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This Thesis for the Ph.D. degree b y

J a c k W i l l i a m Hilf

has b e e n appr o v e d for the

Department of

Civil Engineering

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 Hilf, J a c k W illiam (Ph .D. Civil Engineering)

A n Investigation o f Pore^fater Pressure in Compacted

Cohesive Soils

Thesis directed b y Professor Wi l l i a m H • T homan

The mechanical properties of compacted cohesive soils used, i n the

construction of embankments for dams, levees, highways, a n d airports are

affected significantly by stresses in the w ater h e l d bet w e e n the so i l

particles. These soils generally contain air as w e l l as water in their

voids a n d are only slightly permeable. T h e weight o f superimposed fill

creates stresses b o t h in the solid particles a n d in the pore fluid. In

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moist compacted soil the w a t e r is considered to b e a continuous fil m

covering the grains a n d forming menisci near the contacts between

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grains. Th e pore-water pressure, u, is shown to h e the algebraic sum

of the negative capillary pressure, u c , caused b y surface tension a n d

the pore-air pressure, ua «

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Since w a ter and solid soil particles are virtually incompressible

as compared to sir, t h e volume decrease in a sealed, loaded soil mass

occurs entirely in the air. T h e final air pressure is derived by using

Boyle's law of compressibility of ideal gases combined with Henry's law

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of solubility o f air in w a t e r . Compression of the soil mass results in

an increase in the capillary pressure. Substituting u& + u fi for u in

Terzaghi's relation equating total n o r m a l stress to effective normal

stress plus pore-water pressure, leads to the conclusion that an e xter­

nally unstressed soil, in w h i c h air pressure is atmospheric, is actually

subjected to an ambient effective stress o n its s olid constituents equal

in absolute value to the capillary pressure. T h i s stress m u s t be c o n ­

sidered in defining t h e compressibility o f such soils a n d it also

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explains the existence o f "no-load." shearing strength b y the mechanism

o f friction rather than b y cohesion.

Measurement o f pore-water pressure w a s accomplished b y a simple,

n o —flow device designed for this investigation w h i c h included a porous

t i p inserted i n the soil. A triaxial compression machine w a s con­

s t r u c t e d a n d u s e d to subject compacted soil specimens to ambient stress

w h i l e m e a s uring volume change a n d pore-vater pressure. T h e specimens

w e r e sealed i n rubber sheaths during the tests. Since pressures less

th a n one atmosphere below zero cannot be meas u r e d b y the vacuum gage,

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t he magnitude of the capillary pressure w a s obtained b y a novel m e thod

w h ich consisted o f subjecting the unsealed soil to ambient air pressure

greater than atmospheric, measuring the resulting pore-water pressure

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at equilibrium, a n d subtracting the former from the latter. Triaxial

tests o n a sandy clay compacted at three different placement conditions

showed large differences in pore-water pressures due to differences

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both in pore-air pressure and in capillary pressure, which agrees with

the theoretical concept. The w etter the soil, the larger w a s the pore—

pressure. Comparison of results on identical samples of a silt using

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perforated end plates in the B u r e a u o f R e c l a m a t i o n ^ triaxial compres­

sion machine a n d using the porous insert developed for -this study indi­

cated that the latter device is superior to perforated end plates for

unsaturated soils.

T h e theory o f pore-water pressure provides a n under standi ng of

soil behavior that can be app l i e d to laboratory testing of soils in

compression a n d in shear. Recommended procedures for these tests sure

described. B y plotting the well-known dry density versus w a ter content

compaction curve in terms of v o i d ratio versus w a ter voi d ratio, the

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theoretical variation o f pore-eir pressure with, volume chang e a s we l l

as the variation o f capillary pressure for different placement c o n d i ­

tions are shown. T h e p h e nomenon of settlement o n saturation w h i c h is

characteristic o f soils p l a c e d very dry o f o ptimum w ater content is

explained as shear failure w ithin the mass due to increase in capillary

pressure. Also a new, r a p i d m e thod for construction control of density

a n d water content in compacted embankments o f cohesive soils is

described.

This abstract o f about 600 words is approved a s t o f o r m a n d c o n ­

tent. 1 recommend its publication.

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 ACKNOWLEDGMENTS

T h e w riter is indebted to Professors W i l l i a m H . T homan a n d

L e o n a r d G. T u l i n of the Materials Testing Laboratory, Department of

C i vil Engineering, for their encouragement a n d full cooperation in

p r o v i d i n g the special facilities n e eded to conduct the t e s t s .

T h e soils, the l / 30-cubic-foot split mold, a n d the comparative

test results on Soil B wer e provided b y the B u r e a u of Reclamation's

E a r t h Materials Laboratory Branch, W. G. Holtz, Chief. Discussions

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w i t h M r . Kenneth R . C l a r k a n d M r . F r a n k B . L a r c o m of that Branch

h e l p e d to clarify the me c h a n i c a l problems o f pore pressure measurements

by inserts. IE
S pecial thanks is due to m y colleague, Mr. George C. Rouse, for

suggestions a n d advice w h i c h facilitated the laboratory phase of this

investigation.
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T h e manuscript was t y p e d b y L a ura M. Hagerty.
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 TABLE OF CONTENTS

CHAPTER PAGE

X. I N T R O D U C T I O N .................................................. 1

T he Problem.

Statement of the p r o b l e m ................................ 1

Importance of the study ................................ 3

Definitions ......................................... 3

Cohesive soils ............................................ 3

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C o m p a c t i o n ................................................ **•

R eview of the L i t e r a t u r e ................................... 7

Organization o f Remainder o f Dissertation

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II. T H E O R Y ......................................................... lO

The S olid Constituents of Soil lO

Structure o f compacted cohesive soils . » • • • « . » 11

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Stresses o n the soil Skelton . . . . . . . . . . . . . 12

The Pore F l u i d in Two-phase Systems ..................... 16

The p e r f ectly dry soil m a s s ............................ 16

The saturated soil mas s 18

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T he Pore F l u i d in the Three-phase system . . . . . . . . 19

Soil w a ter . . . . . . . . . . . . . . . . . . . . . . 19

Soil a i r ................................................... 29

Derivation of the Equation for Pore-crater Pressure . . . 57

Pressure in t h e air . . . . . . . . . . . . . . . . . 59

Pore-water pressure . . . . . . . . . . . . . . . . . ^4-1

Effect o n mechanical properties o f soils . . . . . . . *4-5

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 V

CH A PTER P AGE

XII. E X P E R I M E N T S ................................................

Scope o f the Te s t s . . . . . . . . . . . . . . . . . . ^

Equipment ^7

Triaxial. compression machine . . . . . . . . . . . . ^7

Pore-Jwater pressure device . . . . . . . . . . . . . 50

Preparation of specimens . . . . . . . . . . . . . . 57

Tests . . . . . . . . . . . . . . . . . . . . . . . . 60

Description of the soils . . . . . . . . . . . . . . 60

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Tri a x i a l compression tests . . . . . . . . . . . . . 62

Measurement of pore-water pressures . . . . . . . . 65

Discussion of R e s u l t s . . . . . . . . . . . . . . . . 65

IV.
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A P P L I C A T I O N S .................................................. 75

L aboratory Tests . . . . . . . . . . . . . . . . . . . 75

C onfined compression test . . . . . . . . . . . . . 75

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T riaxial sheer test . . . . . . . . . . . . . . . . 7*+

Construction Control . . . . . . . . . . . . . . . . . 79

Placement m o isture . . . . . . . . . . . . . . . . . 79

R a p i d m e t h o d of control . . . . . . . . . . . . . . 85
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V. SUMMARY A N D C O N C L U S I O N S ..................................... 97

Summary . . . . . . . . . . . . . . . . . . . . . . . 97

Conclusions . . . . . . . . . . . . . . . . . . . . . 102

B I B L I O G R A P H Y .............................................. 106

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 LIST O F FIGURES

FIGURE PAGE

1. Average Field, a n d L a b o ratory Compaction Curves for

Three D a m Embankment S o i l s ............................ 6

2. Weight-Volume Relationships for Soils . . . . . . . . . . 13

3. Capillary Pressure 24

4. Air B u b b l e s ............... . . . . . . 35

5. Layout o f Apparatus for Tria x i al Compression Tests

w i t h Pore Pressure M e a s u r e m e n t ....................... 48

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6. Photograph of Apparatus for Triax i a l Compression

Tests w i t h Pore Pressure M e a s u r e m e n t ................ 49

7. Calibration Curves for N o —F l o w Pore-pressure Device

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8. Photographs o f Material a n d Equipment U s e d to

Seal Specimens in Rubber Sheaths ......................... 53

9. Index Properties of Soils T e s t e d . . . . . . . . . . . . . 6l

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10. Tria x i a l Compression Tests o n S o i l A . . . . . . . . . . . 66

11. Tria x i a l Compression Tests on So i l B . . . . . . . . . . . 67

12. Determination of Capillary Pressure b y Translation

of the Origin . . . . . . . . . . . . . . . . . . . . . 71
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13. Safety Factor of a Small Soil Ma s s in Fi l l

A gainst Shear Failure . . . . . . . . . . . . . . . . . 77

14. Compaction Curve — V o i d R a t i o v s W a t e r V o i d R a t i o . . . . 80

15. Settlement on Saturation in Confi n e d Compression

Tests . . . . . . . . . . . . . . . . . . . . . . . . . 84

16. Th e o r y o f R a p i d Construction Con t r o l M e t h o d . . . . . . . 90

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 17 • Curves for Rapid. Approximate Method of Moisture

Control •
18. Example of Computations - Rapid Construction
Control Method . . . . . . . . . . . . . . . .
19. Example of Graphical Solution for Rapid

Construction Control . . . . . . . . . . . .

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 CHAPTER X

INTRODUCTION

I. T H E PRO B L E M

Statement of the p r o b l e m . T h e phenomenon o f f l uid p r e s s u r e

in the interstices o f soil is encountered in a variety o f p r o b l e m s in

civil engineering. Under the names o f hydrostatic pressure, n e u t r a l

stress, hydrodynamic excess pressure, uplift pressure, c a p i l l a r y p r e s ­

sure, pore-water pressure, a n d pore pressure; these stresses a r e of

major importance in studies of g r o u n d w a t e r movement, of seepage u n der

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a n d through dams, of settlement a n d b e a r i n g capacity of foundations,

a n d of stability of earth s l o p e s .

In many of these cases the soil is completely s a t u r a t e d w i t h

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water; hence, the m a s s can b e considered to b e a t w o —phase s y s t e m c o n ­

sisting o f soil grains a n d water. M a j o r contributions i n t h e f i e l d of

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soil mechanics ha v e b e e n m a d e b y analysis of saturated soils, such as

Darcy's law of flow,"*" Terzaghi's theory of consolidation o f soft-clay

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foundations, a n d F o r c h e i m e r ’s a n d Casagrande's works o n seepage t h r o u g h

damsConsiderable effort has b e e n expended in studying the strength

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or saturated clays in connection w i t h the important p r o b l e m o f b e a r i n g

capacity. Altho u g h muc h has yet to b e l earned about soft cl a y

■*"H. Darcy., L e s fontaines publiques de l a ville de D i j o n .

Paris :Dijon, 1856.
Karl Terzaghi, T h e oretical S o i l M e e h a n 1cs (New York: J o h n W i l e y
an d Sons, Inc., 1 9 ^ 3 )> p. 266.
^Arthur Casagrande, Seepage through Dams, Contributions t o S o i l
M e c h a n i c s . (Boston: B o s t o n Society o f Civil Engineers, 19^0),
pp. 295-336.

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foundations, significant advances have bee n m a d e in this subject b y

m e a n s o f devices designed to determine the in—situ strength directly.

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T h e v a n e test is an example o f p r o g r e s s in that direction*

O n the other hand, the soil mechanics of u n s aturated cohesive

soils is still a subject of m u c h conjecture, misconception, a n d contro­

versy. It has b e e n seriously questioned as to -whether pore pressure

is a r e a l i t y insofar as strength characteristics of unsaturated soil is

concerned.^ T h e reliability o f pore-pressure measurement obtained dur­

ing lab o r a t o r y shear tests on unsaturated clays has bee n doubted.^ The

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c r i t erion of failure in laboratory shear tests of compacted cohesive

soil in w h i c h pore pressures are measu r e d has b e e n the subject of d i —

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verse opinions.
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T h e purpose o f this investigation is to explain the phenomenon

o f p o r e < « a t e r .pressure in compacted cohesive soils, to show h o w it can

b e m e a s u r e d accurately, a n d to indicate h o w it can b e applied ad v a n t a­

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geo u s l y in soil mechanics.

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L y m a n Carlson, Determination in Si t u o f the Shear Strength of
U n d i s t u r b e d Clay b y M e ans o f a Rotating Auger, P r o c e e d i S e c o n d
I n t e r n ational Conference on Soil Mechanics a n d Foundation E n g ineering
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(Rotterdam: 19^8), Vol. I, pp. 265-270.

^W. S. Housel,Discussion o f paper Shear Characteristics of R e ­
m o u l d e d E a r t h Materials, Triaxial Testing of Soils a n d Bituminous
M i x t u r e s . S pecial T e c h nical Publication No. 106, A S T M (Philadelphia:
ASTM, 1951), p. 226.
^Gerald A. Leonards, Closing discussion Strength Characteristics
of C o m p a c t e d Clays, T r a n s a c t i o n s . ASCE. Vol. 120, 1955» P • 1^79.
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D. W. Taylor, Discussion of paper Shear Characteristics of R e ­
m o u l d e d E a r t h Materials, Triaxial Testing of Soils a n d Bituminous
M i x t u r e s . Spe c i a l T e c h nical Publication No. I06, A S T M (Philadelphia:
ASTM, 1951), P. 22^.

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 ~*1

Importance of the s t u d y . Cohesive soils are essential in g r e d i ­

ents in earth damn and. levees b ecause of their ability to resist the

passage of v a t e r . These soils are also u s e d extensively in the c o n ­

struction of fills for highways, railroads, a n d airports. Because of

the high cost of transporting large volumes of soil over great d i s ­

tances, earth construction virtually requires utilization of m a t e rials

available close to the site of the structure. In m a n y cases, cohesive

soils are us e d for fills even w h e n imperviousness is not a design r e ­

quirement because no other materials are economically a v a i l a b l e .

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Th e mechanical properties o f c o m p acted cohesive soils such as

compressibility a n d shearing strength must b e given renewed a t t e n t i o n

in vi e w of project requirements for embankments of unprecedented

height.
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Earth dams 500 feet high are now under active consideration

in the western portion of the U n i t e d S t a t e s . T h e soils constituting

the water-barrier zones of these structures w i l l b e subjected to

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stresses w e l l b e y o n d those for w h i c h prototype performance dat a are

available. This emphasizes the nee d for a b e tter understanding o f the

factors involved in transforming loose soil into a structural m a t e r i a l

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a n d of the physics a n d mechanics o f soils subjected to stresses. The

pore-water pressures developed in compacted cohesive soils d uring c o n ­

struction of high embankments pl a y a v i t a l role in the behavior of

these m a t e r i a l s .

II. DEFINITIONS

Cohesive s o i l s . Cohesive soils are those w h ich contain s u f f i ­

cient quantities of silt or clay to affect significantly their e n g i n e e r ­

ing p r o p e r t i e s . Such soils va r y in texture fro m pure clays a n d silts

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(grain sizes smaller t h a n O .07 b mm) t o mixtures containing mor e than

75 percent toy w e i g h t o f s a n d a n d gravel sizes. The fine-grained c o m ­

ponents o f soil exhibit to various degrees the property o f plasticity

w hi c h is the abi l i t y of a m o i s t soil m a s s to change shape under e x t e r ­

n a l pressure without changing v o l u m e .

T h e highest w a ter content that a soil m a y have w ithout flowing

w h e n j arred in a standard device is c alled the l i quid l i m i t . The low­

est w ater content at w h ich a soil can be r o l l e d into threads l/8 inch

in diameter without crumbling is called the plastic limit. The dif­

ference bet w e e n these two w a ter contents is Known as the plasticity

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index w h i c h represents the range of w a t e r contents w i thin w h i c h the

soil is p l a s t i c . The l iquid limit of a soi l a n d its plasticity index

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wer e us e d b y Casagrande to differentiate bet w e e n silts a n d clays a n d
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between types of silts a n d c l a y s .

Soils of high l iquid limit exhibit hig h compressibility; those

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o f high plasticity index show high strength at water contents near the

plastic l i m i t . A l l soils containing mo r e than about 12 percent of silt

or cl a y sizes exhibit l o w permeability w h e n prop e r l y compacted. In

considering the reaction of these soils to stresses imposed upo n them

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as a construction material, it is sufficiently accurate, in m a n y i n ­

stances , to assume that the soils are i m p e r v i o u s .

Compaction. A n important characteristic of cohesive soils is

the fact that compaction improves their engineering properties t remen­

dously. Compaction of cohesive soils has b e e n p r o v e d to follow the

0
A r t h u r C a s a g r a n d e , Classification a n d Identification o f Soils,
T r a n s a c t i o n s . ASCB. V o l . 115 (l-S^-Q), P* 901.

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principles stated b y Proctor Although there are several laboratory

compaction standards a n d m a n y different types o f compactive efforts

u s e d in earth construction, the effect of the vater content of the

soil on the resulting dry density is similar far a l l methods. F o r each

compaction procedure there is a n "optimum" water content w h i c h results

in the greatest dr y d e n sity or state o f c o m p a c t n e s s . The laboratory

standard of compactive effort u s e d b y the Bure a u of R e c l a m a t i o n is

12,375 foot-pounds per cubic foot o f soil10 which is equivalent to the

A S T M standard 11 a l though there are differences in sizes a n d in w e i g h t s

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of e q u i p m e n t . Th e B u r e a u standard has b e e n found to approximate the

compaction a chieved in the field b y 12 passes of a 20—to n d u a l —d r u m

sheepsfoot roller o n 8- to 9-inch loose layers o f cohesive s o i l s .

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Figure 1 shows the a v e rage f i e l d compaction curves for three different

cohesive soils u s e d in earth dams, together w i t h the correspondin g

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laboratory c u r v e s .
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^ R . R. Proctor, Th e Des i g n a n d Construction o f R o l l e d E a r t h Dams,

Engineering Mews - R e c o r d , August 31, September 7, 21, a n d 28, 1933 •
10United States Department o f the Interior, B u r e a u o f Reclamation,
Earth Manual (Denver: B u r e a u o f Reclamation, 1951), P P • 1 65-173•
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'^P r o c e d u r e s for T e s t i n g S o i l s , A m e r i c a n Society for T e s t i n g

Materials (Philadelphia, Pennsylvania: ASTM, J uly 1950), P • 73*
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J a c k W . Hilf, Compacting E a r t h D ams w ith H e a v y T a m p i n g Rollers,
(paper r e a d at th e A S C E Convention, S a n Diego, California, F e b r u a r y 11,
1955)•

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134

132

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-IO O % SATURATION FOR G= 2 .6 5
128

126 - A N D E R S O N R A N C H D A M - --------------
PER CUBIC FOOT

- T O T A L M A T E R I A L ( 2 2 6 3 TESTS)
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F I L L ( - NO. 4-)
-LA B
122

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DRY DENSITY-POUNDS

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_ L - C A C H U M A D A M __
TOTAL M A TER IA L
(1229 T E S T S )
LA B —
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y
F I L L (—N O . 4 - )
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108

106
TRENTO N D A M CO M PLETIO N
104 - ( 2 5 10) T E S T S )
F IL L-
LAB -
102
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100
14 19 20

WATER CONTENT-PERCENT DRY W E IG HT

F IG U R E I

AVERAGE F IE L D AND L A B O R A T O R Y C O M PA CTIO N

CURVES F OR T H R E E D A M E M B A N K M E N T SO ILS

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 XXI. R E V I E W O F T H E LITERATURE

The problem of f l uid pressures in unsa t u r a t e d soil m a s s e s w a s

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first attacked theoretically b y Brahtz a n d experimentally b y

Hamilton1^ , b o t h of the B u r e a u of Reclamation. T h e y correctly c o m b i n e d

B o y l e •s a n d H e n r y 's laws o f ideal gases to determine a i r pres s u r e in a

sealed, compressed specimen of soil. The y incorrectly assumed, h o w e v e r

that this air pressure w a s identical w i t h the pore-water p r e s s u r e .

H i l f showed h o w Brahtz*s equation could b e combined w i t h f i e l d or

laboratory compression data to estimate the magnitude o f pore p r e s ­

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sures during construction of dams a n d he p r o v i d e d a l i m i t e d a m ount o f

f ield evidence indicating that the m e t h o d gave r esults that w e r e o n

the safe s i d e B i s h o p
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u s e d Boyle's a n d He n r y ' s laws to estimate the

effect o f a sm«.l 1 amount o f air in supposedly s a t u rated soils o n their

shearing strength. A s w a s done b y Brahtz, the vapor pressure o f w ater

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a nd the effects of surface tension were neglected.1 ^

.H.A. Brahtz, C. N. Zangar, a n d J. R . Bruggeman, N o t e s on

Analytical Soil Mechanics, T e c h nical Memorandum No. 592 (Denver,
Colorado: B ureau of Reclamation, 1 9 3 9 )> P • 123*
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L. W. Hamilton, T h e Effect o f Internal Hydrostatic P r e s s u r e s

on the Shearing Strength o f Soils, P r o c e e d i n g s . A m e r i c a n Society for
Testing M a t e r i a l s . Vol. 39, 1939> P« H O O .
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J a c k W. Hilf, Construction Pore Pressures a n d Their E f f e c t o n
the Stability o f R o l l e d E a rth Dams (unpublished Master's thesis,
University of Colorado, Boulder, Colorado, 19^8), p. 55*
^ A . W. B i shop a n d G a m a l Eldin, U n d r a i n e d T r i a x i a l T e s t s on
Saturated Sands a n d T h eir Significance in the G e n e r a l T h e o r y o f Shear
Strength, Geotechnique, V o l . 2, 1950, p. 21.

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\ 8

G o u l d anal y z e d the por e pressures developed in cohesive soils

d u r i n g c o n struction o f 25 earth damn using dat a fro m piezometers and

comp r e s s i o n apparatus installed w ithin the e m b a n k m e n t s .I T H e concluded

that drainage a n d the presence of bubbles a c c o unted for the cases where

o b s e r v e d p o r e —water pressures were smaller th a n those computed b y

B o y l e ' s a n d H e n r y ’s laws. U s ing the questionable assumption that the

air i n soil ex i s t e d in the fo r m of a large number o f small spherical

bubb l e s , G o u l d showed that the surface ten s i o n o f the bubbles would

r e d u c e the pore-vater p r e s s u r e . However, it w i l l b e shown that this

h y p o thesis is not consistent wi t h measurements o f capillary pressures

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in soils at different degrees of saturation.

T h ere is n o comprehensive analysis available in the literature

o f the interaction o f water a n d air in the por e fluid of a soil m a s s .

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Suc h a study is n e eded both t o justify the assumptions use d in arriving

at a quantitative value for pore-water pressure a n d possibly to explain

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ce r t a i n persistent variations from theoretical values w h ich occur in

lab o r a t o r y experiments a n d in field m e a s u r e m e n t s .

Specific references to the contributions of others are given

throughout the b o d y o f this thesis in the discussion o f each topic.

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XV. ORGANIZATION O F REMAINDER OF T H E DISSERTATION

I n Chapter II, the concept of the structure or arrangement of

the s o l i d constituents of a soi l mas s into a soil skeleton is intro­

duced; the pore fluid is discussed first in a p e r f ectly dry soil, then

17
J. P . Gould, Construction Pore P r e s s u r e , Draft of Technical
M e m o r a n d u m , U. S. Department o f the Interior, B u r e a u of Reclamation,
1951 (unpublished).

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in a completely saturated soil* and finally in the general case of the
presence of both air and water. The equation for pore-water pressure

is derived.
In Chapter III, the laboratory phase of this investigation is
described as to the scope, the development and characteristics of
triaxial compression and pore-pressure equipment, the soils tested,
and the test procedures. The test results are discussed and compared

with tests made with other equipment.

Chapter IV shows how the results of this investigation may be
applied to compacted cohesive soils in the laboratory and in the field.

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The concept of compressibility in the one—dimensional consolidometer
test is changed, shearing strength is explained without using the term
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"cohesion", and a recommended procedure for the triaxial shear test is
described. The effect of pore^pressure theory on moisture and density

control of compacted fills is clarified. As an aid to the attainment

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of effective field control, a new, rapid method developed during this

investigation is described.
Chapter V contains a summary of the investigation and the con­

clusions that may be drawn therefrom.

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i

CHAPTER II

TH E O R Y

I. T H E SOLID CONSTITUENTS OF SOIL

A soli mass consists of solid, particles a n d pore f l u i d s . The

s o lid particles generally are mineral grains of various sizes a n d

shapes occurring In e v ery conceivable a r r a n g e m e n t . Lamb considers

the soil particle to h e one of the following: (l) a sheet (platelet,

sandwich), the largest repeating structural array of atoms, (2 ) a

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crystal, the largest nonrepeating unit built up of sheets, a n d (3) an
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aggregate or a haphazard agglomerate of c r y s t a l s .

T h e so-called clay minerals are known to consist o f crystals

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containing sheets of silica a n d other atomic groupings linked together

b y bonds o f varying strength. In the montmorillonite clays the inter­

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sheet linkage is weak, often resulting in its splitting off into

single sheets when dispersed in w a t e r , The large expansive properties

of the montmorillonite clays are attributed to this property.

It is a well-known fact that important engineering properties

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of soils, such as permeability, compressibility, a n d shearing strength,

are determined b y the fine particles to a degree entirely out o f p r o ­

portion wit h their percentage in the mass. These fines are c h a r a c ­

terized b y large specific surfaces (surface area per unit volume)

which, for particles smaller than about 0.001 mm, produce what is known

as colloidal b e h a v i o r . Surface phenomena are increased as the shape

Q
T. Wi l l i a m Lamb, The Structure of Inorganic Soil, Vol. 79,
Separate No. 315, P r o c e e d i n g s . ASCE, October 1955, P* 515-8.

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 11

o f a particle deviates fro m that of a cube. Hence, sheets, ne e d l e s or

rod-shaped crystals, characteristic of m a n y clay minerals, a r e conducive

to so-called surface p h e n o m e n a . On the other hand, silt particles,

which m a y b e the m a jor constituent o f a cohesive soil, are b o t h larger

in size a n d mo r e n e a r l y cubical in shape th a n the so-called cl a y m i n ­

erals . The y normally exhibit surface phenomena to a smaller degree

than do c l a y s .

Structure o f C o m p acted cohesive soils ♦ D e p e n d i n g o n the g e o ­

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logical processes w h i c h determined its o c c u r r e n c e , a s o i l i n its n a t ­

ural state in the g round m a y have single-grained structure or c o m p o u n d

structure. I n the former type each particle is s u p p o r t e d b y contact

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with several other g r a i n s . In the latter type large v o i d s a r e e n c l o s e d

in a skeleton of arches o f individual fine grains (honeycomb s t r u c ­

ture) or of aggregations o f colloidal-sized p a r t i c l e s into chains or

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rings (flocculent s t r u c t u r e ) . Compound structure is t h e r e s u l t o f s e d ­

imentation o f particles w h i c h a r e smal1 enough to exhibit a p p reciable

surface activity. Soils w i t h compound structure are u s u a l l y o f l o w

density (large vo i d volume) but m a y have d e v e l o p e d considerable

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strength due to compression o f the arches i n the so i l skeleton. When

these soils a r e remolded, their structure is changed, a n d it app r o a c h e s

the single-grained structure, depending o n the t h oroughness o f r e ­

molding .

T h e mos t obvious effect o f r e m o lding a n a t u r a l cohesive s o i l at

constant w a t e r content is the reduction in size o f t h e voids. In a

saturated soil, this results in a separation of p a r t i c l e s to fill the

spaces; hence, a r e d u ction in strength occurs eve n a t the same m a s s

density. In u n s a t u r a t e d soils, remolding tends t o d e n s i f y t h e s o i l

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 12
1

b y e x p u l s i o n o f air. T h e processes of excavating, placing, a n d c o m ­

p a c t i n g cohe s i v e soils in m o d e r n fills constitutes a h i g h degree of r e ­

m o l d i n g so that the structure of the final product b e ars little r e s e m ­

b l a n c e t o t h e source d e p o s i t . F o r example, the characteristics of

l o e s s i a l deposits w h i c h stand in high vertical cuts as a result of

n a t u r a l structure are entirely absent fro m the compacted soil m ade of

t h e same m a t e r i a l .

S o i l is p o r o u s — that is, it contains interconnected v o i d spaces

b e t w e e n t h e grains, thus permitting the flow of fluids through the soil

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mass. It is a w e l l -known fact that the volume of voids in a soil mass

is less important, fro m the standpoint of permeability, than the size

o f the p ores. Thus, a clay soil with a n average grain size o f 0.002 m m
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containing 50 percent voids b y volume m a y b e 1,000 times less permeable

t h a n a s a n d o f average grain size 0.5 m m containing 30 percent v o ids b y

volume. T h e amount o f v o ids in a soil mass m a y b e expressed as p o r o s ­

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ity, n, the volume o f voids per unit volume of soil mass, usually

e x p r essed as a percentage; or as v o i d ratio, e, the volume of voids per

unit v o l u m e of solid soil particles, usually expressed as a deci m a l .

T h e relat i o n b etween these values as w e l l as the nomenclature a n d the

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w e ight-volume relationships for perfectly dry, saturated, a n d partially

saturated, soils are shown in Figures 2, a, b, c, and d. The vo i d ratio

concept is u seful in analyzing volume changes in soils a n d is use d e x ­

c lusively for that purpose in this i n v e s t i g a t i o n .

S tresses on the soil s k e l e t o n . The solid particles in a c o m ­

p a c t e d soil m a s s of single-grained structure can be considered to b e a

skeleton through w h ich forces m a y be transmitted b y grain-to-grain

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 13
NOMENCLATURE SYMBOL
P o r o s i t y _____________________________________ n
V oi d R a t i o ___________________________________________________________ e
W a t e r Vo i d R a t i o ____________________________________ _______________ e w
A i r Vo i d R a t i o ------------------------------------------------------------------ ------------------------- e a
D r y U n i t W e i g h t ( D r y D e n s i t y ) ___________________________________ X D
W e t U n i t W e i g h t ( W e t D e n s i t y ) ________ __________________________ Xw
S a t u r a t e d U n i t W e i g h t ( S a t u r a t e d D e n s i t y ) _____________________ Xs
B u o y a n t U n i t W e i g h t ( B u o y a n t D e n s i t y ) ------------------------------ ----------X b
W a t e r C o n t e n t in P e r c e n t of- D r y W e i g h t ________________________ w
S p e c i f i c G r a v i t y o f G r a i n s _____________________________________ G
D e g r e e o f S a t u r a t i o n ----------------------------------------------------------------------------- s
U n i t w e i g h t o f w a t e r . ------------------------------------------------------------------------------Y0
a. N om enclature and Symbols

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VOLUM E W E IG H T R E L A T IO N S H IP S
e
<D
a>

A ir O n =
II
0

i+ e
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1

1 Sol id
Soi 1 GXo
GXo

ii
i+e
G r a ins

b. Dry Soil
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ew = e W ater ivG")o ^S =
Solid
l Soil G Yq yB =
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G r a i ns

c. S aturated Soil

e -
^ A ir _ O
ew^ ^ W ater wGXo
So l i d
l Soil G To s =
Grains

d. P a r t i a l l y Saturated Soil

FIGURE 2

W E IG H T-VO LU M E R ELA TIO N SH IPS FOR SOILS

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 contact. T h e percentage of the surface a r e a of a particle w h i c h is in

contact w i t h other particles o f the mass is known to b e small. For

gran u l a r soils, it is less th a n 1 percent. Terzaghi has shown that,

ev e n for clays, it is small enough to b e neglected, i n soil mechanics

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computations .
T h e concept of stress in a soil skeleton is not identical with

that, in a n ideal homogeneous, isotropic m a t e r i a l . Stress at a point

in ideal m a t e r i a l is force per un i t a r e a of a plane surface containing

th e p o i n t . For each of the infinite number of p lanes containing the

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point, the stress (which in general is inclined t o the plane) can be

r e s o l v e d into a component stress at r ight angles to the plane a n d a

component stress parallel to the p l a n e . T h e farmer component is called

normal stress a n d the latter is shearing s t r e s s . Stress in a soil skel-

20
et o n h a s b e e n defined b y Glover as f o l l o w s :
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"To f o r m the concept o f stress in the granu.~l.ar material,
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pass a plane through it a n d find the surface that passes
through no particle, but w h ich lies as close to the plane as
p o s s i b l e . T h e particles on one side of the surface touch
t hose o n the other at several points, a n d at each o f these
points a force is transmitted f r o m particle to p a r t i c l e .
N o w consider a small part o f the are a of the s u r f a c e . The
average stress on the small are a is defined as the resultant
of the farces transmitted from particle to part i c l e across
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it d ivided b y the ar e a of its projection on the p l a n e . C o n ­

ceptions of average n ormal a n d shear stresses c a n b e f ormed
in the same w a y . Since it is apparent that the diameter of
the sm a l 1 are a previously m e n t i o n e d mu s t be large compared
to the diameter of a grain, in order to include enough contact
p oints to y i e l d a v a l i d average, a stress c o m putation made for
a point, as d e s ignated b y coordinates, w i l l represent a n average
stress in the immediate vicinity o f the p o int r ather t h a n a
stress at a point."

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K a r l Terzaghi, Simple Tests Determine Hydr o s t a t i c Uplist,
E n g i n e e r i n g Hews-Record. June 18, 1936, pp. 872-875.
^ R . E . G lover a n d F. E. Cornwell, Stability o f Granular
Materials, Paper Ho. 2172, T r a n s a c t i o n s . ASCE. Vol. 108, 19^3, p. ^7.

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 15

The normal a n d shearing stresses r e f e r r e d to in t h e foregoing q u o ­

tation are k n own in soil mechanics as effective stresses, a a n d x ,

resp e c t i v e l y .

T h e equations of static equilibrium relating the normal, a n d

shearing stresses at a point on a plane to the p r i n cipal stresses at

that point are considered valid for soils, subject to the foregoing

modified definition of a point. T h e finer the soil grains, the closer

will the concept o f stress at a point approach the mathematical concept.

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The equ ilibrium equations for the stress o n the soil skeleton a r e :
— Q g

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a = cos 6 + Oj sin 6 Equation (1)

a, - a,
T = ■ ■■— — sin 20 Equation (2)

where a is t h e effective normal stress o n a plane

T is the shearing stress on the plane

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is the effective major principal stress at the point
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a^ is the effective minor p r i n cipal stress at the point

0 is the angle b e t w e e n the plane o n w h i c h o' a n d T act a n d

the one o n w h i ch af^ acts (the major p r i n cipal plane)

Under t h e a c t i o n o f effective stresses, the soil skeleton g e n e r ­

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ally undergoes elastic deformation a n d its structure is altered b y

particle r e a r r a n g e m e n t . T h e relationship o f the v olume o f the soil

mass to the effective normal stresses a p p l i e d to the soil skeleton is

known as t he compressibility. Similarly, the shearing strength o f a

soil mas s depends o n the ability o f the soil skelton t o resist shearing

stresses. Hence, the mechanical, properties o f soils are controlled

2;LFred B. Seely, A d v a n c e d Mechanics o f M a t e r i a l s (New York:

John W i l e y a n d Sons, Inc., 1952), p. 2 6 .

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