UNDRAINED CREEP BEHAVIOR
OF ATCHAFALAYA CLAY
FROM CU DIRECT-SIMPLE SHEAR TESTS
by
CHARLES E. WILLIAMS
S.B.,
Massachusetts Institute of Technology
(1971)
Submitted in partial fulfillment
of the requirements for the degrees of
Master of Science and Civil Engineer
at the
Massachusetts Institute of Technology
May 1973
:K R--
Signature of Author..
...-...
Department of Ciril Engineering,
May 11, 1973
.. . .. .-.-................
Certified by........... ... '...
Thesis Supervisor
Accepted by.
Chairman, DepartmEAital Committee on Graduate
Students of the Department of Civil Engineering
Archives
(JUN 29
197)
ABSTRACT
TITLE:
UNDRAINED CREEP BEHAVIOR OF ATCHAFALAYA
CLAY FROM CU DIRECT-SIMPLE SHEAR TESTS
by
CHARLES E. WILLIAMS
Submitted to the Department of Civil Engineering on
May 11, 1973 in partial fulfillment of the requirements
for the degrees of Master of Science and Civil Engineer.
The creep behavior of normally consolidated and over
consolidated samples of a highly plastic deltaic clay
from the Atchafalaya Basin in Louisiana is investigated
in consolidated-undrained direct-simple shear tests.
From 49 to 95 percent of the undrained shear strength
was applied over a typical period of one week in the
stress controlled tests. The results of "single incre-mental" tests are compared to those in which the sample
crept under several successive increments.
The rate process theory and other rheologic models for
creep are reviewed and both undrained and drained creep
data are summarized in light of the various theories,
including those for creep rupture.
For initial shear stress increments below 85 percent of
failure, the creep behavior of the clay follows the
Singh-Mitchell rate process model after an initial
transient pore pressure condition. For additional increments, the creep strain rate is initially very slow,
but it changes with log time to eventually converge with
the Singh-Mitchell model.
The creep rupture models of Saito and Singh-Mitchell were
compared to laboratory creep rupture behavior and found
reasonably acceptable for this clay. Creep strengths
in terms of applied shear stress for a given consolidation
stress were found to be 85 percent of that obtained from
-2-
conventional controlled strain CK UDSS tests. This value
o
would probably be lower if the creep process was allowed
to continue for longer periods of time (greater than one
week) to develop sufficient pore pressures for failure.
Thesis Supervisor:
Title:
Charles C. Ladd
Professor of Civil Engineering
-3-
ACKNOWLEDGEMENTS
The author expresses his sincere gratitude to the
following:
Professor Charles C. Ladd, his thesis supervisor, whose
guidance and thought provoking comments made this investigation possible;
Dr. Lewis Edgers, who suggested the topic and aided the
author in all phases of the investigation;
Ms. Patricia Potter, who typed the manuscript;
The U.S. Army Corps of Engineers, Waterways Experiment
Station, Vicksburg, Mississippi, whose financial support
made this investigation possible.
-4-
TABLE OF CONTENTS
Page
Title Page
1
Abstract
2
Acknowledgements
4
Table of Contents
5
List of Tables
8
List of Figures
9
I
II
III
INTRODUCTION
13
1.1
Background
13
1.2
1.3
Descriptionof EABPL Foundation Clays
Scope of Research
15
16
REVIEW OF CURRENT LITERATURE
22
2.1
2.2
Rate Process Creep Theory Development
Creep Rupture
22
35
2.3
Creep Strength
38
2.4
Conclusions
41
DESCRIPTION OF EQUIPMENT AND PROCEDURES
55
3.1
Introduction
55
3.2
Shear Apparatus
56
3.3
Sample Preparation
Testing Procedure
57
57
3.4
-5-
TABLE OF CONTENTS (Cont.)
Page
IV
V
EXPERIMENTAL INVESTIGATION
4.1
Soil Tested
60
4.2
4.3
Test Program
Test Results
61
62
4.3.1
Controlled Strain Tests
62
4.3.2
Controlled Stress Creep Tests
63
4.3.2.1
Initial stress levels
63
4.3.2.2
Additional Shear in
Increments
64
4.3.2.3
Creep Failure
64
DISCUSSION OF TEST RESULTS
5.1
77
First Load Increments
77
5.1.1
5.1.2
77
81
Normally Consolidated Samples
Over Consolidated Samples
5.2
Additional Load Increments
85
5.3
Creep Rupture
86
5.3.1
Singh-Mitchell Creep Rupture
Relation
86
5.3.2
Saito's Creep Rupture
Relation
88
5.3.3
5.4
5.5
VI
60
Strength Decrease Due to Creep
Comparison of Simple Shear Stress
Levels with Triaxial Stress Levels
Use of Multi-Increment Testing
CONCLUSIONS AND RECOMMENDATIONS
90
91
93
123
6.1
Apparatus Performance
123
6.2
6.3
Test Results
Recommendations
124
128
-6-
TABLE OF CONTENTS (Cont.)
Page
VII
130
REFERENCES
Appendix A
List of Symbols
133
Appendix B
Tabulated Test Results
138
Appendix C
Plots of CK O UDSS Creep Tests
164
-7-
LIST OF TABLES
Table
No.
Title
Page
4-1
Summary of Samples for Test Program
65
4-2
Summary of CK U Direct-Simple Shear
Tests on EABPE Clay
66
4-3
CK UDSS
Clay
4-4
Description of Measured Test Parameters
69
5-1
Application of Singh-Mitchell Creep
Rupture Theory of EABPL Test Data
97
5-2
Comparison of Laboratory CK UDSS CreepRupture Behavior to Saito's CreepRupture Relationship
98
5-3
Strength Decrease Due to Creep
100
5-4
Relationships Between D, D , D and
Rotation of Principal Planes in CK DSS
Tests
101
5-5
Computations for Theoretical Strain-Log
Time Curves
102
5-6
Duplication of D T = 65% Stress Level
103
(Creep) Test Results - EABPL
-8-
67
LIST OF FIGURES
Figure
No.
Title
Page
1-1
Pre-Construction Effective Vertical
Stress Profiles, Test Sections II & III
18
1-2
Estimated Maximum Past Pressure, Sections
II and III, 180 ft. Offsetts to LS and FS
19
1-3
Average Unconfined and Field Vane Strength
Data From Test Sections II & III
20
1-4
Average Natural Water Content Profiles
for 105 ft. and 180 ft. Offsets for
Sections II & III
21
2-1
Derivation of Berkley Three Parameter
Relationship Based on Rate Process Theory
42
2-2
Variation of Strain Rate with Deviator
Stress from CIUC Creep Tests on Remolded
Illite
43
2-3
Influence of Time on Strain Rate During
Creep of Remolded Illite
44
2-4
Rheologic Model for Christensen and Wu
(1964) Rate Process Development
45
2-5
Rheologic Model for Murayama and Shibata
(1961) Rate Process Theory
46
2-6
Stress Controlled CIUC Tests on N.C.
Remolded Clay
47
2-7
Barden's Rheologic Model
48
2-8
Drained Triaxial Creep Results on London
Clay
49
2-9
Drained Triaxial Creep Results on
Pancone Clay
50
LIST OF FIGURES (Cont.)
Figure
No.
Title
Page
2-10
Demonstration of the Saito Creep
Rupture Relationship
51
2-11
Singh-Mitchell Creep Rupture Concept
52
2-12
Influence of Consolidation Conditions
on the Pore Pressure Generation of
Two Clays
53
2-13
Typical Stress Path to Failure for an
Undrained Creep Test on NC Clay
54
3-1
General Principle of Direct-SimpleShear Apparatus - Model 4
59
4-1
Range in Plasticity Characteristics of
Atchafalaya Backswamp Materials
70
4-2
CK UDSS Tests on Normally Consolidated
EA9PL Clay
71
4-3
Stress vs. Strain from CK UDSS Tests on
EABPL Clay
o
72
4-4
Stress Paths from CK UDSS Tests on Normally 73
Consolidated EABPL Cday
4-5
Normalized Stress Paths from CK UDSS Tests
on EABPL Clay
o
74
4-6
Compression Curves, CK UDSS Tests, EABPL
Clay
75
4-7
S /5
vs. OCR from CK U Direct-Simple
SRearCTests on EABPL Cday
76
5-1
Shear Strain Vs. Log Time from CK UDSS
Creep Tests on N.C. EABPL Clay
o
104
5-2
Log Strain Rate vs. Log Time from CK UDSS
Creep Tests on N.C. EABPL Clay
0
105
-10-
LIST OF FIGURES (Cont.)
Figure
No.
Title
Page
5-3
Log (Strain Rate X Time) vs. Log
Time from CK UDSS Creep Tests on
N.C. EABPL Cday
106
5-4
Log Shear Strain Rate vs. Applied
Stress Level from CK UDSS Tests on
N.C. EABPL Clay
107
5-5
Shear Strain vs. Log Time from
CK UDSS Creep Tests on O.C.
EAPL Clay
108
5-6
Log Shear Strain Rate vs. Log Time
from CK UDSS Creep Tests on O.C.
EABPL Clay
109
5-7
Log (Strain Rate X Time) vs. Log Time
from CK UDSS Creep Tests on O.C.
EABPL Cday
110
5-8
Log Strain Rate vs. Applied Stress
Level from CK UDSS Creep Tests on
O.C. EABPL ClRy
111
5-9
Comparison of Induced Pore Pressures
for Various Creep Stress Levels
112
5-10
Comparison of Plots of Log Strain
Rate vs. Log Time for N.C. and O.C.
Samples of EABPL Clay
113
5-11
Comparison of Stress Paths from
CK UDSS Creep Tests on N.C. and
114
O.e. EABPL Clay
5-12
Comparison of Pore Pressure
Generation During Creep of N.C.
and O.C. Samples of EABPL Clay
at Various Stress Levels
-11-
115
LIST OF FIGURES (Cont.)
Figure
No.
Title
Page
5-13
Variation of Creep Parameter m
with Stress Level from CK UDSS
0
Creep Tests
116
5-14
Log Shear Strain Rate vs. Log Time
During Later Increments from CK UDSS
Creep Tests on N.C. EABPL Clay o
117
5-15
Log it vs. Log Time from CK UDSS
Creep Tests on EABPL Clay
118
5-16
Plot of Log Strain Rate vs. Log Time
for Steady State Creep at Various Stress
Levels of EABPL Clay
119
5-17
Initial Shear Strain (at t = 1 minute)
vs. Applied Stress Level
120
5-18
Stress Conditions in the Direct Simple
Shear Device - Assumed Pure Shear
121
5-19
Comparison of Laboratory and
Theoretical Creep Curves at Various
Stress Levels
122
-12-
I
1.1
INTRODUCTION
BACKGROUND
For the past fifty years a steadily increasing volume of
water has been diverted from the Mississippi River into the
Atchafalaya distributary.
This is accomplished by means of
a flood levee system within the Atchafalaya basin.
Progressive
siltation of the southern half of the basin along with the
increased capacity requirements for the distributary have made
it necessary to raise the flowline within the Atchafalaya
floodway by means of levees.
Levee construction within the southern portion of the
Atchafalaya Basin Floodway in south-central Louisiana has been
in progress for more than thirty years (Kaufman and Weaver,
1967).
Construction has proceeded in stages so that the thick
deposits of soft alluvial and deltaic foundation clays can
consolidate and achieve sufficient strength to support subsequent lifts of fill.
This procedure has proved to be very
time consuming and unsatisfactory.
Moreover, settlements in
excess of 10 to 15 feet have made it impossible to attain
design heights (20 to 25 feet above the original grade) along
-13-
large portions of the floodway.
Large lateral movements,
thought to be caused by undrained shear deformations, yielding
and creep of the soft foundation clays, have been a major
contributor to the excessive vertical settlements of the levee
crown.
In 1964-65 three extensively instrumented test sections
were constructed along the East Atchafalaya Basin Protection
Levee (EABPL) (Kaufman and Weaver, 1967; USCE, 1968).
Test
Section I, with a four foot crown and a height of six feet,
had a design factor of safety of 1.1 based on a 4 = 0 analysis
using UU triaxial compression test data.
Test Sections II
and III, with a wider crown, a height of ten feet, and wide
stabilizing berms, had factors of safety of 1.1 and 1.3 based
on similar total stress analyses.
Despite very large berms, both Test Sections II and III
experienced very large lateral deformations with a resulting
drop in the crest elevation, and for all practical purposes
failed.
These lateral shear deformations, which continued
long after the end of construction, were particularly large
between elevations -20 to -40 feet (original ground surface
El. = 3-4 ft MSL).
These large deformations are considered
to be caused by undrained shear, which is the subject of separate investigations, and undrained creep.
-14-
Considering the fact that a substantial portion of the
zone of large deformations (El. -20 to -40 ft) is approximated
by a simple shear stress system, any detailed undrained creep
investigation should attempt to duplicate this stress system.
The subject of this report is undrained creep behavior of
EABPL foundation clays with the direct-simple shear stress
system.
1.2
DESCRIPTION OF EABPL FOUNDATION CLAYS
The site of the EABPL construction is composed of sand
and gravels overlain by approximately 120 feet of clay which
can be divided into three categories (Krinitzsky and Smith,
1969).
(1) Poorly drained backswamp deposit (El. -25 to +2 ft)
Presence of considerable organic matter with
several inches to several feet of peat; dark gray
to black in color; concretionary matter includes
carbonates, sulphides and vivianite; soil is typically
CH clay with WL = 110 + 30.
(2) Well drained backswamp deposit (El. -120 to -25 ft)
Light to dark brown in color due to oxidation;
stratification is absent due to reworking by plant
roots; fissures due to dessication are common; soil
is typically a CH clay with WL = 90 + 30.
-15-
(3)
Lake deposits
Deposited in shallow fresh water; gray in color
mostly highly plastic CH clays with some silt and
sand (WL = 95 + 25); well defined layering with occasional silt and fine sand layers; presence of shells
and carbonate concretions; well developed fractures
and slickensides due to shear failures during deposition.
The area, which was originally level at El. +2 ft prior
to levee construction, has the net overburden stress profile
shown in
Fig.
1-1 which was obtained from total weight and
pore pressure measurements.
Maximum past pressure profiles
for offsets from the levee centerline indicate overconsolidated
layers at elevations -45 to -65 ft and -70 to -100 ft (Fig. 1-2).
These findings are also supported by field vane strengths and
water content variations at these depths as shown in Figs.
1-3 and 1-4.
These layers are probably overconsolidated due
to drying of exposed backswamp deposits.
1.3
SCOPE OF RESEARCH
The experimental program involved obtaining representative
samples of the clay in the zone of greatest levee foundation
-16-
deformations
(El. -20 to -40 ft).
A series of standard con-
trolled strain Consolidated-Undrained Direct Simple Shear
(CKfoU DSS) tests were conducted in order to establish a
normalized shear strength versus overconsolidation ratio
relationship.
Subsequently, a program of constant load un-
drained creep tests were carried out with the Direct Simple
Shear device in order to establish strain and strength relationships with stress, time and OCR.
The Singh-Mitchell Theory (see 2.1a and 2.2b) for creep
strains and creep failure and Saito's creep rupture theory
(see 2.2a) will be applied to the test results in order to
evaluate their validity with the EABPL clay.
-17-
H
H
H
H
H
LU.
S
V)
0
-I-)
lb
U)
U)
o
w
L--
I--
-pl
U)
h0
/
L&J
C.)
w
U
w
LL
0
P4
LL
w
lo
a:
w
U)
z
L
UP4
0U)
-II
4U
-rzl
-I)
(7S1W)
1I' NOILVA313
-18-
Figure 1-1
n, TSF
0vo and
0O
+Ic
2.0
I
v
u
r
AA
AAA
30
v
C
S
-IC
-3C(
*
0s
I.
O
I
C----Estimated om
•
-50
IIII
S(
IJ
-70
----
0
f
--/
Ave
105ft
-90
0
FS
-
S
0
-110
1r
*
0
Corps Data
MIT Data from 300 ft offset to LS
ESTIMATED MAXIMUM PAST PRESSURE,SECTIONS II
AND III , 180 FT OFFSETS TO LS AND FS
-19-
Figure 1-2
LL.
C)
I-
I,U)
w
C_1
W
IJ,
0
4d
w,
4~
LA.
U)
ILl
C
0a.
w
LL.
z
0
z
w
4
(7SIN)
4; 'NOI1IVA313
-20-
Figure 1-3
WN ,%
I-
w
w
AVERAGE NATURAL WATER CONTENT
PROFILES FOR 105 FT 8 180 FT OFFSETS
FOR SECTIONS II 8 III
-21-
Figure 1-4
II
REVIEW OF CURRENT LITERATURE
The rate process theory and various rheologic models have
been proposed to represent the creep behavior of soils.
behavior of particular concern are:
Creep
strain and strain rate
as functions of time, creep rupture (failure) phenomenon, and
the effects of strain rate on the shear strength of soils.
Several of the more pertinent publications dealing with this
subject are reviewed in this section.
2.1
RATE PROCESS CREEP THEORY DEVELOPMENT
(a) Mitchell, Singh, et al
Singh, Mitchell and Campanella (1968) use Fig. 2-1
to describe soil deformations in terms of rate process
theory.
The theory considers the displacements of flow
units as requiring a free energy of activation, AF, to
surmount the energy barriers as shown in Fig. 2-1.
Shear
forces in the flow units, f, distort the energy barriers
as indicated by curve B and cause preferential flow unit
displacements in the direction of shear force.
X repre-
sents the distance between successive equilibrium positions
and 6, the elastic distortion of the material structure.
-22-
The resulting theoretical expression for strain rate is:
=
=
2X
FX
-- exp (--AF )sinh(2-)
2X kT
(1)
where k = Boltzmann's constant, T = absolute temperature,
h = Planck's constant and R = universal gas constant.
If
(fX/2kT) is greater than one, which is generally the case for
stresses sufficient to cause creep in soils, then:
fl
sinh (2kT) Z 1/2 exp (fX/2kT)
(2)
and
=
kt
-AF
fX
- exp (R- )exp(Tkf)
(3)
"X" is a time and structure dependent parameter which is also
dependent on the number of flow units in the direction of
deformation and the average component of displacement in the
same direction due to a single surmounting of the barrier.
To simplify analysis, Eq. (1) may be written as:
S
= K(t)sinh(aD)
(4)
in which
-23-
K(t) = 2X(t)
kT
-- exp
-AF(t)
RT
(4a)
and
aD = XF/2kT
(4b)
The authors present consolidated undrained creep data for
remolded illite as shown in Fig. 2-2 which conforms to the
form of the theoretical log C/k versus aD relationships.
For
the range of stresses where the exponential approximation of
strain rate is valid, Eq. (4) can be written as:
K(t)
exp(aD)
2
(5)
and "a" can be evaluated from the slope of the straight line
sections of the log & versus D curves where D is the applied
deviator stress:
d log
dD
dD
a
(6)
(6)
Figure 2-3 presents the typical relationship observed by
the authors between log strain rate and log time and indicates
that the following expression is possible.
-24-
K(t)
2
t1 m
= A(t-)
(7)
where m =dd log
log &
(7a)
d log t
and "A" is found by extending the log E versus D line for tl
to the value of D = 0 in Fig. 2-2.
The resulting modifications
yield the following equation for strain rate:
a
t1 M
A(t
exp (aD)
(8)
(8)
A and a appear to be dependent on the particular test
conditions, such as the stress system, while the authors claim
that "m" is a material property which is only slightly influenced by test conditions.
They further point out that m can
be used as a "creep indicator" since low values of m (m<l)
are found for clays that exhibit high creep strains, lower
strength after creep and creep rupture under sustained loads.
Values of m greater than unity are indicative of rapidly
decreasing strain rates with time and decreasing de/d log t
under subfailure conditions.
The condition where m = 1 implies
a constant value of ds/d log t and long term strength equal
to short term strength.
Strains are computed by integrating Eq. (8) over time,
with knowledge of the strain at a known time; a necessary
-25-
condition.
The equations for
strain are as follows (Singh &
Mitchell, 1968):
E=a+ 1 A
aD
1-m
e
(t)
(m
1)
(9a)
(m = 1)
(9b)
where
a =
A
aD
e
e----
and
S=
+ Aea D In t
The authors present laboratory data on London Clay, Osalsa
Clay, Illite and San Francisco Bay Mud to support their theory
and good agreement appears to be present for stress levels
which are 30 to 90 percent of ultimate strength.
The theory
is rather flexible and can handle cases where strain and log
time are either linearly or non-linearly related, which is
an improvement over most rheologic models.
However, the
greatest advantage of this method is the comparative ease with
which the creep parameters can be obtained in the laboratory.
This model will be called the Singh-Mitchell rate process
model.
-26-
Christensen and Wu (1964)
(b)
Another form of the rate process theory is presented
by Christensen and Wu (1964).
Clay deformations are de-
scribed mathematically by the Kelvin-Maxwell model in Fig.
The spring K, represents the initial elastic response
2-4.
and the dashpot, the flow process, the spring K 2 models
the bond strength at particle contacts which resists soil
creep.
The combination of springs K 1 and K 2 represent
the initial elastic response of the soil.
From this rheologic model, the authors obtain the
following expression:
u
1 + A In
tanh [Z(t) + tanh
exp(-A)]
where
A =
K1
aD
3Kl+K2
1
KIK2
Z(t) = 2 a2
K +K2
U* =
1
la
-(l
)
o
loE
t
(dimensionless strain)
-27-
and a,
8,
K1 and K2 are soil parameters which can be de-
termined from experimental creep results.
instantaneous axial strain,
time, t, and (El),
(el)
is the
l1 is the axial strain at
is the axial strain at large times.
The authors assume that creep stops at some large
time after load application and a unique (el)0
is
reached.
Although this assumption may be true for soil with little
creep tendency (m > 1 from Singh-Mitchell theory) it is
not generally acceptable.
Two major drawbacks of this treatment of the creep
process are:
(1)
it only applies to soils with low creep potential
(m > 1),
of which the EABPL clay clearly is not one;
and
(2)
there are no established relationships between
strain rate and time or strain rate and stress level.
(c)
Murayama and Shibata (1961)
The authors use the Eyering rate process relationship
to model soil creep.
The theory is modified to account
for a lower restraining resistance at particle bonds, below
which movements are elastic and time independent.
arrive at the following:
-28-
They
dab
dt
Ab(a-a
-
o)
sinh(b) bab
(1)
O
where
-E
Ab = 2aakT exp
Bb
where
)
(2)
2bkT
K = Boltzmann's Constant
T = absolute Temperature
h = Planck's Constant
A = average distance between unbalanced molecules
n = number of molecules wiht activation per unit
length in the direction of stress
N = number of molecules with activation per unit
area perpendicular to the direction of stress
a
E
0
= restraining resistance
= free energy of activation
Strain equations are developed with the aid of a
rheologic model as shown in Fig. 2-5 and result in:
E
+
1
+
(a-a)
(a-a o )
+B B2E
E
2
2 _2
-29-
log
A2
t
B2E2t
(4)
(4)
(where Ab + Bb from Eq. (1) are changed to A2 and B 2 ) and:
E
t-+OO
- a
E1
+ (a-
o)
(5)
E2
These equations predict a linear variation of strain with
log time, followed by a decrease in slope and the attainment of a constant ultimate value.
They also point out
that the above relations do not apply when an ultimate
stress is reached which brings on failure.
From laboratory
results from long term anisotropic consolidation tests
the authors report that ds/d log t varies linearly with
applied stress, which is in agreement with their equations,
but in disagreement with Singh and Mitchell who find that
log (de/dt) varies linearly with - = D/Dmax .
The authors
also report that long term undrained strength decreases
linearly with the time to failure.
Although their theory development is straight forward
and agreement between laboratory data and theory is
obtained,the Murayama-Shibata relations do not appear to
be as advanced as the work of Singh and Mitchell and therefore are not as useful.
(d)
Shibata and Karube (1969)
Shibata and Karube mainly extend the work of Murayama &
-30-
Shibata and arrive at the same questionable conclusion
that 6d = de/d log t varies linearly with deviator stress
(where *d is deviatoric strain).
While never stating
whether they still believe that strain varies linearly
with log time, they present the following empirical
equation, which is in disagreement with the Singh-Mitchell
model:
Sd = Constant
• exp (Bad)
where B is a stress factor and ad is the deviator stress.
They maintain that "B" is a function of overconsolidation
ratio and that overconsolidated samples yield a steeper
d versus deviator stress plot.
slope on a
Their most credible work has to do with creep strengths
of clays.
The authors state that there exists a yield
value past which sufficient pore pressures are generated
to produce undrained failure, or so-called "creep rupture".
This relationship, which was developed completely empirically through laboratory observation, can best be shown
by Fig. 2-6.
Although this effort is an improvement over the work
of Murayama and Shibata, the same drawbacks still exist
-31-
and the equations concerning strain rate are questionable.
Their section on creep strength is nevertheless definitely
useful.
(e)
Barden
(1969)
Barden maintains that soil deformation is a function
of stress ratio (U1/U3 or Singh-Mitchell's D/Dmax ) .
He
separates the volumetric and deviatoric components of creep
and by use of rate process and the rheologic models in
Fig. 2-7, arrives at the following:
V= vFINAL +
2.3
Ka+
Y = Y
2.3
aBGt
-- log ( 2
Go-
FINAL +
log (a(SKt
2
The volumetric strain and its corresponding equilibrium
value are represented by v and vFINAL and the shear distortion and its equilibrium value by y and YFINAL
The
parameters a and 8 are constants from the rheologic model
and can be obtained in the laboratory.
The strain rates
follow directly from the above equations:
dv/d(log t)
= 2.3/Kc
dy/d(log t)
= 2.3/Ga
-32-
where Ka and Ga are functions of the effective stress ratio.
Although Barden's laboratory data are completely from
drained tests, he presents the undrained laboratory results
of various investigations (including Singh and Mitchell)
which in general support his equations.
Although Barden concludes that his theory is acceptable, he points out that during undrained creep, possible
build up of pore pressures will change the effective
stress ratio and thus, the strain rate.
be bypassed by using the deviator stress.
This problem can
The main draw-
back of Barden's theory is that K and G are probably as
difficult to obtain in the laboratory as E, the undrained
Young's modulus.
(f)
Bishop and Lovenbury (1969)
Bishop and Lovenbury conducted long term triaxial
compression drained creep tests on London and Pancone clay.
Using D = (a1 -a 3 )/(al-a 3 )f of 17-98 percent, they conducted
the tests until either failure was reached or problems
with equipment developed (some of the tests were still
in progress after three years).
Axial strain versus log time was approximately linear
-33-
for samples that did not fail and plots of log strain rate
versus log time were approximately linear (London Clay
data was especially good in this respect) as shown in Figs.
2-8 and 2-9.
Sudden increases in strain rate at large
times or "instabilities" which were accompanied by substantial volume decreases were unexplained although the authors
maintain that these decreases were due to fundamental
modifications in soil structure and not experimental error.
These excellent laboratory data lend great support
to the Singh-Mitchell theory.
Log strain rates vary
approximately linearly with log time over large time periods and it is demonstrated that creep rupture can occur
at stress levels less than full strength.
The only real
drawback in the paper are the instabilities which are yet
to be explained.
-34-
2.2
CREEP RUPTURE
(a)
Saito, et al (1961, 1965, 1969)
Saito and Vezawa (1961) conducted a series of unconfined and triaxial (CU) compression tests on a number
of Japanese soils in an attempt to determine the range
of stresses and elapsed times for which slow creep movements generate into failure.
On the basis of these tests,
the authors claim to have found a unique relationship
between creep rupture life (time after loading) and strain
rate.
This relationship which is linear on a log-log
plot is shown in Fig. 2-10 and appears below as:
log tr(min.) = 2.33 - 0.916 log e(l/min.) + 0.59
(1)
They also add that the following is approximately true:
•* tr = 2.14
(2)
Saito (1965) later defines ý as the constant strain
rate which develops prior to failure and that tr is the
elapsed time from this point to failure.
Saito claims
that the above relationships apply to all soils (this
is obviously the reason for the rather large range for
-35-
tr in Eq. (1)).
He supports his work with several field
cases which are of questionable worth due to the rather
arbitrary way in which strain is measured in the field.
In a later paper Saito (1969) concerns himself
with the transient creep range which occurs at a time
closer to failure than the steady state creep which he
had studied previously.
From his basic steady state equa-
tion, Saito develops a three parameter equation to model
transient creep behavior and presents a graphical solution
for analyzing field problems.
Saito's work is completely empirical and his claim
as to the generality of his equations with regard to
soil type is questionable but it is a step in the right
direction.
The major drawback of his work is that is
appears to be of little practical significance.
Failure
is not indicated until it is actually occuring and by
then remedial action is out of the question.
(b)
Singh and Mitchell (1969)
The authors deal with the problems of creep rupture
and time to failure by modifying their basic equation
(Eq. (8) in section 1.21a).
-36-
= At1 m exp (aD)t1 -
m
Strains at time "t" (for m # 1) are proportional
to it at that time as shown below:
E = C
1
+ l1-m
where
C = E1
For m > 1, it
Ae aDtD1
l-m
is constant or decreases linearly on
a plot of log 6t versus log t.
However, for m < 1,
t
increases linearly with a slope of 1 - m until a given
value of ýt is reached at which time there is a rapid
change to a much greater constant slope as shown in Fig.
2-11.
Singh and Mitchell (1969) define the 6t at which
this event takes place as indicative of failure conditions.
Thus
(it)f is
independent of stress level and appears
Analytically tf can be
to be unique for each soil type.
found by:
loge (tf)=
1
1 -m (C2 -
where
-37-
D)
C2 = loge
(Et)f - log e
(Atl m)
In comparing this method with that of Saito and
Vexawa (1961), we find it to be much more attractive.
Although Saito and Uezawa also arrive at a unique "ft
,
they weaken its development by making it too general while
Singh and Mitchell claim a unique (ýt)f for each soil.
The main advantage is that the Saito relationship is referring to a time just prior to creep rupture (long after
(ýt)f has been reached) and Singh and Mitchell are concerned with a modest change in creep rate long before
shear failure which makes it a more valuable indicator
and eliminates one of the major drawbacks of the Saito
relationship.
But most important, the Singh-Mitchell
relationship is an extension of a much larger development
of a theory for creep in soils and is not merely an
empirical tool.
2.3
CREEP STRENGTH
(a) Arulanandan, et al (1971)
The authors conducted a series of undrained triaxial
compression creep tests on isotropically consolidated
San Francisco Bay Mud in order to prove the Roscoe (1963)
-38-
relation:
q=
where
M
logM
o
(1-K/A) loge P
M = slope of failure envelope on p,q plot
p 0 = isotropic stress
p = mean normal stress
q = deviator.stress
A = C c/2.3 = Compression Index/2.3
K = Cs/2.3 = Swell Index/2.3
Stress levels ranged from 30 to 90% of failure stress
and loads were maintained for two weeks after which time
the unfailed samples were taken to failure.
Results showed that the yield stress was only 60 75% of the ultimate strength for all consolidation stresses.
Creep stress paths crossed both experimental and Roscoe's
(1963) theoretical stress paths.
The large pore pressures
generated during the test were responsible for this phenomenon.
(1)
Possible reasons for these pore pressures are:
leaks through membranes and seals;
(2) osmotic pressure due to the salt concentration
of San Francisco Bay Mud;
(3) structural rearrangement of particles or a
-39-
drainage into micropores from compression of the
microstructure, which is comparable to secondary
compression in their viewpoint.
The last reason is most likely due to the fact that
mercury jackets and a saline cell fluid were used.
Reason three above was further investigated by consolidating samples of San Francisco Bay Mud and Kaolinite
for 30 hours and then closing the drainage valve.
The
results, as shown in Fig. 2-12, indicate that the Bay
Mud, with a high secondary compression tendency, generates
pore pressures due to the arresting of secondary compression.
The Kaolinite, with lower secondary compression
tendency, begins to generate pore pressures but "thixotropy" is thought by the authors to eventually dominate
the process and pore pressures decrease.
The authors therefore conclude that the arresting
of secondary compression during undrained creep generates
large pore pressures which can fail samples at deviator
stresses much lower than ultimate values as shown in
Fig. 2-13.
These results, which tie in well with the creep
failure data of Shibata and Karube (1969), Bishop and
-40-
Lovenbury (1969), Singh and Mitchell (1969) and Walker
(1969) are very useful and their proposed mechanisms may
be helpful in explaining such phenomena.
2.4
CONCLUSIONS
Of the various rate process and rheologic models, the
Singh-Mitchell treatment appears to be the most attractive.
Although this method is of a more empirical nature than some
of the others, it is by far the most advanced and unrestrictive.
The model parameters can be obtained in the laboratory with
relative ease.
Although the Singh-Mitchell treatment of creep rupture
appears to be somewhat superior to that of Saito, it must be
kept in mind that these two theories apply to two different
events in the creep rupture process and both can be evaluated
in the laboratory.
-41-
/
1
Shear force
force acting
no force acting
DISPLACEMENT
(a) REPRESENTATION
I AJ•.
OF ENERGY BARRIERS
POSITIONS
SEPARATING
EQUILIBRIUM
A
IUUU
500
200
100
50
20
10
1.0
0.5
0.2
0.1
0 'f
(b) 6/K
VERSUS c< 'f ACCORDING
EXPONENTIAL
TO HYPERBOLIC
SINE AND
FUNCTIONS
DERIVATION OF BERKELEY THREE PARAMETER RELATIONSHIP
BASED ON RATE PROCESS THEORY (After Mitchell et al, 1968).
-42-
Figure 2-1
-2
Ix 10
-4
4x104
4
Ix 10
-5
4x1O6
Ix 105
4 x1O
-6
Ix -6
-7
Ix 10 Q2
0.6
DEVIATOR
1.0
STRESS, 1-
3-
1.4
D- kg/cm 2
1.8
VARIATION OF STRAIN RATE WITH DEVIATOR STRESS FROM
CIU C CREEEP TESTS ON REMOLDED ILLITE (After Singh and
Mitchell, 1968)
-43-
Figure 2-2
YII
1
;·~i -"----
a~~~~i~~~o~a·nnai
0.1
.01
'001
.0001
.00001
10
100
TIME ,MINUTES
INFLUENCE OF TIME ON STRAIN RATE DURING CREEP
OF REMOLDED ILLITE (Mitchell et, al. 1968)
-44-
1000
/
RHEOLOGIC MODEL FOR CHRISTENSEN AND WU(1964)
RATE PROCESS DEVELOPMENT
-45-
RHEOLOGIC MODEL FOR MURAYAMA AND SHIBATA(1961)
RATE PROCESS THEORY
Figure 2-5
-46-
~~:;a~i~
:~b-`~,''r`·""-br
.~~l~*Z
b~C
~
~
JII
~I
.~;
ro
cH
l-)
4-)
o
Uo
0
N
_
a.
·.o
0n
U
To
Q)
r-i
U
El)
4-
O
ri)
00
(5
v
Figure 2-6
-47-
~
-11-
F
---
VbAvUHE7rA/e-
I
I
FIGURE 2-7
.,r.
COdfPAE~SS/OA'
=,off
5 HA.
PR
PWA
1
I
P /S,O
l
R/7-cIO
Barden's Rheologic Model (Barden,1969)
Figure 2-7
-48-
_i~o!---
_
I O
IV,
H
t.
01
,o0
O
.0001
0.o
/
T/ffME,
/0
PR YS
/00
/o000
DRAINED TRIAXIAL CREEP RESULTS ON PANCONE CLAY
(Bishop and Lovenbury, 1969)
Figure 2-9
-50-
~
I
i 77-.~N1*?J;~F
77
I
i·.rýV-w
;r.·-n;:;·n
r%
0
4-)
HU)
4
4)
HO
H
12
(fW)..71
/7
/7Jd.f7
d-7-33V
Figure 2-10
-51-
oa
LO
01
C)
Ci)
0r
oo
H
OO
o4
a
ClW,
a)
Q)
a'
,O~
Figure 2-11
Figure 2-11
-52-
4J
0
Cd
Q)
a)
a)
m
ý::I
U)
0
O
•
oO
'
n0
r-
0
S(C
0
m
O
0
o
i0
>)
~
H
u
<
40
>
HO
C)
0)
N
e,
J
I
L1
O
7
r%.
Ah'/)/ .y/d5-5$
-s3
7 H•/•>
-53-
3Y/
.".•n
• d
N(.
Figure 2-12
y
W
0
7
0
0
2'
0
4U)
v
(2)
QJ
0
0
e0
Ic
U
rO
12,
Enr
a
la)
U)
Cd
Cd
Cd
Sa)
Cd7
Ug
(5c·
d~z
Y'IOz/4ap)
g
7igure 2-13
-54-
Li
III
3.1
DESCRIPTION OF EQUIPMENT AND PROCEDURES
INTRODUCTION
The Direct Simple Shear device used for this investigation
was developed by the Norwegian Geotechnical Institute and
manufactured by Geonov.
It is very similar to the machine
used for tests described by Bjerrum and Landva (1966).
The
primary requirements that the machine satisfies are:
(1) Ability to induce fairly uniform horizontal shear
deformations in a cylindrical sample.
(2)
Capability of performing drained or constant volume
tests.
(3) Ability to keep the upper and lower sample surfaces
parallel during testing.
(4)
Controlled stress on strain.
(5) Maximum vertical load of 800 kg, horizontal load
of 400 kg.
(6) Designed for 50 cm 2 by two cm sample confined in
a wire reinforced membrane.
-55-
(7)
Capability of testing soft clays as well as stiff
clays, silt and sand.
A method of sample prepara-
tion was devised that minimizes sample disturbance.
3.2
SHEAR APPARATUS
The shear apparatus (see Fig. 3-1) is composed
of the
sample assembly, vertical and horizontal load units and a horizontal load hanger assembly.
The sample assembly consists
of lower and upper filter caps (16), pedestal (17),
and a plastic reservoir for inundating samples during testing.
The vertical load unit consists of the base (18), tower
(19), lever arm (12), load gauge (4),
piston (20), dial gauge
for vertical deflection measurements (6),
adjustment (21).
and lever-arm
The lever-arm has a load magnification ratio
of 10 to 1 and is built into a U-formed hanger.
A counter
weight (22) balances the weight of the load-gauge, piston and
sliding box.
The horizontal unit consists of a gearbox (11), proving
ring load gauge (10), precision ball-bushing (9) and connection
fork (23), and the sliding box (7).
The present machine,
Model 4, strains the sample by moving the top cap while holding
the bottom cap and pedestal stationary.
-56-
The horizontal load
is transmitted from the horizontal piston through the fork
to the sliding box and top cap.
The limit of travel is 10 mm
in either direction from zero strain.
3.3
SAMPLE PREPARATION
By a system of vertically aligned cutting cylinders, top
and bottom caps, pedestal and membrane streching device, the
cylindrical sample is mounted in position and confined by the
wire reinforced rubber membrane.
The procedure is designed
to support the sample at all times while minimizing distrubance
and is much easier than sample preparation for the triaxial
test (see Landva (1964) and Edgers (1967) for more detail).
3.4
TESTING PROCEDURE
For all tests, the sample was installed in the machine
and consolidated by dead load increments until the desired
consolidation stress was reached.
All samples were consoli-
dated to a stress sufficiently greater than the insitu vertical
stress so as to minimize the effects of sample disturbance.
The reservoir was not filled until
in order to avoid swelling.
v
= 0.4 kg/cm
was applied
The final increment for normally
-57-
consolidated tests and the maximum and final loads for overconsolidated samples were allowed to consolidate for approximately two days in order to develop a constant degree of secondary
compression.
For constant volume controlled strain tests, the shear
procedure was that described by Edgers (1967).
For controlled stress constant volume creep tests, the
horizontal proving ring was removed and the horizontal load
was applied by means of the hanger assembly.
After consoli-
ation was complete, the lever-arm was connected to the vertical
load adjustment screw and the appropriate horizontal load
applied to the hanger assembly.
The test was started by un-
clamping the horizontal piston and readings of horizontal
strain with time commenced.
As in the standard constant
volume controlled strain test, the vertical load was adjusted
in order to maintain constant sample volume throughout the
test.
Most of the adjustments occurred in the first two hours
and usually only one adjustment per hour was needed thereafter
on the first day and only one or two adjustments per day were
needed on subsequent days.
The total number of adjustments
needed for an average test duration of one week (\ 10,000
minutes) was on the order of 25.
test was approximately 690 F.
Room temperature during the
Fluctuations of + 20 F were common
during a 24 hour period.
-58-
i
1 Sample 2 Reinforced rubber membrane 3 Wheels for
applying dead load 4 Load gauge for vertical load
5 Ball bushing 6 Dial gauges for measurement of vertical
deformation 7 Sliding box 8 Dial gauge for measurement
of horizontal deformation 9 Ball bushing 10 Load gauge
for horizontal force 11 Gear box 12 Lever arm
13 Tieights 14-15 Clamping and adjusting mechanism used
for constant volume tests 16 Lower and upper filter
holders 17 Pedestal 18 Base 19 Tower 20 Vertical
piston 21 Adjusting mechanism 22 Counterweight
23 Connection fork 24 Horizontal piston
Fig. 3-1
General Principle of Direct Simple-Shear Apparatus,
Model 4 (Edgers, 1967)
Figure 3-1
-59-
IV
4.1
EXPERIMENTAL INVESTIGATION
SOIL TESTED
The soil for this investigation was obtained from five
inch diameter undisturbed fixed piston tube samples obtained
from three borings offset approximately 300 feet to the landside of Test Section III.
Boring
No.
Station
No.
Offset (ft)
94ues
1395+50
310 LS of BL
10A to 13C
-30.5 to -45.8
95ues
1395+45
305 LS of BL
10A to 13C
-30.6 to -45.6
96ues
1395+55
305 LS of BL
10A to 13C
-30.5 to -45.3
Samples
El. (ft)
Samples used in the investigation ranged in elevations
from -35.9 ft to -44.15 ft.
Values of
vo for this layer,
which appears to be either normally consolidated or slightly
over consolidated (see Fig. 1-2), range from 0.55 to 0.70
kg/cm2 according to Foott and Ladd (1972).
Consolidation
curves for the Direct Simple Shear Tests conducted in the
program yielded maximum past pressures in the range of 0.70
to 0.85 kg/cm 2
-60-
Atterberg Limits were conducted on a number of representative samples and the results are shown, along with those obtained by the Army Corps of Engineers, in Fig. 4-1.
A series of constant volume controlled strain directsimple shear tests were conducted on a number of samples at
various overconsolidation ratios.
4.2
TEST PROGRAM
As previously stated, the testing program was conducted
to achieve the following:
(1) A relationship between s
vc and OCR for CKoU DSS
controlled strain tests.
(2)
Investigation of the applicability of the SinghMitchell Rate Process Theory for EABPL Clay with
regards to strain and strain rate as functions of
time, stress level and overconsolidation ratio for
first load increments.
(3) Investigation of the applicability of the SinghMitchell and Saito creep rupture theories for EABPL
Clay.
(4) The effect of time on the strength of EABPL Clay.
-61-
In addition, the testing program was designed to investigate
the behavior of additional load increments with respect to
strain and strain rate as functions of time, stress level
(applied horizontal shear stress/horizontal shear stress at
failure, TH/Tmax) and overconsolidation ratio.
It was hoped
that a method could be developed for translating second and
third load increment data into the form of initial load performance.
The program designed to achieve these objectives is
outlined in Table 4-1 and is basically of two parts:
(1)
the CKo U DSS controlled strain shear tests, and (2) the controlled stress creep tests.
Tests Nos. 2 through 7 were used
to develop the sU/-vc versus OCR relationship from which
various stress levels for the creep tests can be calculated.
The remainder of the program consists of undrained creep tests
on normally consolidated and overconsolidated samples in which
the number of increments, the stress level and the load duration time serve as variables.
4.3
4.3.1
TEST RESULTS
Controlled Strain Tests
CK U DSS tests were conducted on seven samples of EABPL
Clay.
The results are shown in Table 4-2 and Figs. 4-2 to 4-7.
-62-
CK U DSS-l was lost due to equipment failure and was therefore not tabulated.
The normalized shear strength (Su/6 vc)
for normally consolidated samples was very consistent at
Failure occurred at very high shear strains of 20%
0.23.
and more for normally consolidated samples but this value
was somewhat reduced for highly overconsolidated specimens.
It was interesting to note that the maximum value of TH/'v
occurred simultaneously with the maximum value of TH for most
of the overconsolidated samples though this was not the case
with normally consolidated tests.
A plot of normalized shear
strength versus log OCR yielded the smooth graph in Fig. 4-7.
4.3.2
Controlled Stress Creep Tests
A summary of the 12 CK U DSS Creep tests appears in
Table 4-3.
Appendices B and C contain tabulated test data;
strain, log strain rate and log tt versus log time curves;
stress paths and stress-strain curves for the 12 tests.
Summary
plots of the data are presented in Chapter 5.
4.3.2.1
Initial Stress Levels
Various shear stress levels were applied to the samples
after consolidation was completed.
-63-
These levels consisted of
50, 65, 73, 80, 85, 90 and 94 percent of failure for normally
consolidated samples and 50, 72 and 94 percent for samples
with OCR = 2.
Samples were allowed to creep for one week
(10,000 minutes), except CKoU DSS-12 where D = TH/Tma x = 73%
was left on for 40,000 minutes.
4.3.2.2
Additional Shear Increments
Additional higher shear stress levels were applied to
samples that did not fail under their initial loadings.
These
second and third increments were also allowed to creep until
either creep failure occurred or a week passed.
These loadings
are listed in Table 4-3.
4.3.2.3
Creep Failure
Creep failure occurred in 11 of the 12 tests.
The first
test (CK U DSS-8) was failed by controlled strain after three
shear stress increments had been applied over a three week
period.. For the remaining tests, creep failure eventually
occurred at all applied shear stress levels of 85% or more.
-64-
I
TABLE 4-1:
Test No.
CKoUDSS-1
CK UDSS-2
o
CK o UDSS-3
CK UDSS-4
o
CK UDSS-5
CK UDSS-6
o
CK UDSS-7
CK UDSS-8
CK UDSS-10
o
CK UDSS-11
o
CK UDSS-12
CK UDSS-16
o
CK UDSS-17
CK UDSS-18
o
CKoUDSS-19
CK UDSS-20
CKoUDSS-21
CK UDSS-22
o
CK UDSS-23
Type
Controlled c
SUMMARY OF SAMPLES FOR
TEST PROGRAM
Boring
Sample
W,%
96UES
96UES
11B
liB
72.2
Elevation, ft
-35.9
-36.1
Controlled
Controlled
Controlled
Controlled
Controlled
96UES
96UES
11B
11B
72.6
-36.2
76.3
-36.5
96UES
11C
91.7
-36.9
96UES
11C
86.3
95UES
10B
78.1
-37.1
-32.1
Creep
Creep
Creep
Creep
Creep
Creep
Creep
Creep
Creep
Creep
Creep
Creep
94UES
1IC
73.8
-36.7
94UES
13C
84.9
-45.0
94UES
13A
27.2
-42.7
94UES
13A
86.7
-42.9
94UES
12C
73.4
-40.5
95UES
13A
79.1
-44.0
95UES
13A
79.2
-44.1
95UES
95UES
12D
12D
67.7
-41.2
-41.3
95UES
12D
75.1
95UES
12D
77.3
-41.5
-41.6
94UES
10B
79.5
-32.0
Controlled s
-65-
80.1
0
U)
<O .c
E
0
00
0-
E
1c
L
3
o
8 omo, o o
o o,8,8
ao
o 0 oU o n 0re pO U( OO - r 0o 1o 0
1 o ro I)
+
oo
cm
E
o
c
C
(,
cn
0
=
0
0
(D
So
+1
0
0
OD 0
C0
0
U)
(,
L.
u,
-j
O
-J
a-
z
0
U)
=(0
'z
0"
00-
L0N000 •D 0XI e
•N
(e0
r ocK)
C6
ID
C 000
-•
0to0-0
Ln
cda 0+c0o
O
0
0 00N)' NO
oa Ob' ca N
.0 0
r)U
d N
w
N
0--
0- 0
r 00
0 0LO
It
) 0o
o0
O
0
U)
Ur)
>-U)
rU
0
O0
o
_
U))
U)
00
0 -- 0
o
(D0
N
NO
U)
U~
0
U)
0
0
00
O
_o
0
D
O
c
4-
n
0
0
U)
I
__
_
N-
-
N
N
_
d
_
N
___
-
1-
C
U)00
w50
0N<
o
o
(i
0
N
c
U)-IS
, .,
0V
-66-
Table 4-2
000
0
0
0
0
0
0
co "-I kD
r-I H0
I
4--
Lnr-I r-I
CN
r-! r-t
o 0
CN Cm
000r
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-67-
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-68-
E-1
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TABLE 4-4:
DESCRIPTION OF MEASURED TEST PARAMETERS
Stress Level (DT ) = (TH/TH ma x )
Yo (Initial Shear Strain, %) = y @ t = 1 Minute
%
(Initial Strain Rate, %/Min.) =
'
@ t = 1 Minute
yf (Final Shear Strain, %) = y @ tf
(rt)f (Final Strain Rate X Elapsed Time, %) = ýf X tf
tf (Final Elapsed Time) = Length of Time the Shear Stress
Increment (DT)
Was Left on Sample
Y1 (Steady State Strain) = Strain at Which a Second or Third
Load Increment Began to Follow the
Singh-Mitchell Theory (See Section
5.2)
nl
(Steady State Strain Rate) = Strain Rate at Which a Second
or Third Load Increment Began
to Follow the Singh-Mitchell
Theory
tl
(Elapsed Time) = Elapsed Time at Which y1 and ~l Occur
-1
at t = 1 Minute for a Given DT
(tan- TH/ Yv ) =
ý (tan--f TH/ vv) =
at tf
~f(tan
TH/a )
= $ at tf
-69-
ow
Uj
Cd
r4
zz0
J )-j
o
31'*
i < G1
0CLa w
o
oo
>-u
O
LA
gJ):O
I
oW
0a
~
wjI-.JI ,
UuZnoo
PH
Cl)
C+
*H
C)
0
Q)
4-,
C)
C
4-)
Cl
P4
O:
O;
------ o
O
0
X30NI
0
0
0
A)lI1S.•1d
-70-
Figure 4-1
SO
Ib
SHEAR
STRAIN
, 7,%
164
Ib
I
C
I
I1a
C
C
SHEAR
Symbol No.
----
2
72t 41
-
3
72.- 63.7. 1.02 L5 -36
4
763 5&91 205 1.7 -36
-
--
3.1
1.0 -36
-71-
STRAIN
Y, %,
CKoUDSS
NOR MA LLY
EABPL
TESTS
ON
CONSOLIDATED
CLAY
Figure 4-2
0.8
0.6
'-C
0.4
0.2
0
0.4
IIb
9
0.0
< -0.4
-n)A
0''
5
10.
SHEAR
15
STRESS VS. STRAIN FROM CKoUDSS
-72-
20
30
STRAIN r, %
TESTS ON EABPL CLAY
Figure 4-3
U
a,
0tr
W
I-O
zZ.I-
w
LL
V-
w
F-
a:
w
-i
I-
oE
U.
-r
_-o4
/
'SS3I.LS
iV3HS
-73-
03ZI-VI•VON
Figure 4-4
0
ba.
m
LU
If
w
Z
0
w
U)
I
>
U)
w
HL
H,
a
0
l--
cr
w
0
cr
a
w
LU
-J-
Z0
-J
U)/
'sss
WA5 U1
'SS3d.LS
8V3HS
-74-
'
033ZIflVlIVON
N
Cl
0
Z
Ficure 4-5
0
z
-J
cQ
i-0
ui
vc , TSF
Symbol
--
-- o--
_-
-
-
No.
Wn,% El.,ft.
2
72 t
3
726 -36
4
5
6
7
76.3
91.7
86.3
78.1
-36
-36
-37
-37
-32
CURVES
COMPRESSION
TESTS
CKoUDSS
EABPL
CLAY
-75-
Figure 4-6
U
I16>
q)
OCR =
m/
"vc
SU /Fi& VS OCR
FROM CoU
DIRECT- SIMPLE
SHEAR TESTS
CLAY
ON
EABPL
-76-
Figure 4-7
V
5.1
DISCUSSION OF TEST RESULTS
FIRST LOAD INCREMENTS
The term first load increment refers to the first
increment of shear stress which is applied to the sample
after consolidation is complete.
shear strain is zero.
Prior to this process the
The Singh-Mitchell Rate Process Theory
is concerned with the undrained creep that occurs due to this
loading.
5.1.1
Normally Consolidated Samples
Results from first loadings on normally consolidated
samples are presented in Figures 5-1 through 5-4.
Within
the first minute of loading there occurred an instantaneous
shear strain (y ) which can be determined from Figure 5-1.
From that point the creep process for stress levels (5 ) of
80 percent or less appeared to follow the linear relationship
between log strain rate (f) and log time which is the basis
for the Singh-Mitchell theory (see Fig. 5-2 and 5-3).
For
stress levels greater than 80 percent, the plots of log strain
rate versus log time were initially linear, but the strain
-77-
N
rate then became constant in each case and then increased
as the sample creep ruptured.
This phenomenon will be covered
in detail in a later section.
Unlike the Singh-Mitchell Theory where log-log plots
of strain rate versus time yielded parallel lines for the
various stress levels (D), EABPL clay yielded straight lines
which were divergent with time or in other words, "m" was
not constant but a function of stress level, D , as shown
in Fig. 5-13.
(Note:
Singh-Mitchell's D refers to the deviator
stress ratio in the triaxial test:
al- 03
(a1 - a3 )f
Since the deviator stress cannot be determined in the simple
shear stress system, D T refers to the applied horizontal
stress ratio,
TH/T H
max).
Therefore, "m" which is supposedly
a constant parameter for a given soil and the index of that
soil's creep tendency, is in fact, for EABPL clay, a variable
which demonstrates that this clay has greater creep tendencies
(decreasing "m") at higher shear stress levels.
Another point which is of interest concerning Fig. 5-2
is the presence of discontinuities in the linear plots which
-78-
take place at approximately t = 400 minutes.
For all stress
levels above 50 percent (except for those that caused failure)
the strain rate begins to decrease a few hours after loading
at a greater rate than that of the initial log-log plot of strain
rate
versus time.
At approximately t = 400 minutes, a new
log-log linear relationship is established which results in
a straight line which is "below" the initial line and has
a higher value of "m".
The sudden application of a shear
stress induces positive pore pressures within the sample.
The
vertical stress is reduced to compensate for this but since
Cv is not equal to infinity, time is required before equilibrium returns to the sample.
No doubt the average pore
pressure in the sample is close to zero (because the sample
volume remains constant) but pore pressures within the sample
interior are probably greater than zero and those near the
edges are negative.
The time required for equalization is
on the order of 400 minutes, which is approximately the time
required for primary consolidation in normally consolidated
EABPL clay based on Cv = 0.01 ft2/day.
This value of Cv is
within the range recommended by Ladd et al (1972).
The
hypothesis is further supported by the fact that this
phenomenon is only barely noticeable for stress levels (iT)
of 50 percent.
As can be seen with the hypothetical stress
path in Fig. 5-9, the induced pore pressures for higher stress
levels are much greater.
-79-
I
41
Assuming this hypothesis to be correct, the pore
pressures within the sample interior (i.e. on the potential
failure plane) decrease the effective vertical stress.
Since
the shear stress is unaffected by pore pressures, the resultant obliquity (TH/av) is greater than that applied and
is equal to the obliquity that one would normally obtain from
a higher application of DT.
Only when the induced pore
pressures are dissipated will the obliquity within the sample
and the resultant creep behavior correspond to that level
normally associated with the applied DT
.
This situation makes determination of the remaining
two parameters in the Singh-Mitchell equation particularly
difficult.
The two constants (A, U) are obtained from a
plot such as that presented in Fig. 5-4.
Since the obliquity
at small times (t < 400 minutes) is larger than that normally
associated with the applied 5T, the strain rates at small
times for a given DT are higher than they should be.
Since
this effect is more marked for larger stress levels, the
resulting slope (1) is too large.
A more reasonable result
can be obtained by extending the steady state portions of
the plots (t > 400 minutes) in Fig. 5-2 back to small times.
The resulting data points yield slopes (M) which are probably
more representative of the true soil behavior.
As can be
seen in Fig. 5-4, all laboratory data points lie above the
-80-
I
modified data for all times except t = 1000 minutes where
there is uniform scatter, which is consistent with the
hypothesis.
5.1.2
Over Consolidated Samples
Results from first loadings on three over consolidated
speciments (OCR = 2) are presented in Figs. 5-5 through 5-8.
The creep behavior is essentially that of the Singh-Mitchell
Theory, with "m" decreasing with increasing stress level.
In contrast with the creep behavior of the normally consolidated specimens, there occurred no discontinuity at t = 400
minutes on the log-log plot of strain rate versus time.
The
author believes this to be due to the fact that the stress
path for OC samples is such that initial pore pressure
development is not significant.
As a result, "m" remained
essentially constant throughout a given test.
It was also found that "m" for any given stress level
is significantly less than that for normally consolidated
EABPL clay.
Inspection of Fig. 5-10 shows that initially
the normally consolidated samples exhibit a higher strain
rate but that the curves converge with time due to the lower
"m" value for the OC samples.
At large times the OC samples
exhibit greater strain rates.
-81-
Initially, for a given value of D-,
the OC sample is
closer to the failure envelope (see Fig. 5-11).
Nevertheless,
the strains obtained at t = 1 minute are essentially equal
for the two stress histories
(see Fig. 5-17).
This is to
be expected since Fig. 4-3 shows that equal values of 5 T
yield nearly equal values of strain during standard controlled
strain CK UDSS tests.
o
The plot of normalized pore pressure versus shear strain
for standard CK UDSS tests in Fig. 4-3 shows that initially
o
two entirely different phenomena occur during the shearing
of the NC and OC (OCR = 2) samples.
It is only after
approximately 6 percent shear strain has occurred that the
OC sample begins to develop positive pore pressures (i.e.
develop a positive slope in Fig. 4-3) and behave in a manner
similar to that of the NC sample.
Strangely enough, the
plots of the two samples become parallel at this point and
failures occur at nearly equal strains.
Figure 5-12 is a
plot of Au/o
versus y for standard CK UDSS tests and CK UDSS
vc
o
o
creep tests at DT = 0.50, 0.72 and 0.94 for NC and OC samples.
The author believes that pore pressure generation during
undrained shear and creep behavior (i.e. strain rate) are
closely linked.
Since the NC and OC standard CKo UDSS tests
behaved quite similarly with regards to stress versus strain,
it would appear that one could compare the creep behavior
-82-
of NC and OC samples by looking at the amount of pore pressure
generation with strain (slope of the curve) relative to
that of the standard CK UDSS test for each group (NC and OC).
O
For instance, in the case of D
= 0.50, the two tests (NC
and OC) begin with nearly equal strains at t = 1 minute
though the OC sample is at a stress state in terms of effective stress that is closer to failure.
Inspection of Fig. 5-12
shows that pore pressure generation for a given strain increment for the NC sample has increased over that of the standard
CKRDDSS test.
At the same time the OC sample shows a signifi-
cant decrease from that of the standard test.
At a later
time, the rate of pore pressure increase with strain for
the NC sample decreases while that of the OC sample radically
increases.
As a result, the rate of pore pressure develop-
ment with strain relative to that of the corresponding
standard test is greater for the OC samples.
Therefore,
the rate of strain rate development is greater for the OC
sample though the magnitude of the strain rate may not be
greater.
Inspection of creep curves for b T = 0.72 and their
positions relative to the standard CK UDSS curves shows a
o
similar phenomenon.
On the other hand, the curves for
T =
0.94 are very similar to their parent curves, the standard
CK UDSS test results, but are only displaced to the right.
o
As a result, their creep behavior are very similar.
Figure
5-13 shows that the two plots for NC and OC samples tend to
-83-
converge at high stress levels, which is what Fig. 5-12
implies.
The author realizes that the "m" value for the
NC samples was obtained at small times and is therefore
not the true value which is representative of the stress
level.
But it must be kept in mind that the initial unequal-
ized pore pressures developed in the NC sample effected
strain rate
level to a far greater extent and that "m" was
not greatly affected by the phenomenon.
Due to the small amount of data for the OC samples and
the difficulty with which good pore pressure data can be
obtained in the direct simple shear device, this proposed
explanation is mainly conjecture.
A similar test program
with triaxial equipment would definitely be a great help in
evaluating this hypothesis.
Calculation of T and A presented little problem though
their reliability is questionable due to so little data
(three tests).
The value for T was greater than that obtained
from the normally consolidated tests and "A" was somewhat
lower (see Fig. 5-8).
-84-
5.2
ADDITIONAL LOAD INCREMENTS
For all tests where failure did not occur as a result
of the initial shear stress increment, the stress level was
increased and creep was allowed to continue.
Examples of this second (or third) load creep behavior
are shown in Fig. 5-14 along with results from first load
tests for comparison.
Other examples can be found in Tests
8, 16, 19 and 23 in Appendix C.
initially almost nonexistant.
In all cases, creep is
The strain rate at small
times for a given stress level is much smaller than that of
a comparable first load test (same D ).
Apparently, creep
from the previous increment has caused a modification in soil
structure that results in a more creep resistant sample.
After a period of time, the creep process begins to accelerate
on a log time scale and the plot of log strain rate versus
log time begins to approach that of the first load test for
the same f
(see Fig. 5-14).
At some elapsed time, tl, this
plot intersects the "firstload plot" for that stress level
and takes on the log linear
theory.
behavior of the rate process
This is true for both normally consolidated and
over consolidated samples.
-85-
-I..
There does not appear to be any way of expressing this
phenomenon in quantitative terms.
The values of the initial
strain and strain rate as well as the strain, strain rate
and elapsed time at which the creep process begins to follow
Singh and Mitchell's theory appear to be rather random.
No
doubt they are dependent on AD T as well as the magnitude of
the previous increment and its length of duration.
Analysis of this phenomenon was hindered by the lack
of data as there were only four tests in which either first
or second increments did not cause creep rupture (D
5.3
< 0.85).
CREEP RUPTURE
Creep rupture is the condition when strain rate increases
abruptly and strains become excessive.
As can be seen in
Figs. 5-1, 5-2, 5-5 and 5-6, this phenomenon occurred for
stress levles (DT) of 85 percent or more.
5.3.1
Singh-Mitchell Creep Rupture Relation
As mentioned in Section 2.2 on creep rupture, Singh and
Mitchell define creep rupture as a sudden increase in the slope
-86-
of the log 't versus log time plot as shown in Fig. 2-11.
They claim that the value of it (or it) at which the change
in slope occurs is unique for a given soil.
In the EABPL test program eleven samples were brought
to failure through creep rupture.
For each case a value of
(it)f (i.e. the point at which there is a sudden increase
in slope) was obtained from the appropriate plot by laying
off tangents to the two line segements of significantly
different slope.
For the four tests in which the samples
were brought to failure under the initial load increment,
a consistent (tt)f of 5.2+ % was obtained independent of
stress level and OCR (see Table 5-1).
one test (CK-~bSS-19)
0
There occurred only
in which a steady state condition was
reached by an additional increment just prior to failure
(see Fig. 5-15).
In all other cases the additional incre-
ment which led to failure never attained a strain rate
consistent with the Singh-Mitchell Theory before it reached
the failure condition.
Because of this, the resultant curve
of log it versus log time was much too smooth and yielded
a value of (it)f which is much too low as shown by C-K~ DSS-10
in Table 5-1 and Fig. 5-15.
By contrast, the log it versus
log time curve for CK UDSS-19 quickly changed slope at
t = 500 minutes when steady state was reached and assumed
-87-
a "first increment-like" appearance as shown in Fig. 5-15.
The resultant (it)f of 6.0 percent was also consistent with
first load increments.
All other tests which were failed
by additional increment were rejected due to the fact that
steady state was not reached prior to failure.
It was interesting to note that the average total strain
at t = tf (see Table 5-1) for the five tests (all those in
Table 5-1 excluding CK UDSS-10) was approximately 20 percent
which was the average strain at Tmax obtained for the controlled strain CK UDSS tests at OCR = 1 and 2.
o
Apparently
the occurrence of a unique (it)f which has units of strain
is coincident with a unique undrained yf which are 5.2
percent and 20 percent, respectively, for EABPL soil.
5.3.2
Saito's Creep Rupture Relation
As presented in Section 2.2, Saito (1961) has developed
an empirical relation for creep rupture.
log tr = 0.50 - 0.916 log
E
+ 0.59.
The equation is
The value of e is the
strain rate at which the slope on the log-log plot of
strain rate versus time becomes zero (i.e. constant E with
time).
This phenomenon can be seen in Fig. 5-2 for values
of 5DT greater than 80 percent.
-88-
The variable "tr"is
the
elapsed time that will occur from the attainment of a
constant strain rate to creep rupture (E
+
c).
This relation was applied to the eleven EABPL tests
and the predicted times to failure compared to those actually
obtained in the laboratory (see Table 5-2).
In all cases
the time to failure fell within the range presented by the
Saito relationship, but that range is so large, due to the
gererality of the equation, that it is of little use.
The
+ 0.59 in Saito's relation represents a time range of more
than one log cycle.
that in
For short times to failure such as
CK o UDSS-17 this range only constitutes two hours,
but at large times to failure of perhaps one to four
weeks, a log cycle of 90,000 minutes, or more than two months
is the range.
Another major drawback with the Saito relation is that
failure is not indicated until it is obvious.
By inspection
of Fig. 5-1, it can be seen that failure was imminent for
all stress levels of 85 percent or more as early as 10 minutes after their application to the sample.
-89-
5.3.3
Strength Decrease Due to Creep
Inspection of Table 5-3 shows that stress levels of
85 percent or more caused creep rupture.
of
4
Since the values
at failure were approximately those obtained in
conventional undrained direct-simple shear tests, these
failures were due to the generation of pore pressure of
much greater magnitude than are normally obtained for a given
stress level.
This process can be seen quite easily by
inspection of the creep stress paths in Appendix C.
For
all stress levels, generation of large pore pressure during
creep produced stress conditions which are much closer to
failure than are obtained in the conventional CK o UDSS test.
This phenomenon is particularly marked with the first
increment, such as that (D = 0.729) in CK UDSS-10.
These results agree quite well with those obtained
by Shibata and Karube (1969), Bishop and Lovenbury (1969),
and others.
value of
It is interesting to note that the average
f obtained from the creep tests is consistent
with that obtained from standard CK UDSS tests.
Apparently
the failure envelope for undrained shear of a given soil is
unique and independent of the mode of failure (controlled
stress or controlled strain).
The mechanism of failure
must be the same for both cases.
-90-
It is difficult to believe the concept of a yield value
as presented by Shibata and Karube (1969) (see Fig. 2-6).
If one accepts the Singh-Mitchell model, which the author
does, then given enough time on a log scale, sufficient
strains and pore pressures will be generated to bring about
a failure condition for any significant stress level
(DT> 30%).
The threshold value of 85 percent obtained in
this investigation is the minimum stress level at which
sufficient pore pressures could be generated to cause
creep rupture in a convenient time period (less than a
week).
5.4
COMPARISON OF SIMPLE SHEAR STRESS LEVELS WITH TRIAXIAL
STRESS LEVELS
The original Singh-Mitchell laboratory investigation
which was undertaken as part of their rate process development was conducted with triaxial equipment.
Therefore, the
Singh-Mitchell definition of U(= Aq/AqF) differs from that
used in this investigation with the Direct-Simple Shear Device.
For CKo UDirect-Simple Shear Device:
(Pore Shear Assumption)
From Ladd and Edgers (1971),
-91-
=
,1,
.2
N (I-Ko
=
vc
Tan
p
(TH
4
T
vc
Hvc
H VC
(1-K )/2 + q/U
=
S= 900 - a, Fig. 5-18 indicates rotation of principal
planes.
For CK 0 U Triaxial Compression:
Tvc (1-K)
0
qi=
S
2
qf =
Aqf = qf-qi
=
c
(1-K )
Su
2
vc
S
q
vc
vc
, Aq =
*
Aqf
qi + Aq
q + Aqf
qf
S
[-Ku
+
2
D
o
(S /=
1-Ko
vc
U vc
Calculations are shown in Table 5-4.
Though the exact state of stress in the direct-simple
shear sample is
not known at any time during shear,
-92-
the
direct shear assumption probably gives one the closest
approximation to the actual stress state.
As one can see in Fig. 5-18, the difference in stress
states for the triaxial and direct simple shear samples is
not extremely large for the ranges of stress level with which
the test program was concerned (D- > 50%).
This difference
reduces considerably with increasing stress level and OCR.
5.5
USE OF MULTI-INCREMENT TESTING
By utilizing the Singh-Mitchell equations,a series
of "first increment" strain-log time curves can be developed
from one test.
This can be accomplished by applying a series
of three or four shear stress increments to one sample and
allowing creep to develop for each loading.
If each
increment (after the first) is allowed to pass through its
transient state and begin to behave in the manner predicted
by Singh and Mitchell, an "m" value for each stress level
(D ) can be found and plotted as in Fig. 5-13.
The various
log-log plots of strain rate versus time for the steady state
at large times can then be extended back to small times
(t < 400 minutes), and a plot such as Fig. 5-16 can be
-93-
obtained.
From these data the parameters "A" and "a" are
calculated as in Fig. 5-4.
The final data to be obtained
are the initial shear strains at t = 1 minute which are
shown in Fig. 5-17.
These various parameters can then be used in conjunction
with the Singh- Mitchell equation for strains:
Yt
t = Yoo
Ae
l-m
1-rnt
[
[I
-
t1
(:--)
t]
Since the creep parameter "m" is not constant but varies
with stress level, DT, the values of strain rate at a given
time become more divergent with time in Fig. 5-4.
Although
the curved plots at larger times in Fig. 5-4 are no doubt
correct, the resulting slopes, 3, do not represent the
curves for stress levels greater than 50 percent.
In order
to obtain representative slopes, a "best-fit" line must be
drawn through the data points for t = 10,000 minutes (see
dashed line in Fig. 5-4).
Such a procedure yields an average
value for """ of 4.6 which is approximately the value obtained for t = 1 minute.
This resultant parameter modification along with the
other creep parameters previously mentioned yielded the
theoretical creep strains tabulated in Table 5-5 for
-94-
D
= 0.50, 0.65, 0.72 and 0.80.
The resultant curves are
compared with the laboratory strain-log time curves in
Fig. 5-19.
The results compare quite well at large times which is
the result of the cancellation of two errors.
(1) The initial shear strains (yo) are too large due
to the fact that they are obtained from second and
third increments and not first loadings.
The
discrepancy can be seen in Fig. 5-17 where the two
curves are compared.
(2) The initial creep rate (t < 400 minutes) is too
slow.
This is due to the fact that for a given
stress level, the parameters used to calculate
strains are for that increment in the steady state.
In the laboratory, the internal obliquity (Th/v)
is initially higher than that applied, and therefore, the creep rate is greater.
As a result, the theoretical curves start out too high
but lag behind in the first 400 minutes.
After that period
the two curves are parallel and in most cases, very similar
in magnitude.
-95-
A further example of this point concerning the initial
development of pore pressures can be made by attempting to
duplicate a first loading curve with modified data.
If one
takes the initial shear strain from the first loading condition (y = 1.71%) (see Fig. 5-17) for DT = 0.65 and uses
the "m" obtained for DT = 0.72 for the first 400 minutes
and "m" for D=
T
0.65 for the remainder of the time period,
one duplicates the first loading curve.
These results
are shown in Table 5-6.
Since field problems are concerned with strain-log time
curves at times much larger than 400 minutes, the multiincrement approach can prove to be quite useful.
Strains
at much greater times can be calculated from the SinghMitchell equation for strain and the initial portion of the
curve can be completely ignored by setting tl
> 1000 minutes,
which would be a common procedure for field problems.
-96-
z 4m
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Z
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p
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()
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4
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E-1
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p
r
l
SH
-OH
ro
4.1
0C)
4-d
HrX4
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+
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ro
U
0
H
p
l0
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4-4
-z
CHO
[-1
C)
r•
C)
•
C)
r
0
r.
0
W--
Q
r
H
H
-99-
(Nm
.-,
tC4'WO
+
u
0
TABLE 5-3:
STRENGTH DECREASE DUE TO CREEP
TEST NO.
avc aF
vm
LOAD HISTORY
(OCR=1)
(kg/cm2 )
(Values of D )
CK UDSS-8*
O
CK UDSS-10
2.0
2.0
2.0
2.0
0.73,0.94
CK UDSS-11
2.0
2.0
0.94
21.7
CK UDSS-12
2.0
2.0
CK UDSS-16
2.0
2.0
0.73,0.94
0.50,0.65,0.80,0.95
21.8
24.4
CK UDSS-20
2.0
2.0
22.5
CK UDSS-21
2.0
CKoUDSS-22
2.0
2.0
2.0
0.90
0.85
0.80,0.90
CK UDSS-23
2.0
2.0
o
o
o
o
o
0
0.49,0.73,0.82
0.65,0.80,0.95
ff =tan
(T h /hv )
20.0
19.75
22.5
22.25
23.3
Average 22.0* vs. 21.60+
(OCR=2)
CK UDSS-17
1.0
2.0
0.94
CK UDSS-18
o
CK UDSS-19
1.0
2.0
0.72,0.94
1.0
2.0
o
o
24.75
0.50,0.72,0.94
23.3
27.4
Average 25.10 vs. 25.10+
*
Failed at Controlled Strain
+
Obtained for Constolled Strain CK UDSS Tests on EABPL Clay
0
at (T h)max.
-100-
--- 0-
o\O
O
IQ
N
LO
O
.
O
O
.O
O0
LC) 0
NV Ln
H-
LO
'Q
00O
40
6
L(
0i
0
C
Hl
O
Z
O
II
H
--
0
ON
0)
C
N
r4 r~
II o
z
Lf
e4
M~
o
o•
E-4
0
"
uo
C);
C
CO
ý4
0
o
C;
C;
Cý
N
0
00
r--l
N.
SZ
:4
0O
o
H
00
OO
O c
O
II
to
ik
o\o
II
ioo
H
Hn
ID
mD
O0
>•*
O
N
N
NýO N
N
m
CN
H
00
m
I11
O
N
6*
II
Oo
OH
II
000000
tn
NU
H
MM
d
--
od0000
****
0
H
H4
O
U
O
Lf
o
N"
O
O
O
O',
O
H-
Lm
CN
O0
II
II
o
zIo
Ln
N-
O
O
O
C
O
H-
C.
N
o
O
Ln
0
SII
O
zt
0 ,o
0
II
C-
U
u~iiill>
O
I
-101-
0
TABLE 5-5:
Yt
=
D
= 0.05
o
Ae
1-m
COMPUTATONS FOR THEORETICAL
STRAIN-LOG TIME CURVES
1-
(
1
m
; c = 4.6, A = .014%/MIN.
) t
Y
= 0.8%
t (MIN)
m = 0.937
Y(%)
10
100
1.152
1.547
1000
10000
2.004
2.542
DT = 0.65
m = 0.924
Yo = 2.1%
t (MIN)
y(%)
10
2.796
100
3.639
1000
4.628
10000
5.811
D T = 0.72
y0
m = 0.915
= 3.0%
t (MIN)
y(%)
10
4.003
100
5.165
1000
6.608
10000
8.120
DT = 0.80
y
m = 0.882
= 4.85%
y(%)
t(MIN)
10
6.318
100
8.246
1000
10.777
14.083
10000
-102-
TABLE 5-6:
DUPLICATION OF D
T
= 65%
STRESS LEVEL
Y
O
t
t
1
10
100
1000
10000
-d = 4.6
= 1.71%
=
Yo
Ae
1-m
A = 0.014
t1
1-
(C-)
t
D
= 0.65
m
t
y Theory (%)
m
T
y Lab (%)
1.71
.915
1.71
2.70
.915
3.86
3.75
(.915+.924)/2
5.06
5.05
.924
6.23
6.10
-103-
2.45
0
-J
o.
I
2
z
0
z
w
W
aw
w
")
0
w
C,
I"
N
c
co
wD~·
(%) 'NIV.LS
c
z
H
8V3HS
C/)
U)
-104-
Figure 5-1
W
w
4
Co
ELAPSED
TIME
(MINUTES)
Log Strain Rate vs. Log Time from CK UDSS Creep Tests on
NC EABPL Clay
-105-
Figure 5-2
w
w
I4
z
I-
(1,
10
100
ELAPSED
1000
TIME
1000
(MINUTES)
Log (Strain Rate x Time) vs. Log Time from CK UDSS Creep
Tests on NC EABPL Clay
-106w-
-
Figure 5-3
100,000
1.0
1IO
1-2
Z
.o
w
n-
10
IO
10
10-
OI
INEL
IU
or
9v--1%0
0
20
40
D=
60
80
100
l'h/Thf,9%
LOG SHEAR STRAIN RATE VS. APPLIED STRESS LEVEL FROM
CKoUDSS CREEP TESTS ON N.C. EABPL CLAY
-107-
Figure 5-4
0
Rh
o
m
--
O
o
<
w
d
z
0
o
Cl)
H
C')
w
W
z
Z
w
oE
-
UC)
w
a
Sok
z-o
2j
m
v
Un
"
w
(%) NIV8iS
0
I-
V3HS
W
I
-r
C/)
-108-
Figure 5-5
z
0o
Z
cr-
c)
it
w
I,
(I)
ELAPSED TIME (MIN)
LOG SHEAR STRAIN RATE VS. LOG TIME FROM CKoUDSS
CREEP TESTS ON O.C. EABPL CLAY
-109---
Figure 5-6
w
w
z
I-
(I,
K)10
100I
ELAPSED TIME
1000
o10pOO
100000
(MINUTES)
Log (Strain Rate x Time) vs. Log Time from CK UDSS Creep
Tests on OC EABPL Clay
-110-
Figure 5-7
1.0
-I
10
163
I-.
w
LT6
0
zo
40
60
80
100
Log Strain Rate vs. Applind Stress Level From
CK UDSS Creep Tests on OC EABPL Clay
-111-
Figure 5-8
U)
41
S0
U
O
s-I
r)
0
O
a)
0
0
ar
~~0
0
0
Figure 5-9
-112-
w
uJ
Iz
w
z;a
•9
Iw
ELAPSED
TIME
(MINUTES)
Comparison of Plots of Log Strain Rate Vs. Log Time
for NC and OC Samples of EABPL Clay
-113-
Figure 5-10
E
o)o9
o lb
d7
0
a.
m
L.L
w
a<)
I
C,)
C)
I-l
LL)
O9
C')
0LL
z
0C
O
[1V)
>:
r
ýýJJE:ý
C.
-114-
Figure 5-11
U)
aC
ro
0rd
U
*
0a
It)
$-4-
Ho
00
-4-i
H
0
,4
rr
a
4O
0
U
0
UO
03
Is
a
-115-
Figure 5-12
a
w
w
W
O
U.
C)
Cl)0
0
I-
-J
w
w
=E
-jO
U)
Cl)
SWU)
.
w
E
w
w
0~
cr
w
w
0
cr
LL
0
z
0
I4
4r
Figure 5-13
-116-
\S I
I
I
I
I -I I
I II
I I II
Lines from first loadings
of other
tests at
corresponding stress levels
(95
z
K
0o
3
w IC
n-
z
state
condition
)
CKoUDSS -16
;c =2.0 kg./cm
W,
4 ( ) =values of
I,%
I
<)
Stead
_
6,,,%
SYM
I
2
50
65
0
A
3
80
INCREMENT
5
It"
2
2
4I
I
95
73.4%0
\
-E
0
100
ELAPSED TIME
1000
10000
(MIN)
LOG SHEAR STRAIN RATE VS. LOG TIME DURING LATER
INCREMENTS FROM CKoUDSS CREEP TEST ON N.C. EABPL
CLAY
Figure 5-14
-117-
-7
91
, kI,,.
(10)
(17) (20)
7(19)
(19
A•iii
_L
(r,
c
4-
aloop
1/'
(20)
(-ill,.
21)
0<
I
l10
u
rn
700
P
(16)
loe
II-
~------
'e
S('9)
10d
w
(10)
.00ý
I
D5
4
1.0
1.0
1.0
II
-II
II
-16
i,
-17
94
2.0
94
90
2.0
1.0
1" -19
-20
i,
-21
I
I
I
I
ELAPSED
t
VS. LOG TIME
NO
YES
I,
1.0
85
I
STEADY
STATE SYML
OCR
'
94
94
50
7,
increment
not leading to failure (•r = 50%•
I
INCREMENT
TEST
NUMBER
-2
10
CKdJDSS- IO
'
Typical first
I 1
I
LOG
Typical final increment
steady state
110
-7
IIE\
\IPI
state
/no
_I_
tlO
w
Ir
/
T1Steady
i
100
TIME
I
I
I
1000
(MIN)
FROM CKoUDSS CREEP TESTS
EABPL
CLAY
-118-
I
10000
Figure 5-15
ON
W
I-
z
i
I4
z
U)
o000
ELAPSED
TIME
I1ooo
(MINUTES)
Plot of Log Strain Rate vs. Log Time for Steady State
Creep at Various Stress Levels of EABPL Clay
Figure 5-16
-119-
S --H
Q)
Lo
(1)
U)
C)
C,
0)
H
x
U)
ý4III
N
4-)
4-
H
r-CII
4-)
k
0)
ro
·
U)3
.rq
H
H
to
k"N/@'I~a12
Wb7y5~ 7cY/.1/A'
-120-
Figure 5-17
100
80
60
o= Aq
&qf (%)
40
20
0
80
60
0C
40
20
C
0
c~r
h/hfl
h
STRESS CONDITIONS IN THE DIRECT SIMPLE SHEAR DEVICEASSUMMED PURE SHEAR
-121-
Figure 5-18
I1
i1
U)
0
,Cd
U)
o3
U
a
w
\8
\
4
\-o
.-
U
4-)
ýr
0
\\
w
E-
Q
00
-,0
)
OH
r)
rI
Q4 i
0c 4)
0
C<
(%) NIV.IS
Figure 5-19
-122-
C
VI
6.1
CONCLUSIONS AND RECOMMENDATIONS
APPARATUS PERFORMANCE
The Geonor Direct Simple Shear Device has proven to be
a convenient tool for undrained creep testing.
No modifica-
tions were necessary as the device is equipped with a "frictionless" load hanger for controlled stress testing.
This
is contrasted by triaxial creep testing where constant
temperature
precautions are necessary in order to stabilize
pore pressures, and a number of sample area corrections must
be made throughout the duration of an increment load to
insure the condition of constant stress.
On the other hand,
all dimensions of the simple shear sample are kept constant
during shear and there are no great quantities of water in
the system to be affected by temperature.
In addition,
there are no problems with membrane and equipment leakage
as there is with the triaxial device.
While advantageous in many areas, the simplicity of the
device also presents a number of problems.
drawbacks are:
-123-
The three major
(1) Lack of knowledge concerning the sample state of
stress;
(2) Lack of knowledge concerning sample pore pressures;
and
(3) The unsteady state which exists when the initial
shear stress increment is applied and the first
major adjustment is made on the vertical stress.
6.2
TEST RESULTS
The Singh-Mitchell Rate Process Theory with modifications can be used to model creep behavior for EABPL clay.
Results show this clay to have great creep potential (m < 1.0).
It was found that, contrary to the theory, lines of log 9
vs. log time at various values of DT were not parallel
(m = constant) but were divergent with time (m = f(D ) (see
Fig. 5-16).
Normally consolidated and over consolidated
samples behaved similarly with OC samples more creep
susceptible at large times.
Additional load increments (values of D ) behaved
much differently from initial increment behavior.
Instead
of yielding a linear relation between log i and log time;
the strain rate initially was much lower than the linear
-124-
relationship would yield.
With time this new curve would
converge with the linear relation and adopt its behavior.
Apparently, the previous increment(s) had installed within
the sample a greater structural stability than was initially
present.
The new increment had to overcome this new stability
before first increment-like behavior could develop.
Unfortunately, no empirical relationships could be developed
concerning this initial transient behavior.
It was found that by applying several load increments
to one sample, one could reconstruct the equivalent first
stress level behavior for each increment applied.
This
can be accomplished by allowing each increment to pass through
the initial transient phase and establish the steady state
first increment-like behavior.
This established linear re-
lationship between log j and log time can then be extended
to all times to obtain equivalent first load performance.
It was found that loads of 85 percent or more cause
creep rupture.
This phenomenon was due to high pore pressure
generation rather than a decrease in friction angle, •.
This angle (defined as ( = tan -1 (Th/v)max) was essentially
the same as that obtained from controlled strain tests.
-125-
_1
The creep theories of Saito and Singh-Mitchell were
found to be somewhat useful for predicting failure in the
laboratory.
The Saito relationship was able to yield a time
range for failure which included the actual time to failure
in all cases.
Unfortunately, this time range which covers
more than one log cycle of time can be very large and on the
order of a week for large times to failure.
The Singh-
Mitchell Theory was somewhat of an improvement but only applied
to first load failures and to those additional increments
which achieved steady state creep prior to failure.
average value of (it)f (the value of
The
't at which there is
a sudden increase in slope) was found to be approximately
5.0 percent.
For the five cases in which steady state
creep existed prior to creep rupture as defined by SinghMitchell, failure occurred from 30 to 1700 minutes after
attainment of (it)f = 5.0%.
The test with the upper bound
time to failure was the lone additional increment test
which achieved steady state prior to failure.
time range for this test was 2800 minutes.
The Saito
It was found
that the average strain attained prior to failure* in the
five tests for which the Singh-Mitchell creep rupture
*
This strain is defined as that attained when the loglog plot of -t vs. time has passed (ft)f and becomes
nearly vertical.
-126-
theory applied, was 20 percent, which is approximately the
average strain at failure for the controlled strain CKo UDSS
Apparently, the mechanisms which bring about failure
tests.
under both controlled strain and controlled stress creep are
somewhat similar for the strains as well as the obliquity
(Th/Uv
)
at failure were the same for the two failure modes.
Major drawbacks in the program were:
(1) The inability to ascertain accurate values of
D(=Aq/Aqf) for the various stress levels; and
(2) A great change in creep behavior after approximately
400 minutes of load duration.
The first problem is due to the stress system and made the
selection of -
for use in the theory's equations a diffi-
cult task of questionable success.
The second problem,
the author believes, has to do with pore pressure equalization in the sample.
The rapid application of shear stress
increases pore pressures within the sample.
Reduction of
vertical stress maintains the sample volume and the average
sample pore pressure is in equilibrium with the sample
stresses.
Unfortunately, pore pressures at the sample edges,
which can dissipate more quickly than those on the potential
-127-
failure plane, are now too low and those near the center are
too high.
Sample deformations which are more strongly governed
by the stress state within the interior of the sample (i.e.
on the potential failure plane) are proceeding at an accelerated rate.
Therefore, the linear log strain rate versus
log time relation for an applied stress level, -T, is too
high as the obliquity (Th/Iv) within the sample is greater
than that which would normally result from the applied
stress level, DT.
Only after these excess pore pressures
dissipate does the linear creep rate relation drop down to
that level which is representative of the applied stress,
D .
All data obtained prior to this event is misleading
and presently of little value.
6.3
RECOMMENDATIONS
The two major problems encountered during this investigation were concerned with a lack of knowledge of the stress
state within the sample and measurement and dissipation of
initial pore pressures within the sample.
The first problem has been the object of considerable
effort with little resulting success and the author has
-128-
no suggestions for improving the situation.
The second
consideration can either be handled by measuring
sient excess pore pressure or eliminating it.
this tran-
Measurement
would indeed be difficult and at this time not practical.
Elimination appears to be the only reasonable recourse.
This
can be accomplished by either applying a desired stress
level in smaller increments over a time period within which
a major portion of these excess pore pressures could dissipate
or else loading the sample by means of controlled strain
until the desired stress level is reached.
After transferring
the proving ring load to the hanger assembly, the creep test
could be commenced.
Unfortunately, the data obtained during
the execution of these two techniques is also of little
use so one accomplishes nothing.
Apparently, the best
procedure is to ignore all data obtained prior to t = 400
minutes.
Other aspects of the program which need further investigation are the effects of OCR on creep behavior, long term
testing (t > 1 month) and creep rupture behavior.
Any
program designed to investigate these problems could be
very useful.
-129-
VII REFERENCES
1.
Arulanandan, K.; Shen, C.K.; and Young, R.B. (1971),
"Undrained Creep Behavior of a Coastal Organic
Silty Clay". Geotechnique, Vol. 21, N8.4,
pp. 359-395.
2.
Bishop, A. and Lovenbury, A., (1969), "Creep Characteristics of Two Undisturbed Clays". The Seventh
Intl. Conf. of SMFE, Vol.
, pp. 29-37.
3.
Bjerrum, L. and Landva, A. (1966), "Direct Simple Shear
Tests on a Norwegian Quick Clay". Geotechnique
Vol. XVI, No. 1, pp. 1-20.
4.
Brooker, E.W. and Ireland, H.). (1965), "Earth Pressure
at Rest Related to Stress History". Canadian
Geotechnical Journal, Vol. 2, No. 1, pp. 1-15.
5.
Christensen, R.W. and Wu, T.H. (1964), "Analysis of
Clay Deformation as a Rate Process". ASCE JSMFD,
Vol. 90, No. SM6, pp. 125-156.
6.
Edgers, L. (1967), "The Effect of Simple Shear Stress
System on the Strength of Saturated Clay". M.S.
Thesis, Dept. of Civil Engineering, M.I.T.
7.
Edgers, L. (1973), "Undrained Creep of a Soft Foundation
Clay". Ph.D. Thesis, Dept. of Civil Engineering,
M.I.T.
8.
Fisk, H.N.; Kolb, C.R.; and Wilbert, L.J. (1952),
"Geological Investigation of the Atchafalaya
Basin and the Problem of Mississippi River Diversion".
U.S. Army Engineer Waterways Experiment Station,
Vicksburg, Mississippi.
9.
Foott, R. and Ladd, C.C. (1972), "Prediction of End
of Construction Undrained Deformations of
Atchafalaya Levee Foundation Clays". M.I.T. Dept.
of Civil Engineering, Research Report R72-27.
10.
Kaufman, R.I. and Weaver, F.J. (1967), "Stability of
Atchafalaya Levees". ASCE, JSMFD, Vol. 93, SM4,
pp. 157-176.
-130-
11.
Kolb, C.R. and Shockley, W.G. (1959), "Engineering Geology
of the Mississippi Valley", Trans. of the ASCE, Vol.
124, pp. 633-645.
12.
Krinitzsky, E.L. and Smith, F.L. (1969), "Geology of
Backswamp Deposits in the Atchafalaya Basin,
Louisiana", U.S. Army Engineer Waterways Experiment
Station, Tech. Rept. S-69-8, Vicksburg, MS.
13.
Ladd, C.C.; Williams, C.E.; Connell, D.H. and Edgers, L.
(1972), "Engineering Properties of Soft Foundation
Clays at Two South Louisiana Levee Sites".
M.I.T. Dept. of Civil Eng. Res. Rept. R72-26.
14.
Laing Barden, "Time Dependent Deformations of Normally
Consolidated Clays and Peats". ASCE, JSMFD,
Vol. 95, No. SMI, Jan. 1969, pp. 1-31.
15.
Landva, A. (1964), "Equipment for Cutting and Mounting
Undisturbed Specimens of Clay in Testing Devices".
NGI Publication No. 56, pp. 1-5.
16.
Mitchell, J.K.; Campanella, R.G.; and Singh, A. (1968),
"Soil Creep as a Rate Process". ASCE, JSMFD, Vol.
94, No. SM1, Jan. 1968, pp. 231-253.
17.
Mitchell, J.K., Singh, A. and Campanella, R.G. (1969),
"Bonding, Effective Stresses, and Strength of
Soils". ASCE, JSMFD, Vol. 95, No. SM5, pp. 12191246.
18.
Murayama, S. and Shibata, T. (1961), "Rheological
Properties of Clays", Proceedings of the 5th
Interntl. Conf. on Soil Mech. and Fdn. Engr.,
Paris, Vol. 6, pp. 269-273.
19.
Shibata, T. and Karube, D. (1969), "Creep Rate and
Creep Strength of Clays". The 7th Intl. Conf.
on SMFE, Vol. 1, pp. 361-367.
20.
Singh, A. and Mitchell, J.K. "General Stress-Strain
Time Function for Soils". ASCE, JSMFD, Vol. 94,
No. SM1, Jan. 1968, pp. 21-46.
21.
Singh, A. and Mitchell, J.K. (1969), "Creep Potential
and Creep Rupture of Soils". The 7th ICSMFE,
Vol. 1, pp. 379-384.
-131-
22.
Saito, M. and Vezawa, H. (1961), "Failure of Soil Due
to Creep", The 5th ICSMFE, Vol. 1i,pp. 315-318.
23.
Saito, M. (1965), "Forecasting the Time of Occurrence
of a Slope Failure". The 6th ICSMFE, Vol. II,
pp. 537-541.
24.
Saito, M. (1969), "Forecasting Time of Slope Failure
by Tertiary Creep". The 7th ICSMFE, Vol. II,
pp. 677-683.
25.
USCE (1968), "Interim Report on Field Tests of Levee
Construction, Test Sections I, II and III, EABPL,
Atchafalaya Basin Floodway, La.". Dept. of the
Army, New Orleans District, Corps of Engineers,
New Orleans, Louisiana.
26.
Walker, L.K. (1969), "Undrained Creep in a Sensitive
Clay", Geotechnique, Vol. 19, No. 4, pp. 515-529.
27.
Watt, B.J. (1969), "Analysis of Viscous Behavior in
Undrained Soils", Sc.D. Thesis, Department of
Civil Engineering, M.I.T.
-132-
APPENDIX A
LIST OF SYMBOLS
Note:
Suffix f indicates a failure condition.
Prefix A indicates a change.
A bar over a stress indicates an effective stress.
Stresses
(a - ah)/ 2 or (a1 - a3)/2
q
-9
(v
+
Uh)/
2
= (a
1 + 73) / 2
Pore Water Pressure
h
h
Horizontal Stress
Vertical Stress
v
01
Major Principal Stress
a3
Minor Principal Stress
hc
vc
ahF
v at Consolidation
VO
Initial In Situ Vertical Effective Stress
vm
Maximum Past Pressure
T
max
Shear Stress
Maximum Shear Stress
-133-
LIST OF SYMBOLS (Cont.)
Stress Ratios
q/qf
D
O
Aq/Aqf
Th/Thf in the Direct-Simple Shear Test
--h/cv or --hc/vc
OCR
Overconsolidation Ratio =
vm/vovo or a vm /vm
vc
Strains
Linear Strain
Shear Strain
Strength Parameters and Stress Strain "Constants"
Young's Secant Modulus for Undrained
Loading in Terms of Total Stress from
an Undrained Shear Test
s
U
PU,' 4'
I
f
Undrained Shear Strength
tan-1
v )
at
f in the Direct-Simple
Shear Test
max
at (T/ v )m
max
T at Creep Rupture
-134-
LIST OF SYMBOLS (Cont.)
Strain Rate and Creep Parameters
E
Strain Rate = de/dt
Y
Shear Strain Rate
tr
Time to Rupture
tf
Time to Failure
t
Time at Which Strain Rate Becomes
Constant Prior to the Development of
Creep Rupture
A
D
D (or -D,
D
)
Creep Parameters in
D
max
Singh-Mitchell Relationship
m
See Section 2.1
El' Y1
t
tl
-135-
LIST OF SYMBOLS (Cont.)
The following symbols are used in the derivation of the
Singh-Mitchell relationship from rate process theory.
Shear Force Acting on a Flow Unit
Planck's Constant = 6.624 x 1027
-1
erg - sec
kT
AF
2 x
h exp (- RT )
Boltzmann's Constant = 1.38 x 1016
erg
K
Universal Gas Constant = 1.98 cal °K-1
-i
mole-1
S
Number of Flow Units
T
Absolute Temperature, OK
tl
Reference Time
Parameter Relating Activation Frequency
to Strain Rate
4SkT
2kT
AF
Free Energy of Activation, Calories
per mole
Distance Between Equilibrium Positions
of Flow Units
-136-
LIST OF SYMBOLS (Cont.)
Miscellaneous
Cc
Virgin Compression Index
Cr
Recompression Index
CR
Compression Ratio = Cc/(l + e o )
cv
Coefficient of Consolidation =
kv/(mv
Void Ratio or Napierian Base 2.7183
e
e
w)
o
Initial Void Ratio
k
Coefficient of Permeability
log
Log to Base 10
N.C.
Normally Consolidated
O.C.
Overconsolidated
t
Time
w
Water Content
wn
Natural Water Content
P.I.
Plasticity Index
L.I.
Liquidity Index
-137-
APPENDIX B
TABULATED TEST RESULTS
-138-
CKoUDSS - CREEP TEST
EAB PL
SOIL DESCRIPTION
9
No.
BORING
SAMPLE No.
ELEVATION
Na
CK/UDS- 8
CONDUCTED BY
/0 -,Z/ -7/
CEW
Z. 0
TEST
DATE
le/
-36.7
INITIAL CN
CL• Y
UEgs
73. a
"r
vc( KG/CM2 )
/o
OCR
/-0
PRETEST Ht.(MM)
DATE
VERTICAL
VERT.
ME PROVING RING STRESS
.2z379
" (0/6) Y(%/MIN) ht(%) ELAPSED APPLIED
TIMENPER CENT)
(MINUTES, (PER CENT)
/0-2-7/
/.'oo
3057.6
3o05
2.0
/89
0
o0
. 1.,'/5
538
Z3
1.9
,99
o220o
,.o0/3
2z
/.29
,00o39
.,oks
/7
29
138/
,0oo0229
. 19,3
8s
29YS
1,
,7oo/85
.o8/,
/1,54
.000oo93
,/735
/18
1,78/
, 000o60
,992
18q3
29 1/8
/,882
, oo.Z5o
,/ S/
660
28993
Z,69/
o000/3,9 -. 331
/6go
28.93
.2.17/
,00009/0 ,2225
.2 7/5
296t
/.80o
Z 9 15
2928
/1,73
_
.2 87-4
/.6bZ
2 8 76
284&0
29_59
,o0,•bl
.1099 3275
26/
.O00
0, 0o•0
. 3327
q /&S
Y-ZsI/
y-5 75
z, 399
.O0'tS8,6
.••95(,
Sov/c
Zs,6o
2. 387
r-.25
z29 8
..-399
C000s77 .32Y9
, 0oc338 .A.o31
_2_
1s_9
/1.5-6,
, 34
-•
1/-7-7/
&3n
/,-56
3
~. .3.
----
1 7080
o
. o/8i1
,osS.
3
_8__
2780
Z
,0/5y
,ofgY
4
28 y
2.8.29 .o/o93
./1093
o
.00o67/ .2/0223
/S
aS
_
3,o0a .20067
,Z/53
B-ze
T (APPLIED) /
a3.020
T MAX.
-139-
72.9
K
(35,o Kc)
;2,731
1,,
8
=
-
o0-5
a.688 .098_ 3 ,o98Y3
28.
Dr
i2.5
?2.;20
4 325
-.
.0ot09.29
,)
6
,o o9/5
, /07
-2986
.9
(.2-
,/1~8
./3,•
0
38
PAGE
VERTICAL
VERT.
PROVING RIN( STRESS
DATE/
2 792.
Z 83
Y(%)) *(/(oMIN
3. 099~
00 2,360
$.s4 /
,& 291
3. 78•
.00 197
7
I.S2
.8 26
•
3. 752,
9I
3.8/49
za Ii
,,g/.o
5.o23
z 7o80
s
27790
9·72
/, /93
*2785S
.1/909
53
.'t353
/59
.5,308
.270
.s1 I
.3/o
.0012o 5
4b6
,0oo009
7o 9
, '980
729
.000519 ,72"/o /395
,000 3SS,
,609(
,qgag
-.71
27 814
s.
a782-
s-. 8,S"
.so
2
q400
56
. 333
277/
(MINUTES: (PER CENT)
.3.S
(.98
2Z 777
APPLIED 1:
t(%) ELAPSED
TIME
,oo00 19
9. 269 ,000 6,31
Z
,0O06785
Lf6s(
s.'125 S0ooo000 7
27656
I, 3"93
5.523
a 7 65
1.393
5.523
o603, o•123 )
,oo219
610 '00219
63l ,002-2-
580-5
J2,0.5
1300
a2765
.2765
(53
:yss
7156
(.39, .
.0/3/6
.#3399
IS
,oo loG
67/ , oeo 4 71
so
,ooo 6.
, o0
733
6,oa7
I
-P769
/ ,0
332, ,03979
260
O.302-7
,000 2,63 .,3o2•7 //25
.000.21
.38•36
6.071 .000241 3552
6.102. ,OOo .2.
.3423
b.I (4 ,oo/ 7y
,3/o.'
4. 2• , 0o00 73
1330
/6.5
310Yr C .2.545
-140-
/., )
PAGE
VERT.
DATE/ ME VERTICAL
PROVING RING STRESS
TME
Yt(%)
Y(%/)
)ý%/MINJ
ELAPSED APPLIED D
TIME
(MINUTES) (PER CENT)
ý897
S760
S000 /-Z
17r(o0
2761
6. 366
/,38
6(S38
ý,58 1
1761
,,oool2.-7
oo /27
2-
,OmoI
(c.64.7
b.
.27617 '77
ý2A7s
k _
7L9 I
.179A
,S'1/33
(, 877
•9cso
, 5.a23
6.785 ,0000
90q
YoCc gog
,'777
61872- ,oooo&S
I. 3L
L-1275
,/398
,5334
670
I-
6900
7Bas
8 310
8
/3t
SR999
; Si9:A
Q=1
-141-
-o- ---
3
_L~Zio
CKoUDSS - CREEP TEST
SOIL DESCRIPTION
EABBPL
BORING
99
No.
CI 4Y
ss -/cl
TEST Na _ua
i- 3-7/
DATE
C
CONDUCTED BY
uVs
SAMPLE No.
ELEVATION
/ 3
-15 Fr
INITIAL WN
,p . 9,
vc(KG/CM2 )
OCR
2.0
/.o
PRETEST Ht.(MM)
DATMVERTICAL
ERT.
D
MEPRING RING STRESS
/•-2 Y- 7/CENT)
75.3 05os2
'Y (%)z
29 75
/_5/
5
7
I 2285
5
,o 7860
,7o7lY
9
,057oss
,7725
/5
9,Z96
22
8Y
30
J/
3.2 f9 ,u/o.
A-883
/11/ ;,39
2883
,be 7 ,0-250
2 S83
-,3,7 . 2-08
2883
o83
z2_.3
S
883
._
G
_I.
_8_-&_
s_-_
157
-.••-0
__596
c279 6
,..Z297
/Yb
,772/
93
537
/ ,O/?y2
,6723
so
.42
~
. 7 , o/s-I/
,9go/
s2472,
.o0/2z7
,2733
70
$ 8e8
, 0099/
.a23
go0
6
,oo777
,o90aS
7289
?5-0
,I;
.- I
's,
Dr= T (APPLIED) /
17
l,9/Y /9o
,288 ,00oo53
b
o6
,Y/_
I/o . , I/8 ,977/
1,58
.Y56
.
,ooo/89
172-
9
, poa/'7
~-998 ,o63e9
7./68 0oo007•4
, 00
67i
,639/
, 87/1
/9•
,Zs-y
Z99
.3997
5-22
,936
/395
8,/97 ,o0sS- ,5239 /6/5
2.•9-/
S
IA,/2
9.10'
2195
3
,.938
//,5
a'89'
.838z
,02079
_
Sp•4
O;Z3
,78
£7.2
__
Yy7
/
,70 2
/ 83
0/7
7
2,
3.o33
,,7
/2
,ISo
_
.90oo
ELAPSED
APPLIED
NM
TIME
R CENT)
72.9
bo
_ __
302o.
-0o/
0
2 .o
3osz7
(MIN)()
.2
r
&.73 ,ooViy
. %,C28/870
P/b
P.1
"5a/
9
,oI
000/6
/1,36 Pi 6/,14,000 /1(c
-5v
3 6
.L t-/1./-,,,
..,,7 AzoOO
MAX.
-142-
's.
I
PAGE
DATE/
nTME
VERT.
VERTICAL
PROVING RING STRESS
2 75/
/. 3(.
ELAPSED APPLIED ]•
TIME
(MINUTES) (PER CENT)
R.77?
.ooo i37
'000
9.IC6
12S
,ooooS'72
S&. 2.28
ys30
.6295
so Y•-
,'I097
.(,68o
/o 06
9.157
7t;
9,.87
9"/,//-
27(,3
a72V
, 329
I
,0 23 2- P
.oqs,
S5
2
,o /7'9
,o67253
.?/2,70
, "3
2,76,
2.67f
.2 72S
2-7 (C
2763
/.37
9. 798
9,W
.lo5
-9,926
,•
,00 b17
/.39
9
/6
•
.X324 33
27 &63
,25-2B
Y/
27 62
, 3043
5-0
1,o0
/o.
25;2
,o060-3
,oo60/7
,o 582
75
,Y523
.52935 38
,6// z
,oo 629
/0. 6/9
I03
/3 /
, oo 699
,oo 82
/.32
// 98/7 , o lo69
0 /0oI
-2223
2755
2 ).0
12,929'/
. 700
2,
X:t•-8
,0 /2a
Uz E
13S7
-143-
2,/32.
34
3.34L
7
53/
------
(.'52
z
CKoUDSS - CREEP TEST
SOIL DESCRIPTION
•ABPl.
BORING No.
SAMPLE No.
99/uES
/314
ELEVATION
INITIAL WN
- 42, 7 Fr
72.2 %
c
,9 Y
C K0s55-/I
/2-/o-7/
WcW
TEST Na
DATE
CONDUCTED BY
vc(KG/CM 2 )
OCR
.o
PRETEST Ht.(MM) 2-• 3/61
DAT% M VERTICAL
E
VERT.
PROVING RIN STRESS
r (%) (%/MIN
ELAPSED APPLIEDNC
TIME
MIN UTES (PER CENT)
/2-1/o-7/
30526
y4/
2.6
0.s,,.
/ 774,
2950
19/8
9b
P
/
/. 71
. 21/
6. 78/
2-800
2.5/7
/.
,325
o,"197
/,30]
, /0230
bS83
o, 7'
i,
8 (..
I,V/5
/1"02
. 0b 75
e771
7/4
7
C,
.07
27
.2-7Y7
.03 &(72
1,33
2730
.0366/
2703
/7, 987
6b87
/3.
3/o7
/
/3 8 7
.2-
-7L 3
9.Alt
,02.70
,c'293
3.3 oc
,3.
80
,0 2J1
3,535-
/,23
.2.6 0
/l. 270
a•&o
/. /3 t
/7.97
.x,3o
Dr= t
/.3/o0
,O IA6 o
/8867
/;--/2--7!
*t/u
(APPLIED)
/
3o
2.Sa
1o. 663
~z. 737
28Z
23
T MAX.
-144-
q/
12
7/7
//9
CKoUDSS - CREEP TEST
FQBPzEI
SOIL DESCRIPTION
BORING No.
SAMPLE No.
ELEVATION
INITIAL WN
CL•)Y
9q u=
'3/)
-
CONDUCTED BY
rc( KG/CM 2 )
'L2,9 P7
',"
K
/2
C•IDSS
I2.-2--71
TEST Na
DATE
,
e W
.o
OCR
1o
PRETEST Ht.(MM)
DATM
I
-7-"
&-o
.
2.
2";
./Y9
VERTICAL
VERT.
ELAPSED APPLIED 1
PROVING RIN( STRESS Vr (%] X(V/MIN Yo3%S2
(MINU ES (PER CENT)
3 osr
72, 9%
2.0
o30z57
2
/
os7,
30//5
/ ?Jo
/9/
71? 31
o.3y$7
0.5
0. 30S7
0,17//
2.233 &, /03 7
7
1909
49 00
Z.o
28~oo
2. 88/
,o.3/• •
16
3.o0'/
,5327
3- 220
,5,33
.3. 39o
S0/
//70
30
Yo
.bBOc
.6238c
59 82.
3.6893
3- L89
3~866
S8220
,6900
2z20
7333
,oo153
28/3
4-5-7
2 797
2 70
6P03
,7/88
(, /7I
i-5-79
,000608
277X
(9'32
(
; 73 7
//,33
- 7 /,
/J19
?
..22Z9
,00030•/
,ss5oT
2 82 7
,/8
272//9
Dr= T (APPLIED) /
o30
J90
gbooo 13/o
,OOO/39
573 o
,77
69
4,77/
r MAX.
-145-
P0O0 683
,0000s56
.
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2
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TIME
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SOIL DESCRIPTION
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BORING No.
SAMPLE No.
ELEVATION
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//2
- /-o,5 Fr
INITIAL WN
73 Y-%
No.&C,4aS -//
DATE
CONDUCTED
3 -I5-7_
BY
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2
VERTICAL VERT.
ME POVNG RN STRESS
DAT
TEST
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OCR
PRETEST Ht.(MM)
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2•
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TIME
(MINUTES (PER CENT)
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PAGE
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VERTICAL
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VERTICAL
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I
I
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APPLIED "r
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TIME
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CKoUDSS - CREEP TEST
SOIL DESCRIPTION
E/•SPL
BORING No.
SAMPLE No.
ELEVATION
INITIAL W"N
DAT
CONDUCTED BY
- '¼.O
79. /
VERTICAL
ME PROVING
VERT.
STRESS
_E W
2
)
'vc(KG/CM
FTr
0•
/. o
2.
OCR
PRETEST Ht.(MM) ,J-R-g9
(%)
7
ELAPSED APPLIED a
GTIMF E (PER CENT)
Y(VMIN)
0NUTF.
5-10-72-
7 LS
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Cooss5- /i - 72-
TEST No
DATE
C/-A"Y
2.S7.
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3.127
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0,969
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D-T= t (APPLIED) / T MAX.
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12-
aa
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(. i/
CKoUDSS - CREEP TEST
F4ABPI-
SOIL DESCRIPTION
BORING No.
Q
Y
(~.LA
u_- s
/3 4
SAMPLE No.
ELEVATION
_
-
INITIAL WO
N
/__" FT
7
VERTICAL VERT.
DATME PROVING
RING
STRESS
.5-2Z-72-.
74'o
TEST No
DATE
CONDUCTED BY
575
C~D~SVS-/8
1/--72,
=s Wv
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OCR
PRETEST Ht.(MM)
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7' (%) Y(9/MINM/t(%)
23.
ELAPSED APPLIED 5
TIME
(MINUTE; (PER CENT)
72~/o
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1.932.,
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262.
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PAGE
DATE/TIME
5-2
9-
VERTICAL
VERT.
PROVING RING STRESS
ELAPSED APPLIED ":
TIME
(MINUTES) (PER CENT)
Y"("/o) )(/o/M INJ
72
25b80
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SOIL DESCRIPTION
BORING
EA.P/& C•A Y
No.
TEST No. CX_0,DSs-/9
D ATE
_-__72
te••;W
CONDUCTED BY
Iles
92'-
SAMPLE No.
/42
ELEVATION
-,//. -F
INITIAL WN
g77%
vc( KG/CM 2 )
Zo
OCR
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2 ,Z920
PRETEST Ht.(MM)
DATM
VERTICAL VERT.
PRONG RIN STRESS 7
E
?Y(VMIN It(%o ELAPSEC
TIMEN
(0/]
APPLIED "
(MIN UTES (PER CENT)
6- 7- 72,
So n
.2575
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0.56'
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122 73
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7
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PAGE
VERT.
DATIME VERTICAL
PROVING RING STRESS
2&o6
ELAPSED APPLIED 1r
TIME
(MINUTES) (PER CENT)
Y(/o)
.03 o00
/ tl<
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7
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PAGE
VERT.
DAT E/ME VERTICAL
PROVING RING STRESS
/ 0.2
25987
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hx./o
IN
I
0 f)5
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75
t,5 o,
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1.353
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1, o 3
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9.762-
7. los!
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7,450
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9. 331
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ELAPSED APPLIED D
TIME
(MINUTES) (PER CENT)
5-O
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t oo ro I 3,o2L9
7/2
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22y
y7b9
co v930
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3 ,30,-96
R,
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3
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3
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9,702Z / 786
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CKoUDSS - CREEP TEST
SOIL DESCRIPTION
BORING No.
SAMPLE No.
ELEVATION
INITIAL (ON
DAT%
EARPL
CL4 VY
- VI,3 Fr
yvc(KG/CM2 )
OCR
PRETEST Ht.(MM)
So, /%
VERTICAL VERT. 7 (%
ME PROVING RING STRESS
-72
o7800
9.0i
009
303o
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/
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6,'/17
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2-1•3•
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17
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139
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1"2 y xý2
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7
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107!
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2
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70
1,739 1oS
ly/457 ,Y/,7
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33 & 1c6 1,z
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6
ELAPSED APPLIED r1
(MNIFES, (PER CENT)
o
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l/85'
25•98/
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'ZE6
Dr= "r (APPLIED) / r MAX.
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o
YV,6,3
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3,6/
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(MIN)
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517
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6
TEST Na Co.sS -o20
- 7 7-/7
DATE
tEI
CONDUCTED BY
/s
90%,
g/
(32/m)
CKoUDSS - CREEP TEST
SOIL DESCRIPTION
BORING No.
SAMPLE No.
ELEVATION
INITIAL CON
E-,ABPL CLAgY
TEST
95 UES
- 7-.
Na ctu'u•ss-2/
7-z
DATE
CONDUCTED BY
Kc(KG/CM 2 )
OCR
9"Fr
7.5./%
2.0
I. o
PRETEST Ht.(MM)
DATMVERTICAL
ERT.
DTMEPROVING RG STRESS
-72-
c.LA/
22, 700
)'(MIN) tt(%) ELAPSED
APPLIED
TIME
CENT)
(/o
(MINUS)
(PER CENT)
7-3o -72-
9o4
0s7-4
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ol
2.0
C
____
5l
(2,'751
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/
A,79
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1
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28 7o
7 32,68
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90
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8 220 /5-•0
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1760
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CKoUDSS - CREEP TEST
SOIL DESCRIPTION
BORING No.
SAMPLE No.
•vcs
9,5
/2 D
ELEVATION
CONDUCTED BY
"c(KG/CM )
- I,_ r77 %
_
INITIAL (N
CAfDss--2Z
8-1/t'-7_
CEhV
TEST No
DA TE
Y
c
CL,
f-•BLP
OCR
.o
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22.073
PRETEST Ht.(MM)
DAT
ERT.
VERTICVERTICAL
MEPROVING RING STRESS
._700
ELAPSED APPLIED r
TIME(PER CENT)
(%)/Y(VMIN)
4•
436I9 j3,(
.2930
0.5
O/cmE
N7/
/
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A1I
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/
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7
8 7/
5. SY
•
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S.76
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4.
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6,s71
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2435 .'O/129
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CKoUDSS - CREEP TEST
SOIL DESCRIPTION
BORING No.
SAMPLE No.
ELEVATION
INITIAL WN
••BPPL
C L,4
TEST Na CkVD4s-23
DATE
9-3-72
9 uES
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APPENDIX C
PLOTS OF CK UDSS CREEP TESTS
o
1. STRAIN VS. LOG TIME
Cl to C12
2. LOG STRAIN RATE VS. LOG TIME
C13 to C24
3. LOG(STRAIN RATE X TIME) VS. LOG TIME
C25 to C36
4. SHEAR STRESS VS. SHEAR STRAIN
C37 to C48
Note:Lines with symbols represent the
test being plotted. The remaining
curve is the stress-strain curve
for the corresponding (NC or OC)
controlled strain CK o UDSS test.
5. CREEP TEST STRESS PATH
C49 to C60
Note:Curved stress path is that of
the corresponding CK UDSS controlled
strain test. The remaining stress
path is that of the creep test.
max = tan
-1
(T/-v')
from controlled
strain CK UDSS test
o
TU =
tan
-1
(T/-
vv
) at Tma
from controlled
x
max
strain CK UDSS test
o
t-1 1
S=
tan
(T/l
c
v ) at creep rupture
=
-164-
F,
I
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ELAPSED
TIME
(MINUTES)
C13: LOG STRAIN RATE VS. LOG TIME, CK UDSS-8
o
-177-
w
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ELAPSED
TIME
(MINUTES)
C14: LOG STRAIN RATE VS. LOG TIME, CK UDSS-10
0
-178-
ELAPSED
TIME
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C15: LOG STRAIN RATE VS. LOG TIME, CK UDSS-11
o
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3'
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C16: LOG STRAIN RATE VS. LOG TIME, CK UDSS-12
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ELAPSED
TIME
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C17: LOG STRAIN RATE VS. LOG TIME, CK UDSS-16
O
-181-
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4
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1000
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10000
(MINUTES)
C18: LOG STRAIN RATE VS. LOG TIME, CK UDSS-17
-182-
1oQ000
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z
i
1O
100
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1000
TIME
C19: LOG STRAIN RATE VS.
14000
(MINUTES)
LOG TIME,
-183-
CK UDSS-18
O
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TIME
(MINUTES)
C20: LOG STRAIN RATE VS. LOG TIME, CK UDSS-19
O
-184-
w
z
i
"'
10
100
ELAPSED
1000
TIME
10,000
(MINUTES)
C21: LOG STRAIN RATE VS. LOG TIME, CK UDSS-20
O
-185-
lo0ooo
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TIME
1u000u
(MINUTES)
C22: LOG STRAIN RATE VS. LOG TIME, CK UDSS-21
-186-
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w
z,
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10
1000
100
ELAPSED
TIME
10,0ooo
(MINUTES)
C23: LOG STRAIN RATE VS. LOG TIME, CK UDSS-22
o
-187-
100,000
IV
1WU
ELAPSED
1000
TIME
10,000
(MINUTES)
C24: LOG STRAIN RATE VS. LOG TIME, CK UDSS-23
-188-
o00ooo
10
100
ELAPSED
TIME
1000
(MINUTES)
10000
C25: LOG(STRAIN RATE X TIME)VS. LOG TIME, CK UDSS-8
-189-
10,000
101
I0
9
w
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z12
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ELAPSED
1ooo
TIME
Iooo
(MINUTES)
C26: LOG(STRAIN RATE X TIME) VS. LOG
TIME, CK UDSS-10
-190-
ioo,ooo
10'
10
Iv
o00
ELAPSED
1000
TIME
1Q00
(MINUTES)
C27: LOG(STRAIN RATE X TIME) VS. LOG TIME,
-191-
CK UDSS-11
100,000
10
100
1000
ELAPSED TIME
C28: LOG(STRAIN RATE X TIME)
-192-
100,000
I0,p00
(MINUTES)
VS.
LOG TIME,
CK UDSS-12
0
lIuu
ELAPSED
1000
TIME
10000
(MINUTES)
C29: LOG(STRAIN RATE X TIME) VS. LOG TIME, CK
UDSS-16
-193-
o
100,000
Iu
100
ELAPSED
1000
TIME
10=000
(MINUTES)
C30: LOG(STRAIN RATE X TIME) VS. LOG TIME, CK UDSS-17
-194-
100,000ooo
w
I-
Z
w
Iv
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I.-
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o000
100
ELAPSED
TIME
Ioooo
(MINUTES)
C31: LOG(STRAIN RATE X TIME) VS. LOG TIME, CK
UDSS-18
-195-
oo00,00ooo
lU
100
ELAPSED
1000
TIME
1P000
(MINUTES)
C32: LOG(STRAIN RATE X TIME) VS. LOG TIME, CK UDSS-19
-196-
1I0000,
w
w
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U,
IV
100
ELAPSED
1000
TIME
1•000
(MINUTES)
C33: LOG(STRAIN RATE X TIME) VS. LOG TIME,
CK UDSS-20
-197-
ioo0ooo
I0
100
ELAPSED TIME
100)
IU0J00
(MINUTES)
C34: LOG(STRAIN RATE X TIME) VS. LOG TIME, CK UDSS-21
0
-198-
---
I00,000
w
z
'u
100
ELAPSED
1000
TIME
10,000
(MINUTES)
C35: LOG(STRAIN RATE X TIME) VS. LOG TIME, CK UDSS-22
-199-
oo100,00
w
w
:E
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I
Un
luu
ELAPSED
1000
TIME
10000=
(MINUTES)
C36: LOG(STRAIN RATE X TIME) VS. LOG TIME, CKoUDSS-23
-200-
100,000
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