohesion of Saturated Clays,” ProceedingS_g£ :hg

American Society of Civil Engineers, Soil Wecnaiicc
and Foundations Division, June, 19:2, pp. 1 32.

 

 

 

APPENDIX

U(10‘3 in)

an

 

 

 
  
  

 

 

 

 

 

 

 

I I I I I I I I I I 20 I I. | I l I I I I I
- — . (gg)w=49.23x1o*4m1n—1 _
.. _. E16 _. _
.. _ C\ _. _.
'F' 12 - 5 -
[x
I —- Ln .—
° 8
:1 8 — Q "
.D O
_ H _
4 _ 3% _
/——Uo=o.oooo6 in — —
I l l l l l I l I I I I l I L J I l I
o 0.5 1.0 1.5 2.0 2.5 01.5 1.9 2.3 2.7 3.1 3.5
Time (103 min) 11(10‘3 in)

 

l 10 l l l
Time(min)

Figure A.l. Creep Curves for C—C-l-l; D=O—O.5OOkg/cm2

U-X'

 

..__uo=0.0004 in

 

 

 

 

 

 

Ufl =0.00382 in

 

I‘

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l I I I I I I I I I O I L I L I I I I I
0 0.5 1.0 1.5 2.0 2.5 1.5 2.0 2.5 3.0 3.5 4.0
Time (103 min) U(lO‘3 in)
1.0
//
Dial readi£gs to i 0.000c5 in /’
0.9 Acsu aty . aha yG. t : F‘ L $.013 //
0.8 //
0.7 ///
0.6
= .22 '
0.5 A
// .
0.4 ,
003 /
0.2 o //
//
0.1 =
4.0 O]. //P//
‘ . ,2“
O.
1 10 10 10~ 104
Time(min)

Figure A.2.

 

Creep Curves for C-C-l-2; D = O.500-O.755 kS/cm2

86

 

 

   
  
    

 

 

 

 

   

 

 

lo I I I I I I I I I r 20 l I I I I I I I I I
’ ‘ ' (d_U.) = -l.75xlO"LI ‘
8 - — 1:16 - dU ” min'l -
,\ H c
a - E - H -
H 9 L0
no 6 — .4 l2 — H —
| H
o ‘ fi- ‘ O '
H .
\5 I4 -- g 8 - ('3' _
_ -D _ g _
2 _ LI _ D _
UO=O.0002 in — _I
O I I I I I I I I I I O 1 I I I I I , I
0 ‘ 1 ’ 2 ' 3 4 5 2 4 6 8 10 12
Time(lO3min) U(lO"3in)
U'X-

 

l l

10 10
Time min)

Figure A.3. Creep Curves for C-C-l-3; D = O.765-O.999 kg/cm2

A"

,n,
L,’

 

Ufi‘

 

 

 

 

 

 

 

 
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I I I I I I I I F I 50 I I
’ ‘ ' = -3.0x10"LI min‘l‘
_ _ ,Kuo ._ 1
c
— _. oc-I .... ._
~E
‘ " .5 3O . is. ‘
_ _ b_ _ o _
I m
_ _ 2 _ S
s O s
— _ .B/ _. fl -—4
._. _. lo .. ~41
%
UO=O o OOLI’8 in F '- F —<
I I J L I I I I I O I I I
O 2 4 6 8 10 10 15 20
Time(103min) U(10‘31n)
1.0
Diai readings to i 0.000 S in /////
0 9 Ace racy of data points: U* = + 0.0C23
0.8
0.7 l
0.6 I/
0.5 6/
A 42.30 _o
0.4 )l
0.3 /
/
0.2 //.
O 0 l J. O i. o (1/
w’/
J 0 /’F/F
O I u
l 10 10 10 10 '
Time(min)

Figure A.4. Creep Curves for C-C-1-4; D = 0,999-1.240 kS/Cmg

U-X-

 

 

  

o=0.0004 in

I I I I I I I

   

 

I I

 

1 2 3 4
Time(103 min)

5

{1(10'7 in/min)

U7
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88

 

 

I I I I I

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I I I I I L41

7

(.Eqfl =_2.085x10‘4 “
d min'

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l

 

 

10 15 20 25
U(10-3 in)

30

 

10 1

Figure A.5.

TimeImin)

1

l

Creep Curves for 0—0—1-5; D=l.24O-1.49O kg/crr12

89

 

 

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0
FI
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0

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w._..

.l I I I I I
4 (gg) - 1.8981(10‘LImin‘:L

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(A)
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20 20 F II F
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10 10 - —
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O I I I I I I I I I I O I I I l I I
0 2 4 6 8 10 15 20 25 go 35 40
Time(lO3 min) U(10- in)

 

10 1 1 1 105
Time(min)

Figure A.6. Creep Curves for C—C-1—6; D = 1.490-l.708 k8/cm2

90

 

 

R)
U1

170 I I

   
 
   

 

    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I— I. I I I I I I I I
) = —1.712x10‘“m1n‘l
160 1; 20 4
H
E
150 E. 15 - .2 ~
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140 S 10 ~ 51 ~
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130 5 _ IR _
UO=OcOOll in ’- "‘
120 I I I I I I l I I O I I J I I I I I I L
2 4 5 8 10 12 146 148 150 152 154 156
Time(103min) u(10-3 in)
1.0
Dial readings t°.i 0.0105 in //
Accuracy I data points: U* 4 I 0 C003 ,/
0.9
/V
l
O
8 A///’
O 7 V/,
u* 0.6 ///
F A- ’0 /
0.5 ‘ '3
//
I
0.4 ///
0 3 ///
0 2 //’
//
O 1 4.: JqUU /
//' o .
O F" H// I I
1 10 102 10 10“
Time(min)

Figure A.7. Creep Curves for C-C-1-7; D = l.708-1.890 kg/cm2

 

 

   

 

 

 

 

 

 

 

1‘0 I I I I r I I I I I I I I I
0.8 'U, =0.00105 in. — — _
(estimated) _ _ _
0.6 - _ _ _
r"--‘Uo=0.0005 in — r -
0.4 — _ _ _
0.2 - — _ _
O l I L I I I I I I I I I I I I I I I I I_
0 50 100 150 200 250
Time(min)
1.0
0.9
0.8
007
U*
-0.6
005
0.4
0.3
0.2
0.1
O
0.1 l 10 1 1
Time(min)

Figure A.8. Creep Curves for C-C-l—9; D = l.523—l.112 kg/cm2

 

 

J:
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‘ ‘ 10 ‘ Uw=0.00236 in“
I I I I I I I I I I O L I I I I I I L L
0 1 2 3 4 5 1.8 2.0 2.2 2.4 2.6 2.8
Time(102min) U(1O‘3in)
1.0 /
Diai readings to“: 0.0 5 in /5
Accuracy of data paints U* = 1:0.212
0.9
0.8 ‘ //
/
0.7
‘/
0 6 0 ///
Aizq, 20/
0 5 ///
x
//
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///
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I//
O 2 /
z=0.001 //’m
0.1 ./’
//:I
0 -———4 . -9 2 .
0.1 1 10 10 103
Time(min)

Figure A.9. Creep Curves for 040-1—10; D = 1.112_0.700 kE/cm2

93

 

 

    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5 I I I I I T I I— I I 50 I I I I I I I I I I
F F F (2.9) =-24.1XlO-u min‘l F
LI '- _‘ ALIO F- dU 00 F
5
h— 1 . I- -4
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— (>30 — 5 1
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s 29
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_r-—-UO=0.0006 in _ _ 1
O I ILI L L L I I I I O I I I I
O 2 4 6 8 10 1.8 2.2 2.6 3.0 3.4 3.8
Time(102 min) U(10'3 in)
1.0
Dial. readings o i 0.0 CE; in V
0 Accuracy of data pCints: U* = + 0.165 //
.9 , — ///
0 8 /////
0. /
7 /
U* /
- 0.6 //
/
/
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WI
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/
0.2 ’ /
/
«I ///
O l 2:0.001 ,//’
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00.1 1 10' 103T 105
Time(min)

Figure A.10. Creep Curves for C-C-l-ll; D = 0,700-0.457 kg/cm2

94

 

 

 

 

 

 

 

 

 

I I I 50 I I I I I I I I I |
— ' -4 —l‘
,\ (EH) =-12.6x10 min
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0 5 10 15 20 25 3 4 5 6 7 3
Time(102min) U(10‘3in)

 

1 10 l l 10
Time(min)

Figure A.11. Creep Curves for C—C-l—l2; D=0.457—0.2l9 kg/cm2

 

 

  
   
 

 

 

 

 

 

 

 

lo I I I I I I I T I I 25 I I. I I I I I I 7
’ I ’fl‘ ” (EHIw=-3.60x10’” min'l
_ c 20 _
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UO=O.OOO611’1 _I ’-
O I l I I I I I I I I O I I I I I 7
0 2 4 6 8 10 4 5 6 7 8 9
Time (103min) U(10'31n)

 

 

 

 

‘S\

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

r!—

 

 

 

 

 

1 10 * 10 103
Time(min)

Figure A.12. Creep Curves for C-C-l-l3; D=0.219-0 kg/cm2

U(10‘3in)

 

 

   
    

 

 

 

 

 

 

I I I I I I I I | I 25 I I I I I I I I I
_ _ A 20 ,_ _
L 1 a L 1
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g 15 (dU)w 20.5x10 min
1 W‘ L 1
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r—I
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I l I I I l I I I I O I I I I I I I I I
0 4 8 12 16 20 2.4 2.6 2.8 %.0 3.2 3.4
Time(102min) U(lO' in)

0.7
. 0.6

0.5

O

   

10 1 1
Time(min)

1

Figure A'13', Creep Curves for C-C-l-l5; D=O.3l6-0.727 kg/cm2

U(10’3in)

U-X-

 

-S__.U0=0.0009 in

 

 

 

 

0.4

0.3

10

 

Figure A.14.

11(10—7 in/min)

1
Time(

 

25

20 —

15

10

)

97

 

 

I I I I I I I I I

(_(<§I._I%.I)w=—16.68x10‘LI min'l

0.00358in

U“:

 

~—
I—
I

 

 

1 1

Creep Curves for C—C-l-16; D=O.727-l.l42 kg/cm2

 

 

 

98

 

 

 

 

(

    

I

@
dU

)

00

=-6.97x10‘4 min‘l

 

 

lo I I I I I I I I 20
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O I I I l I I l I I O
0 0.5 1.0 1.5 2.0 2.5 4.0
Time(lO3 min)
U-X-

10

Figure A.15.

l
Time(min)

I
4.5

 

C _
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0
o _
5 _
II
p‘ ‘
l I I I l I I I
5.0 5.5 6.0 6.5
U(lO'3 in)

10

Creep Curves for 0—0—1—17; 0:1.142-1.552 kg/cm9

 

 

 

O . 0013 in

C2
8
II

Uo _ 0.0009 in

I I I I I I

 

 

I I I I l I I I I I I I I

 

 

 

U-K-

2 u 6

8 10

Time(io2 min)

Figure A.16.

 

10
Time(min)

Creep Curves for C-C-1—19; D=l.40-O.726 kg/cm2

U(10‘3 in)

100

 

 

 

 

I I I I I I I I I I I I

(gglc=-28.6x10’umin’l -
dU

   
    
   

0.002835 in
1

Q0:
l

 

 

 

 

 

Time (102 min) U(

Figure A.17.

I—
ID 0
.

_.

_

I.—

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__

10

 

lO 1
Time(min)

Creep Curves for C-C-l-EO; D=O.726—0.3l5 kg/Cm2

101

 

 

     

 

 

 

 

 

 

 

10 T I I I I I I I I l 10 I l I I I I I I I I
_ _ F dfi -4 —l
A _ __)=—l.315xlO min _
S _ _
H 6 - E. -
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II
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‘— Uo=O-0008 in - — —
O I I I l I I I l I I O I I l l I I
o 2 4 6 8 10 1+ 5 6 7 8 9
Time (103 min) U(lO’3 in)
1.0
0.9
0.8
0.7
0.6
U56
0.5
0.4
0.3
0.2
0.1
o
10 10 1 10 105
Time(min)

Figure A.18. Creep Curves for C-C—l-El; D=O.315-O kg/cm2

U(10'3 in)

102

 

 

    
  
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I I I I T I I I I I 50 I I I I I I I I T I
- - - (g%)w=-6,67x10‘u *
- — ,1‘40 ~ min'1 a
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I I I I I I I I I I O I I I I I I I I I I
O l 2 3 4 5 35 36 37 38 39 40
Time (103 min) U(10'3 in)
1.0 o '
DIal readings t0.i 0.0 15 in . '
O 9 Accuracy of data points: U* = :_0.012/4’ '
O 8 /;///
0.7 /;///
0.6 I /,/
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- _ /
O D /r
0.4 /////
0 3 /
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0 2 53 ///
Cl? /
0 1 N ,7
O 2 u
1 10 10 103 10
Time(min)

Figure A.19. Creep Curves for C—C-7-l; D = O-O.987 kg/cm2

103

 

 

   
   
  
 

  

 

   

 

 

 

 

 

25 I I I I I I I I I I 50 I I I I I I I I I I
(dU) =_2 guxio‘umin‘l
2O ' —. A 110 _. W 0° . .
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O I I I I I I I I I I O I I I I I I I I
0 1 5 6 8 10 12 14 16

2 3 4
Time(lO min)

 

10

1
Time(min)

Figure A.20. Creep Curves for F-C—l-3; 0:0.7u9—0.994 kg/cm2

in)

U(10‘3

 

104

 

 

I I | 2 5 I I I I I I I I I I

($71)”o =—8.92x10‘“min’l

I
11(10—7 in/min)
51

   

-——U0=O.OOO75 in —
U, =0.002841n‘

 

 

 

 

 

 

o I I I I I | I I I I O I I I I I I I I
4 8 12 16 20 1.5 1.9 2.3 2.7 3.1
Time (102min) U(10-3 in)

l
3.5

 

10 l
Time(min)

Figure A.2l. Creep Curves for F-C-2-2; D=O.250-O.500 Kg/Cm2

105

 

 

I I I I

I

I. I I I
dU __ —4 _1 _
(afi)°° — 9.37xlO min

 
  
     

0 . 00988 in

00
I

 

 

 

"—U
I

r-—U9=O .0010 in - -
O I l I I I I L I I I o I I I I I I I

0 5 10 15 20 25 7.5 8.0 8.5 9.0 9.5 10.0
Time(lO2 min) U(10‘3 in)

 

I

 

 

 

 

   

1 l

10 1
Time(min)

Figure A.22. Creep Curves for F-C-2-3; D=O.500-O.747 kg/cm2

 

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2‘5 I I I I I I I I I T 50 I I I I I I I I I
I ‘ /\ ” 00 _ - -1 ‘
2.0 _ : _ .E 40 _ (EU) —-124.8X10 min 1
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53 F g I-
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0.5 ~ ~ 10 - Uw=0.001985in“
p _ _ _
I I I I I I I I I I O I I I I I I I I
0 0.5 1.0 1.5 2.0 2.5 1.7 1.8 1 9 2.0 2 1 2.2
Time(102min) U(10-3 in)
1.0
D1al re Ings to :_ 0 >05 in
Accurac 0f data points 0* = i 0.0252 /;/”
0.9 //
/
0.8 /
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U*
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0.5 /
0.4 0 0
0.3 /
0.2 .
/
0 1 Z=N005//
/
a /h/
0 g 3
0.1 1 10 ‘10 10
Time(min)

Figure A.23.

Creep Curves for F-C-2-7; D

0—0.250 Kg/cm2

106

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2'5 I I I I T I I I I I 50 I I I I I I I I I I
' ‘ ,\ ” d0 _ ‘4 -1 *
2.0 ‘_ - _ .2 40 _ (HUlo-'12u'8XlO min
13 _ _ \\ _ _
«—I :1
1 R _ _ H 30 .. _
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O I I I I I I I I I I O I I I I L I. I I
0 0.5 1.0 1.5 2.0 2.5 1.7 1.8 1.9 2.0 2.1 2.2
Time(102min) U(10-3 in)
1.0
Diai ealings to :_c.00>35 in //”
ACCuracy of data points: U* = : 0.0252 /;/’
0.9 /
/
/
//
0.8 l//
0 7 /////
U-X-
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0.5
0.4 { ‘
0.3
./
//
0:1 2:0.001///
. f
j/
E
O _
0.1 1 10 102 103
Time(min)

Figure A.23. Creep Curves for F-C—2-7; D = 0-0.250 Kg/Cm2

107

 

 

 

 

 

 

 

 

 

 

5 I I I I I I I I If 25 I I I I | I I I I I
‘ £32 _ -4 -1
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5 15 - E- —
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I
1 - _ 5 _ :3 _
O I J I I I I I I l I O I l I I I I I I. II
0 2 4 6 8 10 3.0 3.1 3.2 3.3 3.4 3.5
Time(102 min) U(10'3 in)
1.0
0.9
0.8
0.7
U-X-
-0.6
0.5
0.4
0.3
0.2
0.1
0
0.1 1 10 1 103
Time(min)
Figure A.24. Creep Curves for F-C-2-8; D = O.250—0.L199kg/Cm2

 

108

 

 

 

 

..__UO=0.0012 in

 

 

 

 

 

 

2

Time (10 min

 

Figure A.25.

I I ‘I 50 I I I I I I I I I
I ” (ggl‘=e18.84x10'”min'1 ‘
r I; 40 — ~
n—I
_ E _ C: _
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I I O I I I I I I l I I
8 10 3.0 3.5 4.0 4.5 5.0 5.5
) 0(10-3 in)

10 1
Time(min)

Creep Curves for F—C—2-9; D =

 

0.498-O.7u6 KE/cm2

109

 

 

    
 
 

    

 

 

 

 

 

 

I I I I I I I I I I 25 I I I I I I I I I
‘ 7 ' )w=—16 . 5xlO'L‘Lmin'l
- e 1:20 P U _
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Uo=0.0020 in 5 — Ufl=0.0055u in
- ~ — —I
I I l I I l I I I I O I I I I I I I
0 2 4 62 8 10 u 0 4.5 5 0 5 5 6.0 6 5
Time(10 min) U(10'3 in)
1.0
0.9
0.8
0.7
0.6
U-X-

   

   

0

  

1 10 1

1
Time(min)
Figure A.26. Creep Curves for F—C-2—12; D=0.249-0 kg/cm2

[1*

110

 

 

  

 

     

 

 

 

 

 

 

 

I I I I I I I I I I 50 I I I I I I I I I I
_ A 5 d0 -4 —1 _
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I I I I I I I I I l O I I I I I I I I l I
0 2 LI 6 8 10 2.2 2.4 2.6 2.8 3.0 3.2
Time(102 min) U(10' in)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
O 1 10 1 1 1

. Time(min)
Figure A.27. Creep Curves for F-C—2—14; D=O.249-0.498 kg/cm2

U(10‘3 in)

111

 

 

 

 

      
    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I I I I I T I I I I I I I I I I I T T I
‘ " 13 “ (99) =-51.5x10-4min-I
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\\
I— ... C I. _I
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8
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_ _ _ :55 1
I I I I I I I I I I O L I I l I I I I I
0 1 2 3 4 5 2.2 2.4 2.6 2.8 3.0 3.2
Time(lO2 min) U(10-3 in)
1.0 ,3
Dial re dings to‘: 0.00005 In 2’
Accuracy bf data p0intrz U* =.: 0.0159 ///
0.9 T J
. /’
0.8
0.7 I/
//
/ O
0.6
Uy" A4:5 . 3)/ I
0.5 /
0.4 /////
0.3 ///
//
/
0.2 /,
V/
0-1 2:10 . 001d//
,//”"I’/W ,
00.1 l 10 102 103
Time(min)

Figure A.28.

Creep Curves for F-C-2-l5; D=0.498-0.7M6 Kg/cm2

u(10-3 in)

112

 

 

      
  

 

 

 

 

 

 

 

I I I I I I I I I 50 I I I I I I I I I
_ A di)’ -14 _l_.
C‘. __ =—
_ _ E 40 _ (dUZw 8.90x10 min _
\
_ _ C: _ _I
H
- _ fi— 30 _ —
O —. _
I—I
.EJ20 — —
10 - 05:0.0265in—
UO=0.00225 in ' I
I I I I I I I I I O I I I I I J I I
0 0.5 1.0 1.5 2.0 2.5 20 22 24 26 28 30
Time(103 min) U(10‘3 in)

 

1 10 102 1 10)4
Time(min)

Figure A.29. Creep Curves for F—C-2-l6; D=0.7lI6—0.990kg/cm2

 

1 7~—— UO=0.0009 in

I—

 

I I I I

 

I

0(10'7in/min)

 

 

I I
0 2 4 6 8
Time(102 min)

10

Figure A.30.

10

ID
U1

I—‘ I0
U1 0
I

'_l
O
I

113

 

 

I I

(91

dU

I I I I I

I I I

)m=—15.0x10-4min-l

  
 

0.00447 in

Q”:

E‘—

 

1
Time(min)

O I I I I I I I
3.6 3.8 4.0 4.2 4.

u(10‘3 in)

 

10

Creep Curves for F-C-2-l9; D=0.492-O.247kg/Cm2

 

 

U*

 

_?--Uo=0.0012 in _

{1(10'7 in/min)

 

I I I l l I I I

 

 

I
0 0.5

I
1.0 1.5 2.0 2.5

Time(lO3 min)

10

Figure A.3l.

25

20

15

10

1
Time(min)

Creep Curves for F-C—2—20; D=0.247-0 kg/Cm2

114

 

  
 

.I I I I I h I I I
dU __ — -1 _
(5040— 2.63x10 min

0.01335 in

 

 

I

 

10 12
u(10‘3 in)

 

1.15

 

 

   

 

 

 

 

 

 

 

| I I 100 h I. I I I I I I I I
- (EH) =-20.3x10’4min‘1.-
’3 80 U ”

_ fa: _ _

_ :3 _ _

_ H 60» _

_ fi- _ _

O

_ $40- _

_ -D _ _

- 20— ufi=0.0503 in _

’/»——-Uo=0.0018 in - — —

O I I I | I I I I J I O L I I I I I l I
0 0.5 1.0 1.5 2.0 2.5 20 30 40 50 60 70
Time(103 min) C(10-3 in)

1.0
0.9
0.8
0.7
U*0.6
0.5
0.4
0.3
0.2
0.1
0

1 10 1

 

1
Time min)
Figure A.32. Creep Curves for F-C—2-33: D=0.952—l.l52 kg/cm2

116

 

 

     

 

 

 

 

 

 

 

2!: k
I I I I J I I I I I I I j T
‘ A (LU) =-30.0x10‘4 '
— c: 20— CW °° min‘l -
q—I
_ E _ ..
e\
1 H 15" -
.. [I- ,— _
2 - - 3 10- -
.. _ ID _ ..
.—.———Uo=0.0013 in
l - 1 5r- {3%
O I I I I 4! L; J I I
0 0510152025 ‘40 42 44464.8 5.0
Time(103 min) u(1o 3 in)

 

0 1 l

Time(min)
Figure A.33. Creep Curves for F—C-8—l; D=O-0.499 kg/cm2

117

 

 

 
 

 

25 'I I I TT I fit I I 25 1'7. I I I I I IWI I
1; 7 J ,\ 7 (.a.I.J..)w=-2.98x10'J‘tmin’l -
~* 20 r I 5
“3 _ e
'0 I e
:15 . j H
=3 L 4 fi-

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10 :1

ab
5. .
Uo=0.0009

   

 

 

 

I I I I L I I I I

0 1 2 3 4 5
Time(lO3 min)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 O
Dial IeaIings to‘: I. 305 in
O Azcurflcy of data poimq I U 4 :_0.040
.9 , . Vfl//
0.8 ./ /
‘ /
Di turbance?
0 7 - l
U* /
-0.6
/
I
0.5 /
A=5.30/
0.4 //
0.3 7
0 2 -/
,z’r/
0 1 2:0 :01 ' /
' 0 /If
> 0 II #:+//
0 I___-ih—=='"""'wfl ' . 4
l 10 10 103 10
Time(min)

Figure A.34. Creep Curves for F-C-8-2; D=0.499—0.755 kg/cm2

118

 

 

 

 

   
  
 

 

 

 

 

 

 

I I I I I I I I I 50 I I I I I I I | I |
g 40.. (99) =—9.15x10'4min'l
E dU°°
c ” g "
.,—{ 30‘ H
I.\ Ln
I O i
o_ o
:1 20 <5 —
-:>
_ II ..
%
-—- UO=0.0010 in - 10— s —
I I I I I I I I I O I I I | I l I
0 2 4 6 8 10 2.5 3.0 3.5 4.0 4.5 5.0
Time(102 min) U(10-3 in)
1.0
039
0.8
0.7
0.6
U*
.0.5
0.4
0.3
0.2
0.1
0
1 10 1 1 10
Time(min)

Figure A.35. Creep Curves for F-C—8—7; D=0.517—0.770 kE/cm2

119

 

 

I I I I I I I I I I E 50 I I I I I I I I I I
- _. E L... . )4 _
dU _ — —1
_ _ pg 40 _ (5349 ——5.0X10 min 5
I— _I [T I. _I
_ _ g 30 _
p .p _

   
  

Disturbance?“

  

 

 

 

 

 

 

._ 2O __
'3 10 Ugo =000109 11’1"
UO=0.0009 in 7 7 I 7
I I I I I I I I I I O I I I I I J I
0 l 2 3 4 5 7 8 9 10 11 12
Time(103 min) U(10-3 in)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.0 .
Dia. read.ngs to.: 0.33 5 in ///’
Accuracy of data points: U* =.: 0.0459
0.9
/
0 8 l///
0.7 /
/
l/
0.6. /.
A734 6 60/
0 5 //°
0.2. //
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o // J
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0 1 "<///
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d Z==0 .4301 //
I wgd"
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O 1 10 103 10f 104
Time(min) ‘

Figure A.36. Creep Curves for F—C-8—8; D=0.770-1.025 kg/cm2

120

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

250 I I I T I I I I I I 100 I I I I I I I I I I
I ‘ ' (EH) =-1.86X10'um1n'1'I
_ ,~\80 _ d w a
:3
"—1 .1
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— c 60 _ _
or-I
—4 Fl- —- —
— o 40 — —
t—I
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‘ 20 ” Ufi=oo1142 in“
.h__ U020.0190 in a _ I “
O I I J I I I L I I I O I I I I I I I I I I
o 2 u 6 8 1o 80 90 100 110 120 130
Time(103 min) U(lO‘3 in)
1.0 I
Dial ReadIngs to‘: O O b in
7 Accuracy of data points: U* = i 0.00ufl ‘
0.9 .
//
//
d
O 8 V////.
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/
/
0.3
0.2 ¢{/
MK
4/
0-1 v 2:0.001
L”” J
O 3 u,
l 10 10 10 10
Time(min)

Figure A.37. Creep Curves for F-C-9-l; D=O—l.lO3 Kg/cm2

 

121

 

 

  
 

 

 

 

 

 

 

 

2.5 I I I I I I I r I 2.5 I I I I II I I I I
- a 1; - ,
i H ‘ 9H =-h. 8x10’4min‘l
— ‘5 2.0‘— (d La 3
_ 5 _ 5 -
- h— 1.5 — m\ —
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a o _ p. _
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- -::> 1.0’- 8 -
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=.— Uo=0.0002 in - v I ~
0 I I I l l l L J I O I I I I I ‘I J I
O 2 4 6. 8 10 1.3 l.h 1.5 1.6 1.7 1.8
Time(103 min) U(10‘3 in)

U*

103 104

1
Time(min)
Figure A.38. Creep Curves for D-C-9-2; D=O.27-O.47 kg/cm2

I
l

122

 

 

    

 

 

 

  
    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10 I I I I I r I T I I 5 I I . I I I I I I I I
" - A '- dU "LI' -1 --1
=-O.863x10 min
8 _ _ 5 4 _ (atria q
Temperature rise: 25°C S 1. 1
H
W’ 3 _
-« O I— .q
H
— g; 2 _ fl
.. I. _
. _ 1 _ _
«— UO=O.0015 in U.° =0.0063 in
.— —I I" -I
O I I I I I I I I I JL 0 l I I I I I I I I I
0 5 10 15 20 25 3;0, 4.0 5.0 6.0 7.0 8.0
Time (103 min) U(1O'3 in)
1.0
DILaIL e clings to i c 00> 5 in /
Accuracy of data points: U* #.i .C '5
0.9‘ '
T2
0.8
I!
0.7 I
0* /
-O.6 //
A=3.22
0.5 /
0.4 Temperature clrop
V I
I
0.3 T1 ( I
w; /
I/
0.2 /
Z=C 001 (1‘2) - /
/
0.1 0
I. ‘ A21
w’/y‘
i=""‘ :_
O 10 10a 105 104 103

Time(min)

Figure A.39. Creep Curves for D—C-9-3; D=O.u7-O.67 kg/cm2

u(10’3 in)

12

10

 

 

    

 

 

123

 

    
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure A.40.

I I I T I I I I I I 2'5 I I I I I I I I l
_ '4 ’fl\ ' ) =0.750x10-4m1n-1
_ Temperature rise" _ g 2.0 _ ‘” _
1°C 'g A
_ _ \\ -
C1
_ , .. -.—I 1 5 _. —
_ o _ I‘l— __ _
O
— 511.0 ~— ~
_ 'D _. 1
Temperature rise 1 0.5 _ Ufl=0.01u3in _
395°C 2
Uo=0.0025 in I I I
I I I I I I I I I I O I I I I I I I I
0 5 10 15 20 25 11 12 13 14 15 16
Time (103 min) u(10'3 in)
1.0 _
Dial readings to i.C°OODO> in
Accuracy 0f data points: U* = i 0 00350
009
T3
0.8
0.7 '
0.6 2//
A
0.5
21/“
0.4 .
'a11 durves) A=%.22 //
0 3 Erratic temperature variatio s I
° throughout the 136 st. V
‘/
0.2 i/
d
0.1 Z=OOC01 . .
I 0 '1 0 I
0 » 13IT ‘ [T1
10 I 102 105 10 10
Time(min)

Creep Curves for D-Clg-S; D20.87-1.07 kg/cm2

 

 

124

 

 

  

 

 

 

 

 

 

 

250 I I I I I I I I I I 50 I I I I I I I | I I
1 - — d0 __ ,—4 ,m1‘
40 _ (afiJw— 0.672x10 min ‘
13 _ _
.,_I
\E 30 — —
C
-.-—I _ _
IT 20 — —
O
H __ ..
-:
10 - U9=0.14801n‘
,—_Uo=0.0032 in ~ -
O I l I I I I I I J I O I I I I I I II I | I
0 5 10 15 20 25 80 100 120 140 160 180
Time(103 min) u(10-3 in)

 

Time(min)

Figure A.41. Creep Curves for DP—C—l; D=0-0.0838 kg/cm2

125

 

 

  

 

 

 

 

 

 

 

 

l°5 I I I I I I I I I I E60 I I I I I I I I ‘I I
— E at — —
D = kg 2 ___ = 3 1
1.4 o 1.490 /cm _ g-Ao (leo 3.84x10 min
In} (\I
x ' E I
III—3o — I} -
I M
O _. Lfl _
H be
.Q-2O — 2 ~
_ A _
I!
.10 _ Q3 _
1.0 I I I I I I I I J I O . I I I . I I
O 2 4 6 8 10 1.19 1°17 1.15 1.13 1.11 109
Time (102 min) D(kg/cm2)

 

0.1 1 10 1
Time(min)

Figure A.A2. .Stress Relaxation Curves for F-R-S—l;
D = 1.490-1.1075 kE/cm2

 

 

.—

I I

I I I I
00:1.477kE/cm2

I

 

 

 

2 4 6 8
Time(102 min)

 

10
Time(min)

O 1
1.30 1.25 1.20 1.15 1.10 1.05
D(kg/cm2)

126

 

 

 

I I I I I I I I I I
- IggIo= 2.85x10'3min‘l ~
_. (\J _.
E
O
_ \ —
bl)
_. X _
L(\
_ N7 _
I—I
,_ r; -—
_ T 1
I I I l I I

 

Figure A.43. Stress Relaxation Curves for F—R—6-l;

D=1.A77—1.135 k2/cm

127

\.

I
H
O

 

 

M I I I 1{BI I 2I I I . | I I I I I I I I I

I

13(10‘5 kg/cm2min)
5.
I

   

KTemperature rise _ _
. / _2_

_ 05:0.522kak

 

 

 

 

 

o
I '- I

 

I . I
O 1 2 3 4 5 0.60 0.58 0.56 0.54 0.52 0.50

III .- o I

 

 

Time(103 min) DIKE/Cm2)

 

O 0.1 1 10 1 1
Time(min)

Figure A.44. .Stress Relaxation Curves for F—R-8-l;
D=l.070—0.522 ka/cm2

D96

 

 

128

 

 

 

 

1.0

0.9

0.3

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I I I I I I I I I "‘50 I I I I I I I I I I
I I; '— db _ ~3 -1 I
or; -LI'O __ (ED-)w-2.LIBXIO min (\I ...
m _ g _
5 a
Q? -30 “ .x ‘
i ‘51 1
.Q d3
-20 ? "
CI—
-lO — \_
0 . L - I 11 J I . .
1.00 0.98 0.96 0.94 0.92 0.90
Time(102 min) D(kg/cm2)
Load ell readings t0:H 0.0020 ° //
Accuracy of data points D* = : 0.00326”~
- ///
A
Z
/
//
//
3:7.60/
/
//
/
r/
//
,4
//
{/
/////
W29. 01.
1 10 102 103 10LI
Time(min)

Figure A.45. .Stress Relaxation Curves for F-R-8-2;

D=1.

548-0.893 kEll/cm2

ROOM USE 0%!“

r a .
'. 5 1.- 3'};
wt ilk: 7"" d I‘

l ‘g’

hL‘I‘

 

 

 

 

 

 

 

 

   

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