STRESS TRANSFER DUE TO CREEP
EN A SAW-RATED CLAY

The“: for ’rE-te Dogma GE M. S
MICEEE SAN STALLS LNZ LEE? Sui"
3'- iahk J. L‘Emfiday
E963

masts

LIBRARY

Michigan State
University

 

ABSTRACT

STRESS TRANSFER DUE TO CREEP
IN A SATURATED CLAY

by Frank J. Holliday

An experimental study was made to determine the behavior of
friction and cohesion in a clay soil during creep. Creep-CPS tests
were used to determine cohesion and friction at the end of different
periods of elapsed creep time. The results were compared with the
stress transfer curves calculated from Creep tests.

The increase in friction and decrease in cohesion with creep
time measured with the Creep-CPS test were similar to the increase
in frictional resistance and decrease in cohesive resistance computed
from the Creep test° The behavior of the frictional and cohesive
components can be represented by the elastic and viscous elements of

the Kelvin rheological model.

'STRESS TRANSFER DUE TO CREEP IN A
SATURATED CLAY

by I.)
y E’

Frank,J.KHolliday

A THESIS

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

MASTER OF SCIENCE

Department of Civil Engineering

1963

ii

ACKNOHLEDGEMERTS

The writer is indebted to Dr. T. H. wu, Department 6f Civil
Engineering, for his guidance, assistance, and encouragement through-
out the writer's Master's Degree program. Thanks are expressed to A
Dr. 0. B. Andersland for time spent with the writer during Dr. Hu's
absence and to‘the writer's colleagues, A. K. Lab and R. w. Christensen,
for assistance in and out of the laboratory.

The writer wishes to express his appreciation to the National
Science Foundation for the Graduate Research Assistantship which made

graduate work at Michigan State University possible.

I.

II.

III.

IV.

VI.
VII.

TABLE Q§_CONTENTS

INTRODUCTION . . . ..........

APPLICATION OF RHEOLOGY

2.1

2.2 Maxwell and Kelvin Models . . .

Elastic and Viscous Elements . . .

2.3 Application of Kelvin Model to Saturated Clay . . .

EXPERIMENTALPROGRAM. . . . . . . ..

3.1
3.2
3.3
3.4

3.5

RESULTS
CONCLUSIONS . . .

5.1

5.2

BIBLIOGRAPHY . . . .' .

Determination of To

Determination of ‘1’.)

Soil Used . . . . . . . . . . . .
Sample Preparation . . . . . . .

Triaxial Tests . . . . . . . . .

Validity of Kelvin Model . . . .
Suggestions for Future Study . .

mm“ 0 O O O O O O O O O O O O O O

7.1
7.2
7.3
7.4

7.5

O O O O O

Derivation of Data Table for CPS Test

Typical Data for Tests Run . . . . . . . . .

and «2, from Creep Test . .

and‘fie from Creep-CPS Test

Calculations for G1» and c' for Conpacted Clay

Calculations for G1; and c' for Consolidated Clay.

Sample Calculations for c' from Creep-CPS Test

iii

Page

10
10
10
13
20
20
32
37
37
37
38
40
40
40
69
70

71

Table
1.

2.

10.

12.
13.
14.
15.
16.
17.
.18.
19.
20.
21.
22..

23.

LIST 9}; news

Properties of Sault Ste. Marie Clay .
"8" Parameter Test Data . . . . . . .
Summary of c' and «’4; Values . . - .
Summary of Triaxial Tests . . . . . .
Triaxial Test Results at End of Tests

General Data Sheet (Test C-CPS-l) . .

Consolidation Data Sheet (Test C-CPS-l)

cps Data Sheet (Test moss-.1) . . . .
CPS Data Summary (Test CHCPSél) . . .

General Data Sheet (Test F-CPS-l) . .

Consolidation Data Sheet (Test P-CPS-l)

CPS Data Sheet (Test F-GPS-l) . . . .
CPS Data Summary (Test P-CPS-l) . . .

0

General Data Sheet (Test 6-0-7 3. C-C-CPS-7) . . .

Consolidation Data Sheet (Test C-C-7 a Caz-crest)

Creep Data Sheet (Test C-C-7) . . . . . . . . . .

CPS Data Sheet (rest O’C.CPS.7) Q 0 O O 0 O O O 0

:CPs Data Su-ary (Test C-C-CPS-7) . . . . . .. . .

General Data Sheet (Test 'P-C-1 s P-C-CPS-l) . . .

ConsbliEdation Data Sheet. (Test sac-1 r P-C-CPS-l)

Creep Data Sheet (Test F-C-l) . . . . . . . . . .

crs Data Sheet (Test P-C-CPS-l) . . . . . . . . .

CPS Datasumxy (T281: P'C'CPS'1)'0 s s o o o o 0.

iv

Page
10
14
22
23
25
42

43

47
49
50

E51

53
55
56
57
53
so
62
63
64
66

67

LIST 9g FIGURES

Figure Page
1. Spring or Elastic Element . . . . . . . . . . . . . . 4
2. Dashpot or Viscous Element . . . . . . . . . . . . . 5
3. Shear Strain Versus Time Curve for Maxwell Model . . 6’
4. Kelvin Model . . . . . . . . . . . . . . . . . . . . 7
5. Shear Strain Versus Time Curve for Kelvin Model . . . 8
6. Stress Transfer Curves for Kelvin Model . . . . . . . 8
7. Compaction Apparatus . . . . . . . . . . . . . . . . 11

8. Division of Compacted Cake . . . . . . . . . . . . . 12
9. Creep Test . . . . . . . . . . . . . . . . . . . . . 15
10. Schematic Drawing of CPS Test . . . . . . . . . . . . 16
11. CPS Test . . . . . . . . . . . . . . . . . . . . . . '18
12. Creep-CPS Test . . . . . . . . . . . . . . . . . . . 19
13. Mohr's Circle . . . . . . . . . . . . . . . . . . . . 21

14. Creep Curve for Compacted Clay (Test C-C-7) . . . . . -26

15. Creep Curve for Consolidated Clay (Test P-C-l) . . . 27
16. Extrapolation of’ ¢f for Compacted Clay'. . . . . . . 28
17. Extrapolation of 49’ for Consolidated Clay . . . . 30
18. Stress Transfer for Compacted Clay . . .-. . . . . . 35
19. Stress Transfer for Consolidated Clay . . . . . . . . 36
20. Mohr's Circle for CPS Test Data Table . . . . . . . . 40

21. Typical Stress-Strain Curve for Compacted Clay
Creep-CPS Test (C-C-CPS-6) . . . . . . . . . . . 41

vi

Figure Page
24. Stress-Strain Curve for Test C-C-CPS—7 . . . . . . . 61

25. Stress—Strain Curve for Test P-C-CPS-l . . . . . . . 68

vii
NOTATION

¢'= Axial stress

6 = Axial strain
E = Constant associated with spring
é = Strain rate

°<= Constant associated with dashpot
W'= Maximum shear stress

‘6 =-" Maximm shear strain

G = Constant associated with spring

3 = Constant associated with dashpot

Time

Shear stress in spring
Shear stress in dashpot

s Constant maximum shear stress

sheen
II

Shear stress associated with friction

«2.: Shear stress associated with cohesion

A
9
a

C3) = Principal stress difference

431
u

Friction

Cohesion

0
‘
II

’ Effective axial stress

9
|

([3: Effective radial stress

Shear strain at time of negligible,strain rate

Threshold value of shear stress

r< :9 4%
II

Shear stress due to creep load

; INTRODUCTION

Soil engineers have had the problem of creep during sustained
loading of clay soils for many years. Buisman (1936) noted that
results of long duration tests on peat and clay showed total deforma-
tion resulting from a combination of deformation due to "direct load
effect" and a "time dependent" deformation. Buisman observed
"Continuously decreasing deformation" in the consolidation process
and termed this phenomenon the "secular" effect. Geuze (1948) later
reported that Buisman's "secular law" was followed during the Con-
solidation process and at low values of shear stress by cohesive soils.

Casagrande and Wilson (1950) presented data from two types of
tests (creep strength tests and long time compression tests) showing
clearly the time effects on deformation and strength of clays. The
loss of strength with time observed in saturated clays could account
for slides on slopes which failed after standing for many years.
Geuze (1953) and Haefeli (1953) presented field observations of soil
failures after excessive creep. Terzaghi (1953) pointed out that
little was known about creep and stated that much research and study
was needed in this area.

The recognition of the creep problem led to application of the
theories of rheology in an attempt to describe mathematically the
creep in soils. Vialov and Skibitsy (1957) (1961), Geuze (1953),
Geuze and Tan (1954), Haefeli (l9~5'3)and Schiffman (1959) presented ‘-

papers on the rheological analysis of deformation. Murayama and

Shibata (1961) proposed a four element rheologic model to explain

the viscosity, elasticity and internal resistance of clays.

Rowe (1957) presented a hypothesis suggesting that "creep will
lead to a gradual increase in the pressure on structures which resist
movement, the ultimate pressure being that due to soil having only
friction." This suggests that as creep progresses the value of
cohesion should decrease to a small value or zero and values of
friction should increase. This hypothesis was substantiated by
Schmertmann and Hall (1961), Wu, Douglas, and Goughnour (1962) and
Bea (1963). They showed that cohesion and friction during creep
followed time dependent relationships that are visco-elastic in nature.

The soil parameters friction and cohesion are defined according
to Schmertmann and Osterberg (1960) as follows:

Priction - The angle of internal friction, at any strain, is the
angle whose tangent is the ratio of the change in shear
stress to the change in normal intergranular stress
occurring on the plane of Mohr envelope tangency at
that strain, during a stress change occurring without
significant change in soil structure.'

Cohesion - The cohesion of a soil, at any strain, is the shear
stress developed on the plane of Mohr envelope tan-
gency at that strain, if the intergranular stress on
that plane could be reduced to zero without signifi-
cant change in soil structure.

It is the objective of this research to study the behavior of
friction and cohesion of a clay soil during creep as elastic and
viscous resistance components of the material to deformation. One

of the simplest rheologic models of viscorelastic behavior is the

Kelvin model. Although the Kelvin model does not completely describe

the Complex nitfiie of creep, its simplicity is an advantage in
establishing a first approximation of the action of cohesion and

friction during deformation.

' LI; APPLICATION Q; RHEOLOGY

2.1 Elastic and Viscous Elements

The rheologic behavior of materials is represented by visco-
elastic models consisting of dashpots and springs in series or
parallel. The elastic solid is represented by the spring and the
viscous fluid is represented by the dashpot. Figure 1 shows the

schematic of a spring and Figure 2 shows the schematic of a dashpot.
q. ,

V
Figure l - Spring or Elastic Element

The equation for linear elastic behavior represented by the

spring in Figure 1 is

Where

a;
u

Axial stress,

m
I!

Axial strain,

I?!
ll

Constant associated with spring.

 

Figure 2 - Dashpot or Viscous Element

The equation for viscous fluid behavior represented by the

dashpot in Figure 2 is

Where
Q'= Axial stress,
é.= Axial strain rate,
a'(=-"Constant associated with dashpot.
Application of this concept of the rheologic model to soil
mechanics requires the assumptions of continuity and homogeneity.
Under the condition of no volume change all deformations are the
result of shear stresses. The deformations under a set of principal
stresses can be correlated with the shear stress.
By applying the above conditions the equations for the elastic
element and viscous element become reapectively:
(V: G}! . (2.1-1)
(Vega. (2.1—2)

Where
‘1’: Maxim shear stress,

'6 = Maximum shear strain,

G = Constant associated with spring (shear modulus),
3>= Constant associated with dashpot (viscosity),
t = time.

2.2 Maxwell and Kelvin.Models

Series arrangement of the spring and dashpot is called the
Maxwell model. The Maxwell model's characteristic shear strain
versus time curve is shown in Figure 3 where ‘r/G is equal to the
instantaneous shear strain in the elastic element under a constant

shear stress condition.

 

 

Shear

Strain
Maxwell
Creep

LA; Curve
Time

Figure 3 - Shear Strain Versus Time Curve for Maxwell Model

The parallel arrangement of a spring and a dashpot is called
the Kelvin (or Voigt) model. Figure 4 shows a schematic drawing of

the Kelvin model.

 

 

 

 

Figure 4 - Kelvin Model

Since the strain in each element of the Kelvin model is equal to
the total strain of the model and the sum of the shear stress in each
element is equal to the total shear stress on the model, the follow-

ing equations apply:
q2{=(375
we _
<r=¢.. + “3 430% (“‘1’
Where
(fig: Shear stress in spring:

“3

‘6: Shear strain of model.

Shear stress in dashpot,

Solution of equation (2.2-l) under the condition of constant shear

stress ‘l' gives:
.5 = "7c. 0 _ 346/3)“. (2.2-2)

Figure 5 shows a plot of equation (2.2-2) where‘ryc is equal to
the strain in the elastic element at time equal to infinity under a

constant shear stress condition.

 

 

 

Shear
Strain ___
7+
Kelvin '52”
Creep
7
Time

Figure 5 - Shear Strain Versus Time Curve for Kelvin Model

When the Kelvin body is subjected to a constant shear stress
there is a stress transfer from the dashpot to the spring. This
transfer can be shown by substitution of equation (2.2—2) into

equation (2.2-l). The transfer is as follows:

'1’ ‘12, +43 =K (I-é‘G’Qt)+ ref/9t

Where

K

Constant shearing stress.

The shape of the stress transfer curves are shown in Figure 6.

‘ ('3
- K

TB=-Kne4§é§t

 

 

 

 

 

Time Time

Figure 6 - Stress Transfer Curves for Kelvin Model

2.3 Application of‘Kelvin Model to Saturated Clay

Figure 3 and Figure 5 show the shape of creep curve described by
the Maxwell equation and the Kelvin equation. Curves presented by
Casagrande and Wilson (1950), Geuze and Tan (1954), and Wu, Douglas
and Goughnor (1962) have shapes similar to the curve in Figure 5.
This similarity indicates that the creep in a saturated clay is better
represented by a Kelvin model than a Maxwell model.

Wu, Douglas, and Goughnour (1962), and Bea (1963) respectively
proposed and substantiated the increase in friction and the decrease
in cohesion in a saturated clay soil as creep progressed. This
transfer behavior is similar to the transfer behavior of the Kelvin
model. Letting the spring represent friction and the dashpot repre-
sent the cohesion, expressions for the Stress transfer in a saturated

clay can be written as:

Gaza = G3 = K(l' emf.) (2.3-1)
fr}: Tc =3§§= K gen/9+. (2.3-2)
K = ‘1'}. + 'l’c, =6K+jfi (2°3‘3)

Where
'6

'T£’= Shear stress associated with cohesion,

Shear stress associated with friction,

K = Shear stress due to creep load.

Stress transfer curves have the same shape as those in Figure 6.

10

III EXPERIMENTAL PROGRAM

3.1 Soil Used

The glacial lake clay used in this investigation was from a site
approximately 15 miles south of Sault Ste. Marie, Michigan. This
clay was obtained at a depth of about 5 feet below the ground surface.
X-ray defraction tests (Dillon 1963) show the soil contains about 50
percent illite, 25 percent vermiculite, 15 percent chlorite, and 10
percent as a combination of montmorillonite, quartz, feldspar, and

kaolinite. See Table l for index properties.

Table l - Properties of Sault Ste. Marie Clay

Air Dry . Liquid Plastic
Water Content Limit Limit
2.64% 60.5% 23.6%‘

Shrinkage Plasticity Specific
Limit Index Gravity
19.x: 36.2% 2.79

Clay Silt Activity

Fraction Fraction

0.60 0.40 0.63

3.2 Sample Preparation

Compacted and consolidated samples were used in this investiga-
tion.

The soil prior to compaction was prepared by passing the clay
through a muller until it would pass a No. 10 (U. S. Standard) sieve.
The air dry water content was determined and distilled water added

to obtain a water content from 40 to 45 percent. The clay was

11

thoroughly mixed by hand as water was added, placed in an earthenware
crock and stored at about 70 degrees fahrenheit and 100 percent
humidity until the water content was uniform throughout.
a) Compacted clay

Two weeks later the clay was removed from the crock and placed
by hand in a circular mold with an inside diameter of 11.25 inches

0

and a depth of 6.5 inches.

OCT

 

 

Figure 7 - Compaction Apparatus

One inch diameter clay balls were placed in layers and pressed
together by hand to avoid large voids and achieve continuity of the
samples. Sufficient clay was placed in the mold to make a compacted
cake about 6 inches in height. After placement in the mold the clay

was subjected to a pressure of l kilogram per square centimeter for

12

about one hour in a hydraulic testing machine (Figure 7). Next the
two halves of the mold were separated, the cake removed, and cut into
21 pieces. Each piece was given 2 coats of wax, wrapped in aluminum
foil, given 3 coats of wax, and stored under water until used.
Sealing wax used was Gulf Oil Corporation's Petrowax A. Figure 8

shows the scheme used to cut cake.

{if}

 

 

 

/ \
//;, 5 10 15 19 11.25 inch diameter cake
6.0" high
Samples about 2" x 2" x 6"
2 6 11 16 20 Scale: 1.0" = 6.0"
\\3 7 12 17 2}/

 

 

 

 

 

V\V\\E\J 13 ,EE’J//’

Figure 8 -Division of Compacted Cake

 

b) Consolidated Clay

The consolidated cake was prepared in a consolidometer consist-
ing of 6 inch diameter lucite tubes mounted on a brass base. Porous
stones placed on top and bottom of the soil and side drains permitted
water drainage. Approximately 6 inches of clay paste at a water
content close to the liquid limit was placed in the apparatus and
allowed to settle. After settlement the clear liquid above the soil
was drawn off and another 6 inches of clay paste added. This
procedure was repeated until the soil cake was of desired height.
When adding the second 6 inches of clay paste and subsequent lifts,
extreme care was taken not to disturb the clay already in the

consolidometer.

13

After settlement was complete the clay was loaded and consolidated.
The first load increment was 0.003 kilogram per square centimeter and
the increment was doubled until the load totaled 0.36 kilogram per
square centimeter. Bach increment was left until at least 90 percent
consolidation was achieved. The consolidated cake was extruded from
the consolidometer, cut into 6 equal, wedge-shaped sections and waxed.
After waxing the samples were stored as described above for the

compacted samples.

3.3 Triaxial Tests

Triaxial shear tests were used to measure the cohesion and
friction. The samples were trimmed to finished dimensions of about
1.4 inches in diameter by 3 inches long. Three wool yarns were placed
longitudinally in the center of the sample and 3 paper towel drains
1/4 inch wide by 8 inches long were placed longitudinally around the
sample. These drains decreased consolidation time and speeded pore
pressure response.

The samples were hydrostatically consolidated under a pressure
of 2 kilograms per square centimeter for 24 hours. After consolida-
tion, drainage was stopped and a back pressure of 1.5 kilograms per
square centimeter applied to saturate the sample. The back pressure
was applied by raising the cell pressure and the pore pressure
simultaneously by 0.1 kilogram per square centimeter increments until
a pore pressure of 1.5 kilOgram per square centimeter was reached.

The back pressure was maintained for at least 12 hours.

14

The saturation of randomly selected samples was checked by
measurement of the "B" parameter. (Bishop and Henkel, 1962) The

results of a typical "B" parameter test are given in Table 2.

Table 2 - "B" Parameter Test Data

Sample: C-C-CFS-9'

Starting Cell Pressure: Qg= 3.5 Kg/cm?
Starting Pore Pressure: u = 1.5 Kg/cm2
B = change in fl~
change in 0'5
Elapsed 05 u Change in Change in "B"
Time 1 z
in Min. Kg/cm Kg/cm 05 u
0 3.75 1.5 0.25 0.00 -
1 3.75 1.75 0.25 0.25 1
2 3.75 1.75 0.25 0.25 1
5 3.75 1.75 0.25 0.25 1
10 3.75 1.75 0.25 0.25 1
0 4.0 1.75 0.50 0.25 -
1 4.0 2.00 0.50 0.50 1
2 4.0 2.00 0.50 0.50 1
5 4.0 2.00 0.50 0.50 1
10 4.0 2.00 0.50 0.50 1

The three types of tests run on the samples of compacted and
consolidated clay were Creep tests, CFS tests, and Creep-CPS tests.
a) Creep Test

The sample was prepared, placed in the triaxial cell, consoli-
dated and back pressured. It was then loaded by dead weights as
shown in Figure 9.

The change in area of the sample was small during deformation
so the original load on the sample did not need adjustment to keep

the stress essentially constant. The sample was allowed to deform

15

 

 

 

Figure 9 - Creep Test

with no drainage until the strain rate became negligible. Axial
strain and pore pressure readings were taken at time intervals begin-
ning with 15 seconds. The time interval was doubled until 12 hours
was reached, then a 12 hour increment was used. Axial strain
measurements were recorded to nearest 0.001 inch and pore pressure
measurements were read to nearest 0.05 kilogram per square centimeter.
b) CFS Test

The CFS test followed the procedure outlined by Schmertmann and
Osterberg (1960) with some minor changes due to differences in equip-
ment. The procedure used is outlined below.

After the sample was consolidated and back pressured, the piping

system for the triaxial cell was set up as shown in Figure 10.

16

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17

The test was run at a constant strain rate of about 0.3 percent
strain per hour. During the test the strain rate varied between 0.8
percent strain per hour and about 1.0 percent strain per hour.
Schmertmann (1962) reported that small changes in strain rate did
not affect friction and cohesion. Preliminary tests run by A. K. Loh
and the writer show that increases in strain rate from 0.5 percent
strain per hour to 1.0 percent strain per hour increase cohesion by
29 percent and decrease friction by 27 percent for the clay soil used.

During the test it was necessary to keep the difference in
principal stresses (fin - “3) matched by an equal change in pore
pressure. Matching of (V. - T3) by a change in pore pressure held
the effective axial stress ( 0‘, ) constant and continually changed the
effective radial stress (3’3). At specified intervals the weight on
the constant pressure cell in the pore pressure stage was increased
or decreased by a predetermined increment. An increment of 0.5
kilogram per square centimeter in the porewater pressure was used.
This produced an equal and opposite change in (0'. ) and (Q‘s ).1 Under
the new ('0', ) the deviator stress (0“ - W3) behaved differently and
the pore pressure was adjusted so that it was equal to the new
(0', - 03). When the matching operation and the weight changing
operation were superimposed a ( U" - 0‘3) versus social strain curve
was obtained for each level of ( i" ).

Using Mohr's circle and the theory of effective stress, the
friction ( (V ) and cohesion (c') at various axial strains were com-
puted. These computed values were then plotted to give friction and*

cohesion versus axial strain curves. Figure 11 shows CFS test set up.

18

a
‘o‘

né.
9
L...

 

139
r

. 'fi-‘I1
_; ,.' ““

 

Figure 11 - CFS Test

Measurements recorded during the test were ( V. - 03), axial
strain, and elapsed time. Early in the test these measurements were
recorded after each 0.001 inch of axial deformation and later at
increments of 0.1 percent axial strain. The proving ring was read
continuously during the test and (Q, - (1'3) calculated. Corrections
for change in area due to axial strain were made continuously. Bach
calculated value of (V. - 03) was matched by the pore pressure. The

equation used to calculate ( W. - 05) was

(0’ -<I )=gr_o_gi_nflingdial readin x Provin rin constant 1_Axia1 )
‘ 5 Area at end of consolidation ( Strain

(3.3—1)

 

19

c) Creep-CFS Test

The Creep-CFS test was a two-phase test performed on a single
sample. The first phase was a Creep test as described above: After
a certain time interval the CFS test was begun:

The pore pressure recorded at the end of the creep phase was
used as the initial pore pressure for the CFS test and the load from
the dead weight system was left in place. The difference in principal
stresses calculatederom the proving ring readings was added to the
creep load to obtain the total difference in principal stresses
(<n - 03). To simplify recording of data during the test, the differ-
ence in principal stresses calculated from proving ring readings was
matched by the total pore pressure less the initial value of pore

pressure at the beginning of the CFS phase. Figure 12 shows Creep-

CFS test.

.1 1‘}
\tp'. Q‘s-ET:

 

H Effi "4 ,~ g
' 1" W'flmu

 

130

 

 

Figure 12 - Creep-CFS Test

20

3.4 Determination of “fl; and We, from Creep Test
Inspection of equation (2.3-3) shows that a negligible or zero
strain rate (g ) and a constant maximal shearing stress ('r ) would
allow the calculation of G as:
c = fly-5, (3 .4 -1)
Where

‘T’ = 0.5 x difference between principal stresses due to
dead weight,

3;: Shear strain at time of negligible strain rate.

With this value of C it was possible to solve equation (2.3-1)
for T4, at various strains. To was now calculated from equation
(2.3-3) knowing (I? and (r . Equation (2.3-3) could also be solved
for: but 3 was not necessary to determine the stress transfer curves.
Figure 14 and Figure 15 show typical creep curves used to calculate

'13 and To by Kelvin nodel analogy.

3.5 Determination of ‘1’¢ and c' from Creep-CFS Test

To obtain the values for ¢' and c' at the end of the creep phase
of the Creep-CFS tests it was necessary to extrapolate the (V versus
axial strain and c' versus axial strain curves to the axial strain
at end of creep. Since c' changes rapidly during the first stages of
loading, the 41' versus axial strain curves were used forfextrapolation.
Data presented by Schmertmann (1960) show that the d)‘ versus axial
strain curves for a particular saturated clay are similar while those
of c' versus axial strain vary. Ebctrapolation of ¢' is shown in
Figures 16 and 17. From this the value of c' at the end of creep was

calculated. Sample calculations for c' are given in the Appendix.

21

With known values of c' and Q' at the end of creep the values
of 41p and T0 were calculated from Mohr's circle as shown in

Figure 13.

 

 

 

 

 

 

 

 

Shear
Stress Y'=(¢I' '5) Z
‘ Axial
Stress
(W. - V3) = Principal stress difference due to dead load

from creep phase

0
“

Cohesion at end of creep

<5
'12: c' (3.5-1)
«1;: Y. - Tc (3.5-2)

Friction at end of creep

Figure 13 - Mohr's Circle

Calculations for GE} and Tc are presented in the Appendix and
Table 3 tabulates values of c' and T4: using the procedure described.
_ A summary of triaxial tests is presented in Table 4 and typical data

from all type tests run is presented in Appendix.

22

TABLE 3 - SUMMARY or c' AND'W1; VALUES

CREEP TESTS CRBBP-CPS TESTS
Creep Cohesion “’9 Creep Cohesion ‘T'b
Time End Creep End Creep Time End Creep End Creep
Min . Kg/cm" Kg/cn,‘ Min . Kg/cmz Kg/cm‘

COMPACTBD CLAY

60 0.407 0.093 120 0.469 0.031
125 .391 .109 480 .422 .078
460 .375 .125 960 .372 .128
825 .869 .131 1440 .376 .124

4320 .858 .142 4320 .356 .144

CONSOLIDATED CLAY

30 0.485 0.090 60 0.564 0.011
125 .459 .115 240 .420 .155
250 .444 .131 1440 ' .393 .182
500 .428 .147 7200 .879 .196

7200 .401 .175

23

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Desig.

C-CPS -l
C-C-CPS -S
C-C-CFS -3
C-C-CPS-4
C-C-CPS-6
C-C-CFS -l
C-C-CPS-S
C-C-CFS-9
C-C-CPS-lo
C-C-CFS -ll
C-C-CPS-7
P-CPS -l
P-C-CPS-4
P-C-CFS-2
P-C -CPS -3_
P-C-CPS-l

TABLE 5 - TRIAXIAL TEST RESULTS AT END OF TESTS

Strain
%
8.0
6.0
6.0
6.0
6.0
3.0
6.0
7.0-
6.0
6.0
7.0
9.0
9.0
8.0
6.0

 

9.0,

1.42
1.41
1.42
1.34
1.60
1.17
1.69
1.67
1.57
1.44
1.42
1.71
1.71
1.65
1.51
1.41

2.00
2.38
2.20
2.05
2.49
1.75

2.72

~ 2.59

2.48
2.20
2.14
2.50
2.63
2.55
2.27
2.04

Upper Curve
«L"V
Kg/cm Kg/cn Kg

0.58
.97

.78

1.03
.92

.91

.72
.79
.92
.90
.76

.63

f...

 

Lower Curve

Egg/:1: ngcm" Kg/in"
1.86 1.75 0.39
1.33 1.88 .55
1.32 1.70 .88
1.21 1.55 .34
1.47 1.99 .52
1.11 1.50 .89
1.56 2.22 .66
1.55 2.09 .54'
1.44 1.98 .54
1.83 1.70 .87
1.29 1.64 .85
1.51 2.00 .49
1.58 2.18 .60
1.48 2.05 .57
1.81 1.77 .46
1.23 1.54 .81

 

'

25

I

c
Kg/cn" Deg.

0.538
.563
.537
.475
.546
.430
.561
.600
.534
.541
.500
.459
.470
.476
.386

.433

7.8
5.0
6.8
8.3
9.0
7.8
8.9
7.5
8.9
7.1
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12.5

15.0

12.0

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FIGURE 16

CV in Degrees

 

 

 

 

 

 

 

 

Strain in X

FIGURE 17 - mmomnou or 4! FOR CONSOLIDATED CLAY

:-

2T

2*:

”I

d.

*-

eq. P-C-CPS-4

/ Creep Tine 1 Hr.
/ I
I (I): 0.4

Ci : : t % : 1* :-

0 1 2 3 4 5 6 7 8

Strain in X

3.
6!“
H
CF“ T
H
0,.
J.
‘F r’ = 6'i//,~‘r"‘//““‘~*”A\\‘~J:3Z‘ “
Ni" P-C-CFSeZ
-. - Creep Time 4 Hr.
° % . . 1 . . . :

0 1 2 3 4 5 6 7 8

0.40

0. 50
c ' in Kg/cnz

0.40

30

c ' in Kg/cmz

¢’ in Degrees

4)’ in Degrees

 

 

 

 

 

3:.” 4;
..L
H
OT I _,
r-l /’
14>: 9.0
ml.
0:-
fllqu— ‘-
NT F-C-CFS-3
Creep Time 24 Hr.
o : : 4 : : : 5
O 1 --2 3 4 5 6 8
Strain in z
z"
o...
H I I
¢= 12.2 ¢
04:- 5"-
H
fly- 1.
0..
Q". C'7
N“ F-C-CPS-l
Creep Tine 120 Hr.
‘9 § : : % I. : :
0 1 2 3 4 5 6 8
Strain in 2
FIGURE 17 CONTINUED

'

 

 

0155

0.35

0.45
c ' in Kg/cmz'

0.45
c' in Kg/cmz'

0.55

0.35

31

 

32

1! RESULTS

Table 4 sumarizes the results for the Creep-CPS tests under a
creep load of 01:75 kilogram per square centimeter. (Specimens
numbered C-C-CFS-l and C-C-CPS-S to 6). The friction angle at the
end of all the creep periods was zero or nearly zero. This indicated
that the entire creep load was resisted by the cohesive comonent of
resistance with no stress transfer to the frictional component. A
typical stress-strain curve for such a Creep-CFS test is shown in
Figure 21. A curve of friction and cohesion versus axial strain is
also plotted ”in Figure 21. These curves clearly show a value of zero
for friction at the end of creep. From the results of the CPS test
(Figure 22) it was noted at (Q3 - 0;) equal to 0.75 kilogram per
square centimeter the two stress-strain curves are coincident,
indicating a cohesive resistance only. Frictional resistance exists
only if the two curves with different ( fi. )8 yield different
strengths. Hence, a larger creep load was tried. It was decided to
choose a creep load larger than the ( Q" - “3) value at which the
two stress-strain curves in a CPS test separate. Examination of
Figure 22 and Figure 23 led to the choice of a creep load of 1.00
kilogram per square centimeter for the compacted specimens and 1.15
kilograms per square centimeter for the consolidated specimens.

Examination ”of the values of c' and ¢ ' from the Creep-CFS tests
in Table 4 indicates ¢' for the compacted clay increased from 1.0
degree to 7.4 degrees with increasing time of creep. (Specimen

numbers C-C-CFS-7 to 11) However, c' did not drop to zero but

33

dropped to a shear stress of 0.35 kilogram per square centimeter.
This was slightly below the shear stress at which the two stress-
strain curves in Figure 22 started to separate. The value of w'

for the consolidated clay increased from 0.4 degree to 12.4 degrees
with increasing time of creep. As before, c' did not drop to zero
but to a shear stress of 0.37 kilogram per square centimeter. This
shear stress was slightly below the shear stress at which the two
stress-strain curves in Figure 23 separated.

It was evident from this observation that the Kelvin model
described creep only after the creep load exceeded some constant
value of cohesive resistance. The writer has called this value of
. cohesive resistance the threshold shear stress and denoted it as (G- .
WT was taken as 0.35 kilogram per square centimeter for the
compacted clay and 0.37 kilogram per square centimeter for the
consolidated clay. The threshold values are shown in Figure 18 and
Figure 19. Calculations for q1p and c‘ are presented in the Appendix.

Figure 18 and Figure 19 show stress transfer curves for the
compacted clay and the consolidated clay. The two curves in each'
figure are the stress transfer curves calculated from the creep
curves shown in Figures 14 and 15 and measured from the Creep-CFS
tests. If the friction and cohesion actually behaved as the viscous
and elastic elements of the Kelvin rheological model the two curves
should be the same.

The shear stress transfer from a viscous or cohesive resistance

to an elastic or frictional resistance is clearly shown. Both types

34

of clay exhibited a stress transfer behavior similar to that of the
Kelvin model above the threshold shear stress‘T} . The numerical
values computed for the two types of specimen used agree only approxi-
mately. For the compacted clay (Figure 18) the agreement is poor at
shortdtime intervals (less than 700 minutes). In this time range
values of 45' measured from the Creep-CFS tests are lower than those
computed from the Creep test. Conversely, the values of c' are
higher. For the consolidated clay (Figure 19) the agreement is poor
at long-time intervals (longer than 1500 minutes). In this time
range values of Q' measured from the Creep-CFS tests are also lower
than those computed from the Creep test. Conversely, the values of
c' are also higher. In spite of these differences the shape of the
stress transfer curves measured from the Creep-CFS tests and computed
from the Creep tests are similar.

The choice of ‘T-y affects the values computed from the Creep
tests. Since this value is chosen somewhat arbitrarily it could
account for the differences. Another possible explanation for the

differences could be variation of G as creep progresses.

35

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37

1 CONCLUSIONS

5.1 Validity of Kelvin Model

5.2

The conclusions drawn here apply to the two types of clays tested.
1. Creep in a saturated clay may be represented approximately
by the Kelvin model.
2. The clay behavior is such that stress is transferred from
the component of cohesive resistance to the component of
frictional resistance. This takes place only when the creep
load exceeds a threshold shear stress.
3.- The component of frictional resistance increases from zero
and approaches its ultimate value after long-creep times.
The component of cohesive resistance drops to the threshold

shear stress after long-creep times.

Suggestions for Future Study

1. Clays of different mineral contents should be tested as
described in this thesis to establish the general usefulness
of the procedure.

2. A study should be made to find a simple rheologic model that
will describe creep in a saturated clay to a closer approxi-
mation than the Kelvin model.

3. The threshold shear stress should be investigated.

38

‘11. BIBLIOGRAPHY

Bea, R. 0. "Discussion of Friction and Cohesion of Saturated Clays,"
pp. 268-77. Journal Lf the Soil Mechanics and Foundations
Division, vol. 89, SM 1. Ann Arbor: American Society of
Engineers, 1963.

Bishop, Alan W., and D. J. Henkel. The Triaxial Test. Second
Edition. London: Edward Arnold Ltd., 1962.

Buisman, A. S. Keverling. "Results of Long Duration Settlement
Tests," pp. 103-06. Proceedings_ of the International COnference
Ln Soil Mechanics and Foun ation Engineering, vol. 1.
Cambri idge: 1936.

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

Dillon, Howard 8. "Structure and Identification of Clay Soils."
Unpublished laboratory report, Soil Science 945, Michigan State
University, East Lansing, 1963.

Geuze, E. C .W .A. "Compression, an Important Factor in the Shearing
Test," pp. 141-42. Proceedings_ Of'the Second International
Conference Ln Soil.Mechanics and Foundation Engineering, vol. 3.
Rotterdam: 1948.

Geuze, E. C .W .A. Introduction by General Reporter for Session 2,
pp. 119-21. Proceedings Lf the Third International Conference

Ln Soil Mechanics and Foundation_ Engineering, vol. 3.
Switzerland: 195 .

Geuze, E.C.W.A. and T. K. Tan. "The Mechanical Behavior of Clays,"
Rheology, Ed. V. G. W. Harrison. New York: Academic Press
Inc., 1954.

 

Haefeli, R. "Creep Problems in Soils, Snow and Ice," pp. 238-50.
Proceedin s of 323 Third International Conference g£_Soil
Mechanics Egngoundation Engineering, vol. 3. Switzerland: 1953.

 

 

Murayama, S. and T. Shibata.. "Rheological Properties of Clays,"
pp. 269-73. Proceedings_ of the Fifth International Conference
Ln Soil Mechanics and Foundation Engineering, vol. 1. Paris:
1961.

 

Rowe, P. W. "Ce=0 Hypothesis for Normally Leaded Clays at Equilibrium,"
pp. 189-92. Proceedings Lf the Fourth International Conference
Ln Soil Mechanics and Foundation Engineering, vol. 1. London:
1957.

39

Schiffman, R. L. "The Use of Visco-Elastic Stress-Strain Laws in
Soil.Testing," pp. 131-55. ASTM Special Technical Publication '
No. 254. Philadelphia: American Society for Testing Materials,
1959.

Schmertmann, John H. and Jorj O. Osterberg. "An Experimental Study
of the Development of Cohesion and Friction with Axial Strain
in Saturated Cohesive Soils," pp. 643-94. Research Conference
Ln Shear Strm mgth_ of Cohesive Soils. Ann Arbor: American
Society 0 Civil Engineers, 1960. '

Terzaghi, Karl. Discussion of "Earth Pressure, Retaining Walls,
Tunnels and Shafts in Sbils," pp. 205-06. Proceedings_ of thg_
Third International Conference Ln Soil Mechanics an Foundation
Engineering, vol. 3. Switzerland: 1953.

Vialov, S. S. and A. M. Skibitsky. "Rheological Processes in Frozen
Soils and Dense Clays," pp. 12-24. Proceedings gflthg_Fourth
International Conference on Soil Mechanics and Foundation

E? ineerin , vol. 1. London: 1957.

Vialov, S. S. and A. M. Skibitsky. "Problems of the Rheology of
Soils," pp. 387-91. Proceedings_ of the Fifth International
Conference Ln Soil Mechanics and Foundation Engineering, vol. 1.
Paris: 1961.

Wu, T. H., A. G. Douglas, and R. D. Goughnour. "Friction and
Cohesion of Saturated Clays," pp. 1-23. Journal Lf the Soil
Mechanics gnd_Foundations Division, vol. 88 SM 3. _Ann —Arbor:
American Society of Civil Engineers, 1962.

21.1. APPENDIX

7.1 Derivation of Data Table for CPS Test

 

40

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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FIGURE '2'0 - man's CIRCLE FOR CFS

AB=CD and AC=BD

ta“ °‘ " “=4“ )/(Xz -X. )
8‘“ 4’" “=4" ”(XE-X.)
tan d = sin q;

¢ = 811;. (Y; ~Y‘ )/(x1_x‘ )

z = ¢'/tanq>' and z =a/tano<

c' cos 45'

c' = a/cos q),

TEST DATA TABLE

7.2 Typical Data for Taste Run (See following tables and figures)

41

 

 

 

 

 

 

 

 

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Strain in X
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Strain in X

FIGURE 21 - TYPICAL STRESS-STRAIH CURVE FOR COMPACTED
‘ CLAY CREEP-CPS TEST (C-C-CPS-é) ’

42

TABLE 6 - GENERAL DATA SHEET

Date 3/21/63 Test C-CFS-l
Operator Holliday Cell 4

Sample C 16

TRIMMINGS

Container No. 41 Cont. Wt. & Dry Wt. 59.27
Cont. Wt. 29.47 (grams) Water Wt. 11.85

Cont. Wt. & Wet Wt. 71.12 Dry Wt. 29.80

Water Content 39.8%
SPECIMEN
Length 3.00 in = 7.62 cm Volume 76.2 cm3

Area 10.0 cm2

Initial Final
Wt. of Spec. 137.73 127.10
Dry Wt. of Spec. 96.28 96.28
Wt. of Water 41.45 30.82

Water Content. 43.0% 32.1%

43

TABLE 7- CONSOLIDATION DATA SHEET

Cell 4 Test C-CFS-l
AV = 10.0 cm3 v=vo -AV = 66.2 cm3
L=Lo(V/Vo) = 2.82 in A=Ao(V/Vo) = 9.11 cm‘
Chamber Pressure 2.00 Kg/cmz Back Pressure 1.5 Kg/cfi?
Date Time Elapsed Burette Drainage
WTime
(Min. cc cc
3/21/63 1606 0.0 0.0 0.0
0.25 1.5 1.5
0.50 1.8 1.8
1.00 2.0 2.0
2.00 2.4 2.4
5.0 3.2 3.2
10.0 4.2 4.2
23.0 6.2 6.2
30.0 6.9---0.0 6.9
60.0 2.4 9.3
136.0 4.8---0.0 11.7
2108 302.0 1.2 12.9
3/22/63 0842 996.0 1.2 12.9
1502 1356.0 1.3 13.0
1621 1455.0 1.3 13.0

1634 Back Pressure Applied

Cell 4

TABLE 8 - CPS DATA SHEET

Chamber Pressure 3.5 Kg/cm?
Proving Ring Number 684

Proving Ring Constant. 0.1470 Kg/div.

**

( q}..q3) = Elgggl-(l-E) = !%%%%2(1-Q)

Time

0915
0930
0940
0946
0949
0953
1008
1012
1016
1021
1042
1050
1119
1125
1139
1148
1220
1228

Load
Dial

N x 10"

0.0600

.0630

.0646.

.0653
.0655
.0656
.0661
.0661
.0662
.0662
.0664
.0664
.0640
.0650
.0660
.0669
.0667
.0667

Strain

Dial
in.

0.0

0.0028

.0056
.0071
.0085
.0099
.0155
.0169
.0183
.0197
.0282
.0310
.0424
.0451
.0508
.0536
.0649

.0676

Strain

.%

0.0

0.1

.25
.30

.35

1.00
1.1
1.5
1.6
1.8
1.9
2.3

2.4

( 91‘ Q3)
Kg/cm‘

0.0
0.484

.742

. .854

.889
.902
.930
.980
9.994
.994
1.025
1.03
1.03
1.035
1.05
1.09
1.065
1.055

Test C-CI-‘S -1
Date 3/25/63

g Wt. Added
g Wt. Removed

_ Constant
D. u— Pressure
( q.‘ -' Q3) C811
Kg/cm‘ Kg/cmz
0.0 1.5
0.484 1.5
.742 1.5
t
.854 1.75
.889 1.75
.902 1.75
*4
.980 1.50
.980 1.50
e
.994 1.75
.994 I 1.75
to ‘
1.025 1.50
1.03 1.50
e
1.03 1.75
1.035 1.75
*4
1.05 1.5
1.09 1.5
t
1.065 1.75
1.055 1.75-

45

TABLE 8 CONTINUED

Cell 4 Test C-CFS-l
Time Load Strain Strain ( V. - W3) A u= 19:22:32:
Dial 0151 cr. - 03) Cell
N x 10" in. % Kg/cm‘ Kg/cm" Kg/cmz
1300 .0673 .0790 2.8 1.14 1.14 **1.50
1308 .0674 .0817 2.9 1.155 1.155 * 1.50
1321 .0673 .0874 3.1 1.14 1.14 1.75
1327 .0673 .0904 3.2 1.14 1.14 **1.75
1343 .0677 .0959 3.4 1.20 1.20 1.50
1347 .0677 .0986 3.5 1.20 1.20 * 1.50
1413 .0676 .1071 3.8 1.18 1.18 1.75
1419 .0676 .1100 3.9 1.85 1.85 **1.75
1445 .0681 .119 4.2 1.25 1.25 1.50
1451 .0682 .121 4.3 1.26 1.26 * 1.50
1508 .0680 .127 4.5 1.23 1.23 1.75
1515 .0679 .130 4.6 1.22 1.22 ..1'75
1537 .0684 .138 4.9 1.30 1.30 1.50
1544 .0685 .141 5.0 1.31 1.31 * 1.50
1600 .0683 .147 5.2 1.27 1.27 1.75
1608 .0683 .149 5.3 1.27 1.27 **l.75
1634 .0688 .158 5.6 1.34 1.34 1.50
1637 1.0689 .161 5.7 1.35 1.35 * 1.50
1741 .0689 .1861 6.6 1.35 1.35 1.75
1749 .0689 .1890 6.7 1.34 1.34 **1.75
1805 .0692 .194 6.9 1.39 1.39 1.50

46

TABLE 8 CONTINUED

Cell 4 Test C-CP's-1
Time 1153: 83:31: Strain ( Cf. - V3) 023:9.) 19:23:33
N x 1074 in 75 Kg/cmz Kg/cmz Kg/cmz‘
1812 .0692 .197 7.0 1.39 1.39 * 1.50
1824 .0690 .203 7.2 1.35 1.35 1.75
1830 .0690 .205 7.3 1.35 1.35 **1.75
1846 .0693 .2110 7.5 1.39 1.39 1.5
1853 .0695 .2138 7.6 1.41 1.41 * 1.5
1908 .0692 .220 7.8 1.37 1.37 1.75
1916 .0691 .222 7.9 1.35 1.35 1“1.75
1930 .0695 .2285 8.1 1.41 1.41 1.50
1938 .0697 .231 8.2 1.42 1.42 1.50

47

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FIGURE‘ZZ - STRESS-STRAIN CURVE FOR TEST C-CFS-l

49

TABLE 10 - GENERAL DATA SHEET

Date 6/18/63

Operator Holliday

Sample P 5

TRIHHINGS

Container No. 210

Cont. Wt. 20.61 (grams)

Cont. Wt. & Wet Wt. 63.86

SPECIMEN
Length 2.8 in = 7.11 cm

Area 10.0 cm:

Initial
Wt. of Spec. 129.06
Dry Wt. of Spec. 86.13
' Wt. of Water 42.93

Water Content 49.8%

Test P-CPS-l
Cell 1

Cont. Wt. & Dry Wt. 50.53
Water Wt. 13.33
Dry Wt. 29.92

Water Content 44.5%

Volume 71 . 1 cm?’

Final
114.12
86.13
27.99

32.5%

50

TABLE 11 - CONSOLIDATION DATA SHEET

Cell 1 Test P-CFS-l

AV . 17.3 cm3 Vavo ~AV = 53.3 ems
I"'LoW/Vo) = 2-54 in. A=Ao(V/Vo) = 8.26 cm2
Chamber Pressure 2.00 Kg/mnz Back Pressure 1.5 Kg/cmz
Date Time Elapsed Burette Drainage
Time
Min. cc cc
6/18/63 1431 0.0 10.0 0.0
.25 8.6 1.4
.5 8.2 1.8
1.0 7.6 2.4
2.0 6.8 3.2
5.0 5.2 4.8
10.0 3.1 6.9
15.0 1.7---l0.0 8.3
35.0 6.1 12.2
60.0 3.5---10.0 14.8
1631 120.0 7.8 17.0
1715 164.0 7.2 17.6
2131 420.0 6.5 18.3
6/19/63 1031 1200.0 6.1 18.7
1431 1440.0 6.0 18.8

1442 Back Pressure Applied

51

TABLE 12 - CFS DATA SHEET

Cell 1 Test P-CPS-l
Chamber Pressure 3.5 Kg/cmz Date 6/20/63
Proving Ring Number 3144 *1 Kg Wt. Added
Proving Ring Constant 0.0455 Kg/div. ”1 Kg Wt. RemoVed
<3. -<r.) = " PRC 1-e) = M3323.-.)
Time Load Strain Strain ( ‘1'. - (1’5) A u= 333$
Dial Dial (W1 - 93) Cell
N x 10“ in. % Kg/cm" Kg/cm" Kg/cn"
0826 0.0200 0.0 0.0 0.0 0.0 1.50
0349 .0290 .003 .1 .495 .495 1.50
0914 .0376 .005 .2 .970 .970 .*1.50
0951 .0422 .020 .3 1.215 1.215 1.00
0956 .0427 .023 .9 1.240 1.240 t 1.00
1011 .0429 .030 1.2 1.249 1.249 1.50
1016 .0431 .033 1.3 1.255 1.255 ..1'5°
1053 .0461 .053 2.1 1.410 1.410 1.00
1104 .0465 .056 2.2 1.430 1.430 * 1.00,
1125 .0454 .069 2.7 1.360 1.360 1.50
1123 .0455 .071 2.3 1.368 1.368 "1.50
A 1223 .0494 .967 3.3 1.560 1.560 1.00
1227 .0496 _ .099 3.9 1.560 1.560 * 1.00
1244 .0473 .112 4.4 1.435 1.435 1.50
1250 .0474 .114 4.5 1.440 1.440 **1.50
'1335 ' .0510 .135 5.3 1.615 1.615 1.00
1340 - .0512 .137 5.4 1.622 1.622 ‘21.00

1358 .0485 .150 5 . 9 1.475 1.475 1.50

Cell 1

Time

1401
1446
1452
1514
1516
1556
1604
1621
1627
1714

1720

Load
Dial

N x 10“

.0485
.0526
.0528
.0495
.0495
.0535
.0537
.0502
.0502
.0545

.0547

Strain
Dial
in.

.152
.173
.175
.190
.193
.211
.214
.229
.231
.252

.254

TABLE 12 CONTINUED

Strain

%'
6.0
6.8
6.9
7.5
7.6
8.3
8.4
9.0
9.1
9.9

10.0

(tn-03)
Kg/cm‘

1.475
1.671
1.685
1.505
1.505
1.690
1.701
1.510
1.510
1.710

1.713

Test F-CPS-l

1.701
1.510
1.510
1.710

1.713

52

Constant

.Pressure

K3786:

1.50
0*

1.00

1.00
0

1.50

1.50
*0

1.00

1.00
0

'1.50

1.50
**

1.00

1.00

53

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55

TABLE 14 - GENERAL DATA SHEET

Date 4/20/63

Operator Holliday

Sample C 7

TRIMHINCS

Container No. 211

Cont. Wt. 20.34 (grams)

Cont. Wt. & Wet Wt. 46.92

SPECIMEN
Length 3.00 in I 7.62 on

Area 10.0 on}

Initial
Wt. of Spec. 137.80
ny Ht. of Spec. 97.69
Ht. of Water 40.11

Water Content 41.2%

Test C-C-7 & C-C-CFS-7
Cell 1

Cont. Wt. & Dry Wt. 39.37
Water Wt. 7.55
Dry Wt. 19.03

Water Content 39.8%

Volume 76.2 cm?

Final
129.15
97.69
31.46
32.2%

Cell 1
AV =- 12.6 cm!

Chamber Pressure 2.00 Kg/cmt

Date

4/20/63

4/21/63

TABLE 15 - CONSOLIDATION DATA SHEET

Time

1014

1214
1414
1714

1035

1040

56

Test c-c-7 s. C-C-CFS-7
v=vo - AV a 63.6 cm3
A=Ao(V/Vo) ' 8.87 cm?

Elapsed Burette
Time
Min. cc
0.0 10.0
.25 8.2
.5 8.0
1.0 7.7
2.0 7.3
5.0 6.4
13.0 5.0
15.0 4.6
30.0 2.8--10.0
60.0 7.5
120.0 5.1---10.0
240.0 8.6
420.0 8.1
1461.0 7.6

Back.Pressure Applied

Back Pressure 1.5 Kg/cm?

Drainage
cc
0.0
1.8
2.0
2.3
2.7
3.6
5.0
5.4
7.2
9.7

12.1
13.4
14.0
14.5

 

If .;.

57

TABLE 16 - CREEP DATA SHEET

Cell 1

Chamber Pressure 3.5 Kg/cmf

Dead Load 8.87‘Kg

Date Elapsed

Time
Min.

4/22/63 0.0

.25

.5
1.0
2.0
5.0

10.0

15.0

30.0

60.0

120.0

240.0

480.0

840.0

4/23/63 1440.0

avvwfiv 1740.0
4/24/63 2940.0
3240.0

4/25/63 4320.0

Strain
Dial

in.

0.0230

.0255
.0265
.0275
.0290
.0320
.0351
.0378
.0421
.0481
.0525
.0559
.0585
.0602
.0610
.0615
.0624
.0629

.0630

Test C-C-7 & C-C-CPS-7
Back Pressure 1.5 Kg/cIF
(G}- 93) 1.00 Kg/cn‘

Strain Pore
Pressure
% Kg/ c1
0.0 1.52
.083
.124 1.90
.159 1.95
.212 2.00
.248 2.08
.427 2.12
.524 2.18
.675 2.25
.886 2.30
1.081 2.35
1.165 2.40
1.259 2.41
1.318 2.47
1.345 2.55
1.361 2.60
1.394 2.74
1.415 2.70
1.417 2.86

‘1?

 

‘r ~7 ja3'". .

Cell 1

TABLE 17 - CFS DATA SHEET

Chamber Pressure 3.5 Kg/cm2

Proving Ring Number 3144
Proving Ring Constant 0.0455 Kg/div.

(0'. " Q’s) _N:RC 196.) =

Time

0853
0915
0920
0951
0955
1025

1028

1120
1152
1153
1222
1226
1250
1255
1326
1332
1357

Load
Dial

N x 10-4

0.0100

.0147
.0149
.0169
.0170
.0139
.0138
.0159
.0160
.0143
.0143
.0163
.0165
.0149
.0148
.0168
.0172

.0156

Strain

Dial
in.

0.040

Strain

.%
1.417
1.451
1.486
1.735
1.770
2.265
2.300
2.760
2.795
3.255
3.290
3.675
3.745
4.160
4.230
4.65
4.72

5.20

58

Test C-C—7 & C-C-CFS-7

Date 4/25/63
*1.Kg Wt. added
**1.Kg Wt. added

N(.0455)( _
.87 1.6)

(‘L - 9%)
Kg/cmF

1.00

1.242
1.250
1.348
1.353
1.195
1.191
1.295
1.302
1.216
1.216
1.310
1.320
1.240
1.235
1.332
1.352

1.272

£5u=\-
(qt "' W3)
Kg/cmz

0.0
.242
.250
.348
.353
.195
.191
.295
.302
.216
.216
.310
.320
.240
.235
.332
.352

O 272

Constant
Pressure
Cell
Kg/cm?

2.86
2.86

2.86
it

2.36

2.36
a

2.86

2.86
9*

2.36

2.36
t

2.86

.2.86
4*

2.36

2.36
a

2.86

2.86
*4

2.36

2.36
a

2.86

Cell 1

Time

1406
1446
1453
1520
1526
1603
1614
1641

1645

Load
Dial
N x 10‘4

.0153
.0181
.0184
.0161
.0159
.0185
.0188
.0163

.0162

Strain

Dial

1n.
.153
.167
.170
.187
.190
.204
.206
.223

.226

TABLE 17 CONTINUED

Strain
.%
5.4
5.9
6.0
6.6
6.7
7.2
7.3
7.9

8.0

59

Test C-C-7 & C—C-CFS-7

( q,-q3)
Kg/cm‘

1.258
1.391
1.405
1.288
1.284
1.405
1.415
1.298

1.296

bsu=|'
( ¢;- V5)
Kg/cm‘

.258
.391
.405
.288
.284
.405
.415
.298

.296

Constant

Pressure
Cell
Kg/cm1

.2.86
at

2.36

2.36
a

2.86

2.86
*4

2.36

2.36
*

2.86

2.86

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Strain in%

FIGURE 24 4 STRESS-STRAIN CURVE FOR C-C-CPS-7

62

TABLE 19 - GENERAL DATA SHEET

Date 5/20/63

Operator Holliday

Sample F l

TRIMHINGS

Container No. 211

Cont. Wt. 20.34 (grams)

Cont. Wt. & Wet Wt. 57.09

SPECIMEN
Length 3.00 in = 7.62 cm

Area 10.0 cm2

Initial
Wt. of Spec. 135.41
Dry Wt. of Spec. 89.77
Wt. of Water 45.64

Water Content 50.9%

Test P-C-l & P-C-CPS-l
Cell 1

Cont. Wt. & Dry Wt. 45.34
Water Wt. 11.75
Dry Wt. 25.00

Water Content 47.0%

Volume 76 .2 663

Final
120.02
89.77
30.25
33.0%

Cell 1

AV = 18.6 663

TABLE 20 - CONSOLIDATION DATA SHEET

Chanber Pressure 2.00‘Kg/cmz

Date

5/20/63

5/21/63

Time

0949

1349
1549
2049
0749
0949

0955

Elapsed
Time
Min.

0.0
.25
.50

1.0

2.0

6.0

10.0
15.0
30.0
60.0
80.0
132.0
240.0
360.0
660.0
1320.0

1440.0

Burette
cc
10.0
8.8
8.6
8.4
7.8
6.5
5.7
4.3---10.0
7.3
3.1
1.2--10.0
7.5
6.1
5.5--10.0
9.5
9.2

9.2

Back.Pressure Applied

63

Test F-C-l & P-C-CPS-l
V=Vo - AV II 57.6 cm5
AIAO(V/Vo) - 8.31 cm2
Back Pressure 1.5 Kg/cmF

Drainage
cc
0.0
1.2
1.4
1.6
2.2
3.5
4.3
5.7
8.4

12.6
14.5
17.0
18.4
19.0
19.5
19.8
19.8

64

TABLE 21 - CREEP DATA SHEET

Test P-Cv-l & P-C-CPS-l
Back.Pressure 1.5 Kg/cm?
(0" - 03) 1.15 Kg/cn‘

Cell 1
Chamber Pressure 3.5 Kg/cmz
Dead Load 9.56 Kg

Date EIApsed Strain Strain Pore
Tine Dial , Pressure

Min . in . % Kg/cm"

5/22/63 0.0 0.008 0.0 1.60

.25 .029 .770
.50 .031 .825 2.20
1.0 .032 .886 2.23 '

3.0 .035 .986 2.27

5.0 .038 1.110 2.32

10.0 .045 1.364 2.39

15.0 .048 1.450 2.41

30.0 .055 1.705 2.50

60.0 .063 1.995 2.52

120.0 . .070 2.260 2.59

240.0 .077 2.540 2.62

360.0 .081 2.677 2.69

480.0 .083 2.755 2.70

756.0 .087 2.890 2.76

5/23/63 1440.0 .090 3.010. 2.85
1680.0 .092 3.074 2.88

1920.0 .093 3.120 2.89

2160.0 .094 3.150 2.89

TABLE 21 CONTINUED

Cell 1 Test P-C-l 8 P-C-CPS-l
A Date Elapsed Strain Strain Pore
Tine Dial Pressure
Win. in. ‘ % Kg/cn"
5/24/63 2880.0 .096 =3.220 2.92
3120.0 .097 3.270 2.98
3360.0 .099 3.325 2.99
3600.0 .100 3.350 2.99
5/25/63 4320.0 .102 3.440 3.00
4560.0 .103 ' 3.490 3.03
4800.0 .105 3.550 3.05
5/26/63 5760.0 .109 3.700 3.10
6600.0 .111- 3.760 3.10

5/27/63 7200.0 .118 4.01' 3.11

66

TABLE 22 - CFS DATA SHEET

Test P-C-l I. P-C-CPS-l
Date 5/27/63
*1 Kg Wt. Added

Cell 1
Chamber Pressure 3.5 Kg/cm”
Proving Ring Nunber 3144

Proving Ring Constant 0.0455 Kg/div.

(v. - v.) - "-L—HRC 1-0 = "L—Rg‘f‘gis l-e)

**1Kg Wt. Removed

Time Load Strain Strain ( (I. - 0’3) A u=L|57 3:22:32:
Dial Dial G}-WS) 0611
N x 10""r in. % Kg/cm" Kg/cm‘ Kg/cnlz
0815 0.0100 0.109 4.01 1.150 0.0 3.11
0841 .0125 .112 4.11 1.281 .131 3.11
0843 .0125 .113 4.14 1.281 .131 3.11
0845 .0125 .114 4.175 1.281 .131 1“3.11
0928 .0147 .127 4.64 1.398 .248 2.61
0931 .0148 .128' 4.68 1.400 .250 * 2.61
1007 .0114 .145 5.30 1.223 .073 3.11
1009 .0114 6.146 5.33 1.222 .072 ”3.11
1150 .0152 .180 6.59 1.416 .266 2.61
1152 .0152 .181 6.63 1.416 .266 2.61
1155 .0152 .182 6.66 1.416 .266 * 2.61
1318 .0116 .219 8.02 1.231 .081 3.11
1320 .0116 .220 8.06 1.228 .078 **3.11
1420 .0150 .240 8.77 1.400 .250 2.61
1422 .0151 .241 8.80 1.405 .255 * 2.61
1448 .0118 .254 9.30 1.242 .092 3.11
1454 .0117 .256" 9.40 1.234 .084 3.11
1500 .0117 .259 9.50 1.232 .082 3.11

 

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FIGURE 25 - STRESS-STRAIN CURVE FOR P-C-CPS-l

7.3 Calculations for T0 and c' for Compacted Clay
a) Creep Test (C-C-7)

21c: <r. - 03 = 1.00 Kg/cmZ

Threshold shear strain =‘KT = 0.0%

0.35 Kg/cmZ

’11 = x Jr. =(ngfi )-¢1-— ‘—'—§-9 - 0.35 = 0.15 Kg/cmz

Threshold shear stress =(Ft

From equation (3.4-1)

 

c = TE = 0"5 = 10 Kg/cmz

From equations (2.3-1) and (2.3-3)

(FP= G‘s;
(T;=fllr‘T$
From Figure 14
‘Ur= 9.25 x 10'3 t. = 60 min
'62: 10.9 x 10'3 t2 = 125
‘63: 12.5 x 10" t. = 460
1;: 13.1 x 10" t4.= 825
‘65: 14.2 x 10‘3 t5=4320
Increment (Taficflfj To =Tk'TQ 0' =‘F+’|E
J
1 0.093 0.057 0.407
2 .109 .041 .391
3 .125 .025 .375
4 .131 .019 .369
5 .142 .008 .358

b) Creep-CFS Test

Y. c' q$= Y;-c' Creep phase
Time in min.
0.500 0.469 0.031 120
.500 .422 .078 480
.500 .372 .128 960
.500 , .376 .124 1440

.500 .356 .144 4320

69

 

7.4 Calculations for (Up and c' for Consolidated Clay

a) Creep Test (P-C-l)

2K ~= <r. - Cr5 = 1.15 Kg/cmz

Threshold shear strain =UT= 0‘:0%-~

Threshold shear stress = (Fr = 0.370 Kg/cmz

‘6? = (1r- : 4.0%

(“5‘ K 4'. = (3:292. ) Ar. :5;— - .037 = 0.205 Kg/cmz
From equation (3.4-1)

(ll 0.205‘
G =13; = 0,04, = 5.13 Kg/cm"

 

From equations (2.3-'1) and (2.3-3)

“1% 6 VJ
CE=rlTL-‘T¢
From Figure 15
-2
‘K.= 1.75 x 10 a t. = 30 min.
3.: 2.24 x 10‘ t2 = 125
93’: 2.55 x 10“ t3 = 250
'U.= 2.87 x 10“ t. = 500
3.: 3.40 x 10" t5 = 7200
Increment T43 =(a‘63 'TE, =TK-‘FQ c' = (ENE,
j
1 0.0899 0.115 0.485
2 .1155 .089 .459
3 .1310 .074 .444
4 .1475 .058 .428
5 .1745 .031 .401
b) Creep-CPS Test
Y. 0' q; =Y.‘ c5 Creep phase
Time in min.
0.575 0.564 0.011 60
.575 .420 .155 240
.575 .893 .182 1440

. 5'75 . 379 . 196 7200

70

 

71

7.5 Sample Calculations for Extrapolation of c' from Creep-CPS Test
Test C-C-CFS-7

2K= ( <1} - (rs) = 1.00 Kg/cm2

thrapolated (p, = 7.40

Constant effective stress ET. = 1.640 Kg/cm"

Effective radial stress at end creep = 0.640 1(g/cmz

x, = 1/2 (1.00) + 0.640 = 1.140

Y. =-l/2 (1.00)= 0.500

Sin 7.40 = 0.129 = tano<

X. tano< = 0.147

a = 0.500 - 0.147 - 0.353

c' = 0.353/cos 7.40 = 0.356 Kg/cm‘

 

 

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MI HIGAN STATE UNIVERSITY LIBRARIES

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