CREEP OF CLAY SUL UNDER STATiC LOAD

de la Voirie de 'Québec su_ol

ftené Robitaille, B.Sc.A.,Ing.P,M.Sc.A. Ingénieur en Sol

1- loB

Northwestern University

Ministère des Transports

' Centre de documentation

" 700, boul. René-Lévesque Est,

21e étage Québec (Québec) G1R 51-11

RECU • CENTRE DE

AOU 15 e3 .

TRAN3PORTS QUÉBEC

CREEP OF A CLAY SOIL UNDER STATIC ' LOAD

MINISTÈRE DES THAMP''"7ç CENTRE DE DOC IMF ni'A-nOM

e

QUielegier> ) --QULL11-.

Thesis Submitted to the Department of Civil Engineering

in Partial Fulfillment of the Requix7ements for the degree

Mawter of Science

Field of Civil Engineering

i ' Minisre des Transports 1 Centretè

cle documentation

!

f 700, b

-LévesqueEst,

21oul. René e étage

b y

i

Québec(Québec)G1R5H1

Rcbitaille Evanston, Illinois

June, 1962

je MINISTÈRE DES

COMMUN!CATIONS BIBLIOTi-IÈQUE

A DMINIsTR ATI VE "H"

nene

ACKNOWLEDODENTS

The author wishes to express his gratitude to Dr. J. O.

Osterberg for suggesting the topic of this investigation and for

supervision and advice during preparation of this thesis. He aise

wishes to thank Dr. R. L. Kondiler for the indispensable help and

guidance in accomplishing this work.

TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS

TABLE OF CONTENTS Ii

NOTATIONS Iii

LIST OF TABLES iv

LIST OF FIGURES

INTRODUCTION 1

THEORETIÇAL ANALYSIS 2

Review 2

Creep Phenomenon 3

Types of Creep 5

EXPERIMENTAL INVESTIGATION 6

Types of Test 6

Test Procedures 6

Preparation of Samples 7

Soil Tested - 9

,RESULTS OF TESTS 10

Seriea A 10

Series B 12

Results 19 Problem 12 Swelling Test 13 Glycerin Test 13

Series C 16

Series D . 17

Thixotrope 17

Ii

TABLES OF CONTENTS (Cont'd)

Page _RHEOLOGIC ANALYSIS OF EXPERIMENTAL RESULTS 18

Linearity- 18

Stress-Strain-Tina Re1ationship 19.

Viscocity 24

Quasi-lengham Materïal 25

CONCLUSIONS 27

LIST OF REFERENCES 49

ii

MUTIONS

The followin rnbols bave been ad&pted for use in tnis

thesis :

= water content of trimming,3

wo = initial water content of sampie

we = final water content of semple

Ws

weight of solids (D.Ç' semple

W initial weight of wet sample

S0 initisl degree or saturation

Ge = final degree of saturation

G = specific u.avr,y

t = Ume.

= strength

al - (J 3 deviator Stress

J(t) = creep compljance

E. = strain

k = rate of strain

y = shear strain

= rate of shear strain

LIST OF TABLES

Page

TABLE J. Results of Tests of Ssries A of the'Uncoelned Compression Typo 30

TABLE 2 Recuits of Tests of Series B of the Consolidated undrained gempression Type. Rydrestatie Pressures of. 1 Kg/cm4. 31

TABLF. 3 Results of Tests of Series C and D Of em Consolidated Undrained CoMpreSsion Tye. Bydrostatic Pressur33of 2 and 4- Kg/cm . 32

TARIR, 4_ Summary of Values of Figure 12. RelationShip between FaCtor A and Deviator Stress 33

TABLE 5 Strain Values CompUted by Means of the' Stress-Strain-Time Equation. Qualitative Analysis of Rate of Strain 34

iv

LIST OF FIGURES

Figure 1

Figure la

Figure 2

Page'

Stress -Time Curve 4

Schematic Creep Apparatus 8.

Strain-Time Curves for Unconfined Creep Strength Tests. Series A 35

Figure 3 Deviator Stress -Strain Curves for Unconfined Creep Strength Tests. Series A 36

Figure 4 Strain-Time,Curves for Consolidated Undrained Triaxial Creep Strength Tests. eries B. Hydrostatie pressure of 1 Kg/cm. 37

Figure 5 Deviator Stress -Strain Curves for Consolidated Undrained Triaxial Creep Strength Tgsts. Series

Hydrostatic pressure •of 1 Kg/cm 38

Figure 6 Strain-Time Curves .for Consolidated Undrained Triaxial Creep Strength Tests. ,Series C. Rydrostatic pressure of 2 Kg/cm' 39

Figure 7. Deviator Stress-Strain Curves for Consolidated Undrained Triaxial Creep Strength Tgsts. Series

Bydrostatic pressure of 2 Kg/cm' 40

Figure 8 Deviator Stress -Water Content curve 41

Figure 9 Non linearity of Soil. Strain-Time Curves. Series C. 42

Figure 10 Non linearity of Soil. Creep Compliance-Time Curves. Series C. 43

Figure 11 Basis of Stress -Strain Time Relationship. Time/Strain-Tima curves. Series C. 44

Figure 12 Relationship beWeen Factor A and 'Deviator Stress. Factor A/Deviator Stress-Factor A Curve. Sanies C. 45

Figure 13 Comparison between Experimental and Theoretical Deviator Stress -Strain Curves 46

Figure 14 Viscosity Variation. Shear Stress-Rate of Shear Stress Curves 47

Figure 15 Binghame Quasi -Bingham and Newtonian Materials. Stress -Strain Rate Curves 48

INTRODUCTION

In almost ail sou l mechanice phenomena, creep plays a part, hidden

. or open. An embankment, a slope or a eut can hold for weeksand even for

years and then fail. Creep occurs in any loading test; 'it applies to the

settlement of shallow foundations as weli. as pile foundations.

Often in sou mechanics, predictions are made based on a hypothesis,

but any assumption needs experimental data to prove its validity. In their

study of stress-etrain characteristics of compacted clay under varied rates

(1)* of strain, Osterberg and Perloff hypothesized that at constant stresses

lower than the maximum, clgy would yield with time and perhaps fail, because

the strength decreases with decreasing rate of strain.

The aim of this thesis is partly to vetify this hypothesis and to

study the sou l behaVior under sustained loads los than ultimate loads.

Stresses ranging from 60 to 95 percent of the ultimate strength are applied to

. the semples and thon maintained constant.

Series of tests of two basic types were performed at various water

contents. The first sonies is of the unconfined compression type, the others

are of the consolidated undrained triaxial compression type. Since data are

insufficient- for poMparison between different Bories, a special study is made

,of Series C which had given excellent results.

A rheologic analysis of the experimental results of this series

is made to study the sou l response during creep. Properties as linearity and

viscosity are considered and a stress-strain-time relationship based on triaxiel

oreep tests le developed and applied to the case of a triaxial compression test

for a constant rate of strain

* Numbers in ( ) refer to references listed at thé end of this paper.

1

TUEORETICAL AEALYSIS Review

, In 1931, Terzaghi(2)

emphasized the importance of slow plastic

flow of clays in the design of foundation structurés. Based on the reslilts

of undrained compression tests,ho noticed that clays had shown plastic

deformations at a shear stress below the shearing strength determined by

laboratory tests, and that tbey may deform for a long time.

(3) In a series of tests on undisturbed semples, Casegrande and Wilson

have found that brittle clay and clay shales creep under a sustained lOad

less than the load required to produce the ultimate compressive strength.

They pointed out that sustained loads reduced the strength of saturated

clays and explained the occurence of the slides along the Panama Canal by

means of this theory. In a few tests, they found that the strain at failure

was not influenced by the test dutation whereas in some others an increase

in failure strain with increasing test .dation was observed. It was also

noticed that for saturated clays, the strength decreases linearly with the

logarithm of time.

On the other hand, Goldstein(4) gave the results of tests on

samplês having the saine properties, i.e0 size of samples, consistency of

the clay, water content, stress history, etc. He stated that the samples

failed after a different time under different loads, but the strain at

failure stayed the saine . He defined the failure strain as that at which

the straip rate increased. He also found that it was independent of testing

procedure state of consolidation and test-duration. On this basis, Goldstein

- 3 -

could dotermine the tima of failurs by extrapolating tho strain-time carve

Inasmuch as the deformation ai.. reliure ha s the same ..nagnitude.

Bjerrum-Simen\s-Torblaa(2; worked on a normally consolidated marine

clay in •its undisturbed state, usine controlled-étrain type of 10ading. They

found a definite decrease in failure atrain with increasing test daviation.

Craep Phenomenon

The problem of creep is first'a problem of.shear stress(5). As

e soon as the critical shear stress is exceeded, a slow change In ;ho structure

'of sou]. takea place. The resultant'plastic doformation ié therefore quit°

different from the elaatic deformation.

Slow deformation is a function of time, and it eau be seen (fig. 1)

that strength dedreases to a value depending on the duration of Ioading, if

thora is no strengthening during test.

This decrease in strength is due principally to a structurai

rearrangement of particles. During deformation, particles move relative

to each othar. $ome bonds are destroyed since they depend upou their

relative arrangement and the distance tetween particles. Soma new bonds

are formed but it is believed that a long•unioaded period is required to

have a complote renewal. Therefore this slow and continuous defarmation

causes a graduai weakening of the sou.

Stress

\\\

gl

••••,.

•

02'

Alee.

Time

1 -------. ___................- ----- .. __, ..,- .. ,

t2

FIGURE I

Stress —Time Cueve

5

Tyrqs

In natuze difforent tyies of plastic deformaticn Uelly OCCIC'

depending on the amaunt o load which is applied on the son. i lahoratory

teste three ty/es cf creap cm be obsomed depending on the typa of clby one‘

the stress couditilns. Wher the appli.ad load is mai], tue clay creeps very

little and deformation stops. For a greater load› th soi]. can 0a2an,1 a

e.ccreaaing rate for an Indefinite perioa of time, or xt dnform ac a

naarly constant strain rate until the rate increases rapidly te cau;,-;e

EXPERIMENTAL INVESTIGATION

Tvpps of Test

In thie Inveetigation, two typos of test were performed

1 - Unconfincd Creee Streneth Tests: For these tests, the

spocimens were encased in two thin membranes separated by 9 thin contirpg

of silicone grease. The semples were set up in trieeial chambers and were

subjected to air at atmospheric pressure. They were weighed both before

and after test to determine the initial and final water contents. When the

test lasted less than 5 deys, the water contant change was usually less than

0.6%, but it was about 1% for a test of 30 days.

2 - Consolidated-Undrained Triaxiol Creer Strengpi Teste: The

sample is first consolidatcd under an hydrostetic pressure and thon, without

permitting further consolidation it je subjected to a sustained load. For

a lateral pressure of 1 kg iicm2, only one membrane bas been used. However,

it was net eafficient to protect the saMple from contamination by glyeerin,

the surrounding liquid. Fr a lateral pressure of 2 Kg cm2 or more,

two membranes separated by grasse were used.

2pst Frocedures

For ail tests, the procedure of loading was sim:Ilar. The

specimen was subjected to incremental axial loading, the elapseà tinte

between increments being kept constant. Tho size,of load increment was

one kilogram up to the final increment which depended upon the desired

stress levai, Al2 lcads were applied, quickly but without impact by.

r7

means of dead weights on the loading eradle supported by the piston. The

load was then maintained ta study the soi? behavior under nearly constant

stress at constant volume. Thé schematic djagram of the apparatus usêd

is shown in Figure la.

The regular Ume interval between lcads was 30 seconds. The

deformation readings were taken hall' a minute after load increments.

This is the reason why there is no sndden break in the exaln-Ume curve.

The analysis of the application of each load increment shows that a

sudden deformation occurs followed by a creep deformation which decroases

rapidly with Ume.. Since the deformation readings are takan when the-

strain change decreases, the curve is smooth and a stop strain-time curve

is avoided.

In order to run the aboya tests, siMilarity of samples is n

highly desirable featûre. They must be uniform and their stress history

oontrolled. The only %Jay to fulfill these requirements is to work with

remolded samples. Undisturbed semples would be more useful in order te

compare the results wi.h what happons In nature, but the imPossibility of

getting uniform duplicated semples is sufficient net to use undisturbed

ones. MorecIr the samples must be prepared at as high a degree of

saturation as(practicable. This is required to eliminate the volume

changes during testing and therefore eliminate strength variaticn.

The apparatus used for the preparation of the somples was a

Vac-Aire extruder. It consista of an extrusion auger whiqh orients the

t ' • fr,

-

loading platform

load

o. sou l specimen

d. porous stones

,

e•i•

e, indicator dial

hanger system

chamber

FIGURE la

Schematio Creép Apparatus

- 9 -

II particles spirally. Thia,method has the advantage of giving a uniform

structure to the soil. Tho semples aise pass through a vacuum chamber which

prevents the formation of air voids and eves highly saturated semples. •

The dry sou l was first mixed with a certain amount of wator to

get a water content of 31%. Then the clay Passed 5 times in the machine to

get the best haMogeneity possible It was extruded es a circuler bar Of

3.5 cm in diameter and cut into 10-cm lengths. The specimens Were sealed'

with 4 layers of wax and kept in storago,in the humid room to prevent any

los$ of water. Since the influence of thixotropy is importante a special

discussion of its affects is done et the end of the section; Results of

tests..

Before testing a semple, the wax wae carefully peeled off, and

the length was reduced to 7.6 cm. Tho trimmings were used as a. check up

of the initial water content.

Soil Tested

The sou l used was a clay of the Potapsco Formation, Potomac

Group, Lowor Gretaceous Period. It was obtained tram approximately 6 miles

north of Baltimore, Maryland(6)

The Atterberg limita are: Liquid Limit = 42%

Plastic Limit = 21%

The specific gravity is 2.68.

-10.

RESULTS OF TESTS

Series A

The first series of tests (fable 1) was of the unconfined com-

pression type. At first, the compressive strength was determined. For a

moisture content of about 31%, it was found to be 1.43 and 1.51 g/cm2:I for

tests A-1 and A-2. Bur latere 4 consolidated undrajned compression tests

with a lateral pressure of 1 kg 1cm2 and a water conbent, of about 32%

successively gave the following stresses: 1.51, 1.33, 1.40 and 1.34 kg lcm2 '

for samples B-2, 13-13, 13-14 and 13-15. It was decided to take 1.40 kg 1 cm2

as the ultimate compression strengthe which corresponded to a maximum load

of 16 kilograms. The different dead loads to be applied were then cal-

culated frein this last value.

Sevan testa were run with different applied stresses to study

the soi]. behaVior. The applied loads correspond to 95, 85, 80, 75, 70,

65 and 60 percent of the maximum load and the recuits are plotted in

Figures 2 and 3. In Figure 2, the strain-time curves show that for the

first three minutes, which corresponds to a loading up to seven kilograms,

the strain varies very little. But from this time until the end of loadjng,

the strain increases rapidly with time. The curves should coïncide for

that portion, but they spread.somewhat. This is probably due to small

changes in water content and thixotropic effects. It can be seen that

for samples having lower wator contents it takes longer to get the same

strain than for specimens having higher water contents.

- u-

In Figure 4, the stress-straln curves show a similar sequence.

The 1oWer the water content, the steeper the modulus of deformation. •

This sequence cari be botter visualized in rearrangirg the results of tests

in the following manner

terest

,

% App]ied Èoad w0 Time in Min. at 2% Strain from Figure 2

Stress in Kg cm at 2% Strain frum Figure 3

Date of Test

A-3 ' 95 31.8 3.5 min. .75 4-20

A-6 75 31.5 4.0 .79 4-23

A-5 65 30.2 4.2 .82 4-20

A-4 85 30.3 4.7 .94 4-20

A-10 70 29.4 4.7 1.00 5-24

A-8 60 29.2 5.3 .95 4-27

A-9 80 29.3 5.8 1.15 5-24

- 122 -

The only discrepancy is for semples A-10 and A-9. But these

were tésted five weeks later than the others, and they were probably

affécted by strengthening due te aging as will be explained.

When 1oading, was completed for the spécimens which had net

failed, the strain rate decreased rapidly and attained a constant value.

It seems to be indePendent of the percentage of applied stress.

Only two semples failed, A-3 and A-4, which represented 95 and 85%

of applied load. The first failure occured at the end of loading whereas

the second one happened in less than one hour.

Series B

Results:

The tests of this series were of the- consolidated undrained

compression type. The semples were first consolidated to an hydrostatic

pressure of 1 kg/cm2. The compressive strengths of two semples were 1.08

and 1.05 kg/cm2 (B-1, B-3), which.correspond to a maximum load of tWelve

kilograms.

The results of eight tests are• given .in Table 2 and in Figures 4

and 5. Five out of eight semples failed between .f ive and twenty -four

heurs, two failed atter ton deys and one did net rail.

Problem:

These results do /lot agree with those of the first series. Sirice

the semples were consolidated before testing, they_should have a lower

water content and therefore a greater compressive strength. But it was

follind that the strength was smaller in the second case. Moreover seVen

MINISTÈRE DES

, COMMON§CATIONS rsisLI O -rHÈ QuE'

ADMINis-rn:A-rivE "H"

out of net, specimens falleCL whe.eas only two oample.. with 85 and 95%

of maximum load had fatIed in the first ;1(.1:d0S. 11,D expie-3 4.n such in-

cogsistercien a program of .*eciet types of tosts was oesignrci.

Swel]ing Test:

Generally the water content was highor at the ,wid of the te4.+n

than et the beginning. Thub a sw,lling test wan designod to deteel:Ine the

swelling properties of the cLy. A sampDe was cceiu3l7 weighed and

measured and placed in the triaxlal apparatus.' Water was cproe,1 throuh

and arougd the sample by means of a vamum creeLed at the top of the

specimn. The volume increase was only 2.2% and thus could not be the

cause of the discrepancy.

Glvcerin Test:

In the eries A of unconfired compression tests the sample ;ero

found uniform enough and the weight of nolids was 10c).50 + 1.8 gram. In

series Be the weight cf solide was usually geeetee than 114 grains. The

only reason for this increase in weieht la that a non volatile materitI

oould have coma into the semple during the test. nlycer.Lg used in the

triaxial ehamber e cou:!d have played e part because cf ita special

properties. It was thon de.dded to run a test te study the bchevior oe

semple when contamineted 1D;v glycerin.

A dry .semple wao soaked in glycerin overnight and theb dried in

the aven • The Specimen was weighed at different times and the resuâta can

be summarized as followb

- 14 -

Weight of dry sample prior to test : 109.20 grams

Weight of soaked sample : 118.90 grams

Weight of dry sample after one day in the oven : 115.51 grams

11 II 11 1t two days " 11 11 : 114.92 It

three " 11 II : 114.71 11

To discover how glycerin could contaminate the clay, three

consolidated undrained compression tests were run in different wsys.

It has been suspected that the vacuum which helps the water going through

the sample may favour the infiltration of glycerin and that the use of

only one membrane may not be sufficient to protect the sample. A summary

of recuits and procedures is the following

# Test We Prddedures

109.16 No vacuum 1 membrane

108.49 Vacuum - 2 membranes

109.00 2 No vacuum - 2 membranes

B-13

B-14

B-15

For these three samples, none was affected by glycerin. The

dangerous case is thon when vacuum is Used with only one membrane

surrounding the specimen, as it was employed in the other tests of the

Sertes B.

It can easily be seen that the contamination by glycerin causes

an more ace in the weight of souda and thérefore changes the velues of

degrees of saturation, water contents, void ratios and volumes of couds

and voids.

- 1.5 -

To get a certain degreo or consistency in results, corrections

must be made. Since the water content of trlmmings is usually known, it

is assumed that it represents the conditions of the entire sample. The

calculations of the corrected weight of solids are donc using this

relationship

Wt

Ww Wo Ws

-or 1'10

Ws 1 + wt

where Ws Weight of solids

Wo = Weight of specimen Wet before test

wt = Water content of trimmings.

However, for samples B-1, 13-3 and 13-5, the average value of

109.50 grams is taken since the water contents of trimmings had net been

determined. The difference between the non corrected and corrected W is

equal to the weight of glycerin in the sample. Substracting this value

from the weight of specimen wet after test, the actuel weight is obtained.

The rest of calculations is done as usuel. The results are shown in

Table 2.

If the assumption of contamination is true, the discrepancy of

lower strength at a lower water content may be easily explained by

(7) examining the properties of glycerin. Glycerin possesses rewarkable

solvent powers and it is aygood dispersing agent. In solution with

water in a sample, it reduces the strength by changing the structure of

- 16 -

Wreover the specific gravity which is approximately 2.5 - 2.6 and

the high boiling point (290°C) are the causes of an increase in weight

when the soil is dry.

Bories C

This series of tests is of the consolidated undrained compression

type with a latere pressure of 2 kg/cm'. The maximum load was determined

by means of 4 tests C-4, C-5, C-6 and C-8 which gave an average compressive

strength of 1.90 kg/cm2. Ninety, eighty, seventy and sixty % of the

maximum load were applied on four semples but none failed as it is Clown

in Figure 6 and Table 3. Dead loads were added until l'allure, in order

to verify the ultimate strength of each semple. The stress-strain curves

in Figure 7 give a similar compressive strength of 2.56 ± 0.05 kg/cm2. But

this value is much higher than that determined by the earlier four tests.

This is probably due to a lower water content and to thixotropic affects

during tests.

It can be hypothesized that when the sou l is under sustained

loads, creep or slow plastic deformation may facilitate a new orientation

of particlee and bring the sou l in a more stable condition. It wculd

explaimthe strength increase dUring the creep tests.

Although le have only a limited number of tests for a single

consistencys the strain-time curves in Figure 6 show that during creep, the

strain rate is nearly independent of the pereentage oC applied stress.

Mbreover, under àustained loads, creep is proportional to the logarithm

of time.

- -17

Series D

To determine what the strength' is at a lower water content; one

consolidated undrained compression test was made with an hydrostatic

• pressure of 4 kg/cm2 • The compressive strength was. 3.21 kg/cM

9 for a

final water content of 27.8%. The reSults are'given in Table

Thixotr_gm

Thixotropy is the phenomenon of strength gain with time of

(8) remolded Poil. Mitchell offers an explanation based on the aspumption

that the internai energy and stress conditions in a thixotropic sojl

immediately after remolding are not equilibrium conditions.

To verify if thixotropy could affect the results, two unconfined

compression tests (A-11, A-12) were made two months later than the first

two (A-1, A-2). An increase of 28% in strenght was found. A difference

of 1% in water content may change considerably the strength, as it can

be seen in Figure 8. The stress-water content curve shows that a decrease

of 1% in moisture content corresponds approximately ta a gain strength of

20%. Thersfore thixotropy had a smaller influence on strength in the

tests -chan the water content.

18 -

RHEOLOGIC ANALYSIS OF EXPERIMENTAL, RESULTS

iinearitv

Since the first two series of tests gave inconciusive results,

it was decided to concentrate the analysis on the third series :of tests

which was much more consistent. To study the sou l response during creep,

the reeults ware plotted in various wàys.

Firste the strain-time curves in Figure 6 are replotted, the

initial strain being maken as the last load incremaat is applied. In

othc,r wordse the tibia t = 0 correoponGs to the etrain at the tima of

application of the last load incremente neglecting the past history of

specimens. Such a plot is shown in Figure 9. The units now used are p.s.i.

for easier comparaison with pravious published workse Kondner (6), (9)

Normalizing the results, the creep compliance J (t) is plotted

versus log. time in Figure 10. The creep compliance is defined as follOws:

J (t) creep'complianee tanction of time where

e:(t) = strain at time t

o = stress during creep

For linear materialse a unique relation exista between J (t) hand

t whatever the applied stress. As it cari be seen in Figure 10, the sali

is nonlinear aines the four curves are well,apart;

* This analysis is based on the presently unpublished work by Kondner on creep reeponse of a clay sol.

C t 33

(1)

Ar9.8s:PrIIPP

The main problem in soil meohice is to lind a stress-straln-

time relationship which can be applied to any sou l under a varety

conditions. In order to anticipate the sol1 rensee an equation is

developed based on the results of creep tostà end then applied and

Sompared with recuits of triaxial tests.

To do se, data from Figure 9 is plotted as follows in Figure

log th in ordinate and lo t in abcissa for the four nearly uonstau

love]. stresees. What reaults is four oarsllei Unes. The agnation for-

any of these lines can thon ho uritten

log t/e. log C B log t

where

log C lntercept at time equal to one unit e wbich ln thi case ls one minute.

= slope of the lines.

Rearranging the tenu) we get:

' log tk - log C = 8 log t

log VeC = B log t

t/$7: t

9."

Let 1 = A

d

Equation (1) becomes :

e = A td

The value of the slope B is A log (.J.)

D = - 0.989 A log t

Thon d = 1 B -,:. 0.011

Ta evaluate A, let t = 1 minute in equation (2)

) = A = 1

Since = C f (o) in Figure 11,

It must be noted that the factor A depends on the applied. stress,

Plotting Aie versus A (Fig.12) gives the following equation

Ale =a+bA where

A = intercept on the — axis

b = clope of the Une

or

O (°1 03) = o

ri A = a ft:74

deviator stress

(4)

The values in Figure 12 are taken from Figure 11 and are

summarized in Table 4.

Substituting equation (4) into equation (2) gives :

E . ; A td = a I _21 td Il bo-

which cari be called the créep equation since it was determined from

(5)

creep

É = jd

-21-

tests. Equation (5) may be applîed to the case of a triaxial test for a

'constant rate of strain to give the following development;

Since the strain rate is constant, one may write:

Strain rate = constant = = k

Therefore, = k

and t= (6)

Substituting equation (6) into equation (5) gives:

a T1 1-1 k 1 - ba

Taking the root of both sidas gives:

.B

Let

and (9)

Substituting equations (8) and (9) into equation (7) gives :

(10)

' 1.011

1 1.13 x 10-}

0.011 z 0.001 R =

av

(0.01)

-22-

and using o = al - 03 gives

R -,u3

which is the stress-strain-time equation for a triaxial compression test

at'constant strain rate as determined*from the results _of triaxial cresp

tests.

Ta verify the applicability of equation (11) the stress-streln

response for the triaxial tests of Series C was calculated from equation (11)

and compared with the actuel experimental response.

The values are the stresses developed during the loading period

for the test C-10. Thus, the strains computed can be compared directly

with the strains measured in test C-10. Since ninety percent cf maximum

stress had been applied for test C-10, it represents a nearly complote

triaxial test.

To use equation (11) the strain rate must be constant. Since

the loading procedure was incremental an overall average strain rate

must be assumed.

Aésuming the strain raté It= 0.01 in. per in. per minute gives

an average value for R:

- 23 -

-3 A • where . a = 13 x 10 intoK;ept on the _ axis in Figure 12,

o 1 1

1.011 ,

B 0.989

d = 1 B 0.011 .

Using stress values indicated and the average loading time,

strain values were computedly means of squation (11). The•results are

summarized in Table 5 and the oxperimental and theoritical stress:-strain

curves are shown in Figure 13.

A5 it can. ha seen in Gigure 13? both the theoraticbl and

experimental ourves coincide for strains greatcr thaa Cive vorcent. For

smaller strain, the discrepancy is due ta the assumption of constan.

strain rate. By the load jncrementr,1 method, the strain rate at small

strain is not constant, but as tho soli is more susceptible to deÇormation

with increasing load, lt deforms more constantly after a certain emount

of time. If a controlled constaut eerain rate had beea used during the'

triaxial compression test, the two curves would have probably beon cLaser

ta each other.

However, tho stress-strain-time relationship is.valid only for

triaxial tests similar ta those of Sertes C. The equation changes if

the latere pressure, sou, or the water content is different.

- 24 -

Viscositv

The maximum value of Shear stress in the epecimen for a par-

ticular value of deviator stress (o ) 03

max 2

Since the creep test is undrained„ there is no volume changé

in the speemen. Therefore the first invariant of the strain tensor, 0,

'is zero and one can write

G = 1 e2 0

and because symmetry

r

There fore,

2 e:

and

t43 (12)

On the other hand, plotting the shear strain versus the axial

strain in the Mohr strain space gives

y = max

C I 3 2 (13)

Therefore y = max

=

3 4

3

ç

max 4 (14)

where = maximum rate of shear strain max

= rate of axial strain

-25—

?o aae how the viscosity acts during creep testa, a graph of

shear stress, versus rate of shear strain, has been plotted at

different Urnes. Figure 14 shows that there is no constant relation,

between shear stress and rate of shear strain. Since the viscosity

is defined as the slope of the curve of T versus it can be seen that

the viscosity is not constant during creep tests, which is another p2oof

of non linearity of the material. The viscosity depends on time, water

content and applied stresses, but it is impossible to deterMine how

it varies because the data are insufficient.

Quasi-Bingham Material

A Newtonian material has a linear relationship between stress

and strain rate, which passes through the origin while non Newtonian is

any other curve. A Bingham response is also linear, but deformation

occurs when a certain amount of stress is developed, that is, when a

"yield value has been exceeded.

Rearranging the ternis of equation 7, we get . 1 . ,1

a a

J 1 - b o.

1 a ( [ a al - '3 1

Fll 1 - b (01-03)j

where a = 1.13 x 10-3

(15)

b = 0.0301

1 1 = 91 . d .011

91 - 1.13 x 10-2)

G Ib

1 (16)

- 26 -

Let B = 1

and Er- 10

and equation (15) becomes

-1

Several values of E91 are caleulated and. given in Table 5.

As it can be easily seen, to calculate the values of g one must take 1

the 91 power of 9I and, this gives difficulties. But one can maka

a qualitative analysis and estimate the approximative curve.

1 For É 91 .

• $ î.=i • For smaller values, decreasos

very rapidly. Thereforee the relationship between strain rate and atress

will indicate a Quasi-Bingham behavior. It means that the strain rate

increases with the increase in stress level in a non-linear manner.

Figure 15 shows the different relationships between strain rate and

stress for the various types of viscous response.

-27-

MINISTele DES TRANSPORTS CENTRE DE DOCUENTATiON

200, RUE DORCHESTER SUD, 7e .QUÉBEC, ‘(QUÉBEC).

G1K 5Z1

CONCLUSIONS

The hypothesis, that at constant stresses lower thcn the

ultimate strength clay would yield with time and perhaps fail is only

partly verified. Under sustained load, creep occurs and this- slow

plastic deformation may be of great importance for the structure foundations.

The few samples which failed show a similar behavior. They

creep for a while at a constant rate and then the rate of strain increases

rapidly to cause failure. This increase in the rate of creep coincides

with the reversai of the slope on the strain-time curve.

From the tests in which the samples did not fail, it can be

concluded that:

1 - creep is approximately proportional to the logarithm of

time under sustained loads.

2 - the strain rate is nearly independent of the amount of

the applied stressé

Hvorslev(2)

noticed that investigations of the long-term

rheological properties of clays were by nature time consuming, but

he pointed out that basic research into the problem would lead to short-

term tests or methods for making reliable estimates. The results of

the tests of the Series B„ even if they are not reliable with the

results of other series, prove that creep may be accelerated by tue

-28—

use of a dispersing agent.

The difficulties in creep tests are the changing conditions .

during tests. The sou l may be affeoted bypa dissipation of pore water

and by new bonds created when there is a reorientation of particles.

The use of a dispersing agent may avoid these difficulties since it

redUces the strength and causes failure sooner. A relationship between

time of failure and stress and strain which has not been found yet,

might possibly be determined.

If glycerin is used in triaxial chambers, adequate membranes

should be used and special care taken to avoid contamination of.samples..

A rheologic analysis was made of the experimental results of

Series C. A creep equation was developed to give

= a °1 °3 d 1 - b(al-a3)

Then this equation was applied to the case of a triaxial test

for &constant rate of strain. The following stress-strain-time equation

resulted (°1 °3) I

: R il - b (a - o )1

1 3 j

where the parameter R contains the time (strain rate) dépendency.

This equation was verified with data obtained from a triaxial

test. There was good agreement between the predicted and actuel response

-29-

with almost perfect coincidence for strains greater than five percent. For

strains smaller than rive percent, the discrepancy is probably due to the

assumption of constant strain-rate since the actuel loading was incremental.

Time can then be taken into account in the development of the equation of

the stress-strain curve. Nowever the relationship is valid only for triaXial

tests similar to those of Sanies C, i.e. for the sou l of the Pdtapsco

Formation and for semples subjected to en hydrostatie pressure of 2 Kg/cm2

and having a water content of 29.0 percent.

No unique relation bas been found between creep compliance and

time for these four creep tests. Creep comdliance depended on the applied

stress and this proved that the sou l was not linear.

ey definition, the slope of the curve shear stress versus rate of

shear strain is the viscosity. Curves were plotted for times equal to 50,

500 and 3000 minutes and they showed that the viscosity was not constant

during creep tests.

A qualitative analysis of thé relationship between stress and

strain rate indicated that the sou l had a Quasi-Bingham behavior. It means

that the material hada linear response only after a certain amount of stress-

had been developed.

Generally thixotropy have affected the results to a certain extent.,

In the unconfined compression tests made one day and two months after molding

the semples, and, increase of tan percent in strength was due to this

- 29a -

phenomenon. Moreover in Series Ce a strengthening was noticed during

the creep tests which lasted seven and nine days. Being loaded until

failure the four samples failed at the saine ultimate strengthe but at a

much higher value than predicted.

PTest Date

A-1 4-18

A-2 4-19

A-3 4,20.

A-4 4-20

1 A-6 4-23

A-5 4-20

A-8. 4-27

-'-- A-9- 5-24

A-10 15-24 ' 1 A-11 6-10

A-12 16-11 I

Inn MB MI 11•11 MB MB Mn Bill MIK MM 11111111 11111111 MB NUI MI Mn MI

TABLE 1

wt in ,

wo in %

wg,„ in-%

1,7 ,s in gins

So in%

Se e in p

0 2 in kg/cm

% of ultimate Strength

Time to failure in min.

30.6 31.3 109.84 101.7 104.4 1.43

31.4 30.9 109.27 101.0 103.1 1.51

32.4 31.8 107.75 100.9 105.5 1.30 95:r, 7

30.3 30.3 110.71 101.8 99.6 1.30 85 30-190

32.9 32.0 31.5 107.64 100.0 104.6 1.11 75

30.6 30.2 110.16 101.5 104.4 0.99 65

31.2 30.9 29.2 109.99 101.9 106.0 0.94 60 le> o 30.4 30.-1 29.3- 111.33 101.2 1032- 1.27 80

30.8 30.7 29.4 110.34 104.6 101.8 1.11 70

30.1 i30.2 30.0 110.26 104.1 103.8 1.78

29.9 30.0 29.9 110.73 102.6 105.2 1.83

Results of Tests of Series A of the Unconfined Compression Type

1111111 Inn MIN MIN 11111111 111111 111•11 11111111 111111 NB Mill MB MI 1111111 IBM 111111 MB

TABLE 2 .

#Test Date wt in %

wo in %

i° '

Ws nt corr. in ems

Mrs Corr. in gins,

s ._ ino ;, S in e % h.- G3 in kg/cm D of Ultimatd Strength

Time to failure in min.

B-1 4-19 30.1 30.0 111.96 109.50 97.0 101.0 1.08

18,-3 4-23 31.3 29.3 114.85 109.50 102.1 95.6 1.05

I

B-2 4-21 31.6 32.2 109.80 109.80 102.7 99 1.51

B-7 4-25 30.7 27.0 119.06 110.30 103.3 97.0 1.05 90 28-1120 D-6 4-25 31.0 1 30.9 26.7 109.59 109.59 100.1 97.6 0.94 80 ,12 days B-11 5-3 30.8 29.2 117.95 110.20 98.8 101.1 0.94 80 600-1300 B-9 4-28 32.3 26.7 118.94 108.00 103.5 94.0 0.89 75 300-1740 B-5 4-21 31.7 _28.8 114.55 109.50 103.2 101.0 0.85 70 300-1410 B-10 4-30 31.9 28.6 117.26 109.00 106.0 106.5 0.86 70 1530 B,12 5-3 30.8 30.5 25.0 110.49 110.49 104.1 99.9 0.81 65 12 days B-4 4-25 31.2 25.4 118.12 - 110.00 102.7 99.7 0.72 60 B-13 5-11 31.6 31.4 31.9 109.16 105.0 106.9 1.32

3-14 5-19 31.5 31.9 32.4 108.49 103.8 106.9 1.40 B-15 .-5-21 31.8 31.7 31.2 109.00 104.8 103.3 1.34

-

Results of Tests of Series B of the Consolidated U4dra1ned Compression Type. Bydrostatic Fressure of 1 Kg/Cm'.

IBIS Mal MM MI 11•1 MI MI MI MI IBM MIN MI 11•11 MM IBM

TABLE 3

eest Date wt in %

wo in %

w ine

1% in gms

S inc)%

S._ in -,-'0

ci-a ie. kg/cm

%of Ultimate Strength

C-4 5-24 31.9 30.6 30.3 110.36 104.4 104.0 1.93

C-5 5-25 1 31.5 31.6 31.2 109.01 103.0 103.0 1.85

C-6 5-26 31.4 31.6 31.1 108.67 101.0 104.0 1.84 C-8 5-29 31.3 31.2 39.6 108.65 .99.8 107.6 1.90

C-11 6-1 30.4 30.2 29.0 111.15 100.1 107.8 1.29 60 0-7 5-31 30.4 30.0 28.7 111.72 102.1 99.8 1.47 70 C-9 5-31 30.4 30.2 28.8 110.90 102.2 104.4 1.64 80 C-10 6-1 31.6 30.9 29.2 109.45 103.4 104.0 1.81 90

D-3 6-11 29.8 29.7 27.8 111.97 103.0 104.8 3.21

Results of Tests of Series C and D of the Consolidated Uneained Compression TyTe ledrostatic Pressures of 2 and 4 Kg/cm .

--33-

TABLE 4

a in p.s.i. A A/a X 10-3

17.8 0.0379 2.13

20.3 0.0630 3.10

22.8 0.0806 3.54

25.2 0.1100 4.37

_

Summary Of Velues of Figure 12. Relationship between Factor A and Deviator Stress.

1

- 34 -

1 TABLE 5

ri Ic-gcs om2-1.i la-

cji Pl . 1

-,a3 1-b(034-103') al- 03 -° ls 3 i

E- 1-b(ara) -b(al-a3). )

0:424 5.90 0.178 0.822 7.19 .0073 . .0814

0.528 7.35 0.221 0.779 9.45 .0097 .1066

0.635 8.83 0.261 0.734 12.03 .0124 .1360

0.740 10.30 0.310 0.690 14.9 .0154 .1685

0.842 11.70 0.352 0.648 18.0 .0187 .2040

0.945 13.10 , 0.394 0.606 21.1 .0219 .2440

1.05 14.55 0.438 0.562 26.1 .0270 .2950

1.14 15.90 0.479 0.521 30.5 .0319 .3450

1.23 17.20 0.520 0.480 35.8 .0370 .4050

1.33 18.50 0.557 0.443 41.7 .0430 .4720

1.41 19.70 0.594 6.406 48.5 .0505 .5480

1.50 20.80 0.626 0.374 55.7 .0580 .6300

1.58 22.00 0.662 0.338 65.2 .0690 f7360

1.66 23.00 0.693 0.307 75.0 .0781. 48490

1.73 24.00 0.723 0.277 86.6 .0900 .9790

1.80 25.00 0.753 0.247 101.3 .1060 1.142

Strain Values Computed hy Me-ans of the Stress-Strain-Time Equation. Qualitative Analysis'of Rate of Strain.

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-49—

LIST OF REFERENCES

J.O. Osterberg and William H. Perloff, Jr. Stress -Strain Characteristics of Compacted Clay under Varied Rates of Strain. H.R. B. Proceedings, Vol. 39, 1960.

M. Juul Hvorslev. Physical Components of the Shear Strength of Saturated Clays. Research Conference on Shear Strength on Cohesive Soils. 1960.

A. Casagrande and S. D. Wilson. Effect of Rate of Loading on the Strength of deys and Shales at Constant Water Content. Geotechnique„ Vol. 2, 1951

M. Goldstein. The Long -Term Strength of Clays. Froc. Fourth Int. Conf. Soil Mech. and Found. Eng., London, Vol. 2, 1957.

R. Haefeli. Greep Problems in Soils, Snow and Ice. Proc. Third Int. Conf. Soil Mach. and Found. Eng., Vol. 3, 1953.

R. L. Kondner. A Non -Dimensional Approach to the Vibratory Cutting, Compaction and Penetration of Soils, 1960.

G. Leffingwell and M. Lesser. Glycerin. Its Inâustrial and Commercial Applications.

J. K. Mitchell. Finadamental Aspects of Thixotropy in Soils. Transe Â.S.C. Vol. 126 1961.

R. L. Kondner and R. J. Krizek. Correlation of Load aring Tests on Soils. 1962.

W. L. Wilkinson. Non-Newtonien Fluids, 1960.

MIN ST ME DE TRANSPOR S

IuI IuDflOIuuu QTR A 102 497