Alpan1970 The Geotechnical Properties of Soils

 

E a r t h - S c i e n c e R e v i e w s - Elsevier Publishi Publishing ng Company - Print Printed ed in The Netherlands

T H E G E O T E C H N I C A L P R O P E R T I E S O F S OIL S

I . ALPAN F a c u l t y o f C i v i l E n g i n e e r in in g , I s r a e l I n s t i t u te te o f T e c h n o l o g y , H a i f a

I s r a e l) l)

It is easy to distinguish those who argue from f a ct and t hos e who ar gue f r om not i ons . . . The princi principles ples of every scienceare scienceare derived from experience. RISTOTLE

The sci sciences ences,, blo w n up by facts , need a perpetual slimming diet. diet. RAYMOND QUENEAU

SUMMARY T h e s o l u t io i o n o f p r o b l e m s i n s o il i l e n g in i n e e r in i n g r e q u i re r e s a d e t a il il e d k n o w l e d g e o f t h e m e c h a n i c a l p r o p e r t ie i e s o f s oi o i ls ls w h i c h a re re , p e r h a p s , a m o n g t h e m o s t c o m p l e x m a t e r i al a l s t o b e s t u d i e d f r o m t h is i s p o i n t o f vi v i ew ew . T h e p r e s e n t p a p e r e n d e a v o u r s t o p r e s e n t a r e a s o n a b l y c o m p r e h e n s i v e a c c o u n t o f th t h e r e l a t io io n s g o v e r n i n g t h e r e s p o n s e o f so s o i ls ls t o a p p l i e d f o r c e s . A n i n t r o d u c t o r y p r e s e n t a t io i o n o f th t h e a s p e c ts t s i n v o l v e d a n d t h e i r p la la c e w i t h i n t h e g e n e r a l f r a m e w o r k o f th t h e s t u d y o f m a t e r ia i a l p r o p e r t i e s is i s fo f o l l o w e d b y a d i sc sc u s s i o n o f r e l e v a n t m e t h o d s u s e d i n d e s c r i b i n g a n d c l a s s if i f y i n g s o il il s. s. A s e p a r a t e s e c t i o n t re r e a t s t h e i m p o r t a n t s u b j e c t o f s o il i l w a t e r a n d t h e f a c t o r s i n f lu l u e n c i n g it it s m o v e m e n t t h r o u g h t h e c h a n n e l n e t w o r k o f t h e s oi o i l s k e le le t o n . T h e g r e a t e r p a r t o f t h e p a p e r i s d e v o t e d t o c o n s i d e r a t io io n s r e g a r d i n g t h e f u n d a m e n t a l s t r e s s - s t r a in i n - t i m e r e la l a t io i o n s h i p s . T h e i m p o r t a n t p r i n c i p le l e o f e f fe f e c ti ti v e s t re re s s is is p r e s e n t e d , f o l l o w e d b y a d i s c u s s io io n o f s t r e s s - d e f o r m a t i o n r e l a t i o n s h i p s . T h e p r o c e s s o f c o n s o l i d a t i o n , i .e . e ., . , t h e t i m e - d e p e n d e n t d i s s i p a ti ti o n o f p o r e - w a t e r p r e s s u r e a f t e r l o a d i n g , i s t r e a t e d i n s o m e d e t a il i l . T h e a p p l i c a b i l it it y , w i t h i n a l i m i t e d r a n g e , o f l in i n e a r s t r e s s - s t r a i n r e l a t i o n s t o s o i ls ls i s d i s c u s s e d f o l l o w e d b y a n a c c o u n t o f f a i lu l u r e c r i te t e r i a a n d s h e a r i n g r e s i s t a n c e w i t h s p e c ia ia l e m p h a s i s o n t h e p r e v a i l i n g d r a i n a g e c o n d i t io i o n s . T h e i n fl f l u e n c e o f t h e s t ra r a i n r a t e o n s t r e n g th t h f o r m s t h e s u b j ec ec t o f t h e l a st s t s e c t i o n o f t h e t r e a t m e n t o f s t r e s s - s tr t r a i n - t i m e r e la l a t io io n s . In con clusion, several special topics are presented: a discussion o f the pressures and volume changes in expansive clays, the behaviour associated with t h i x o t r o p y a n d s e n s i ti t i v i ty t y a n d , l a st s t ly l y , t h e r e s p o n s e o f s o il i l s t o d y n a m i c f o rc rc e s . E a r t h - S c i . R e v . , 6 1970) 5-49

 

6

I. ALPAN

INTRODUCTION A s c o m m o n l y a c c e p t e d , s oi o i l m e c h a n i c s i s a b r a n c h o f c iv i v il i l e n g i n e e r i n g d e a l in in g w i t h p r o b l e m s i n w h i c h s o i ls l s a n d t h e ir ir r e l e v a n t p r o p e r t i e s a r e o f p r i m a r y c o n c e r n . T h e n a t u r e a n d v a r i e t y o f t h e s e p r o b l e m s a r e w e ll l l i l l u s t r a te t e d b y t h e c la l a s s i f ic ic a t i o n p r o p o s e d b y C OO O O LI L I N G ( 19 19 4 5 ) a n d s h o w n i n T a b l e I . TABLE E N G I N E E R I N G S O IL IL P R O B L E M S

Stability problems

Deformation problems

Stability of slopes (slips in cuttings; embankments, hillsides, river banks, sea coasts, etc.); Earth pressure on retaining walls, quay walls, sheet-piling etc.; Design Desi gn of earth dam s and see seepage page Excavations and pressures on timbering and bracing;

Settlement Settl ement of buildings buildings (with and with out piles) and structures of all all kinds

Bearing cap acity of footings, footings, pile piles, s, subgrades for roads and airfields;

De f o r m a tio n o f f ill illss a n d d a m s Dis tribution of pressur pressuree o n walls walls pressure on tunnels, conduits, sewers, etc. Cumulative deformations under repeated stresses, e.g., road slabs

1 After COOLING 1945).

I n s p i t e o f t h e w i d e r a n g e o f p r o b l e m s l is i s t ed e d i n t h e t a b l e, e, i t a p p e a r s t h a t t h e s o il i l p r o p e r t i e s i n v o l v e d i n t h e i r s o l u t i o n a r e e s s e n ti t i a l ly ly r e l a t e d t o t h e f o l l o w i n g t w o b e h a v i o u r p a t t e r n s : ( 1) 1) s t r e s s - s t r a i n - t i m e

r e l a ti t i o n s h i p s; s ; ( 2) 2 ) p e r m e a b i l i t y to to

f l u id i d t r a n s p o r t . A s a m a t t e r o f f a c t , o n l y t h e f ir ir s t o f th t h e t w o q u a l i fi fi e s a s a m a t e r i a l p r o p e r t y i n t h e r i g o r o u s s e n se s e o f t h e d e f i n i t i o n g i v e n b y R O S EN E N TH T H A L ( 1 9 64 64 ) i n t h a t it it c o n c e r n s t h e r e s p o n s e o f t h e m a t e r i a l

soil

to the stimulus of impo sed

forces. T h e s y s t e m a t i c d e s c r i p t io io n o f t h e b e h a v i o u r p a t t e r n s i n d i c a t e d a b o v e c o n s t it i t u t es e s , t h e n , t h e s t u d y o f t h e m e c h a n i c a l p r o p e r t i e s o f s o il i l s, s, a n d t h e c o n s i d e r a b l e c o m p l e x i t y o f th t h e s u b j e c t c e r t a i n ly l y w a r r a n t s i ts ts s e p a ra ra t e t r e a t m e n t a s o n e m a j o r s u b d i v i s i o n o f s o il i l m e c h a n i c s . T h e u s e o f th t h e r e s u l ts t s o f t h i s s t u d y i n t h e a n a l y s is is o f m o d e l s o f e ng n g i n e er er i n g p r o b l e m s

would

p r o p e r l y c o n s t it i t u te te

another

major

s u b d i v i s i o n : t h e s t a t i c s a n d d y n a m i c s o f s o il il m a s s e s . METHODOLOGICAL OBSERVATIONS I t c a n b e s t a te t e d w i t h s o m e c o n f i d e n c e t h a t t h e s y s t e m a t i c in i n v e s t i g a ti ti o n o f t h e m e c h a n i c a l p r o p e r t i e s o f s o il i l s h a s b e e n p r o c e e d i n g e s s e n t i a l ly l y o n t w o l e v el e l s: s: ( 1) 1) O n t h e

struc tura l ,

o r p h y s i c a l , le le v e l t h e o r i g i n o f t h e i r m e c h a n i c a l

Earth-Sci. Rev. 6 ( 19 19 7 0) 0) 5 4 9

 

THE GEOTECHNICAL PROPERTIES OF SOILS

p r o p e r t i e s i s s o u g h t i n t h e n a t u r e a n d a r r a n g e m e n t o f th t h e b a s i c c o n s t i tu t u e n t s o f so s o il il s . T h e l o g ic i c a l c u l m i n a t i o n o f t h is i s a p p r o a c h w o u l d b e t h e s uc u c c e ss s s fu fu l f o r m u l a t i o n o f a

kinetic theory of particulate me dia

a n a l o g o u s t o th t h e s ta t a t is i s ti t i c al al t h e o r y o f

g a s es e s . W e a r e , a s y e t , v e r y f a r f r o m s u c h a d e s i r a b l e s t a te t e o f a f fa fa i rs rs . ( 2) 2 ) O n th t h e p h e n o m e n o l o g i c a l l ev e v e l, l, a d o p t e d i n t h e v a s t m a j o r i t y o f investigations, soils are viewed as continua whose deformational response is s t u d i e d i n l a rg r g e - s c a l e t e st s t s , e a s ie i e r t o p e r f o r m b u t n e c e s s a r i l y o f li li m i t e d r a n g e a n d v a l i d it i t y . T h e g r e a t v a r i e t y o f s o il i l t y p e s le le a d s h e r e t o a n e v e r i n c r e a s i n g v o l u m e o f experimental work. A l l t h e s a m e , t h e t e n d e n c y h a s b e e n t o d i s c o v e r u n i f y i n g p r i n c ip ip l e s , t o a c h i e v e e c o n o m y o f t h o u g h t l e a d i n g t o e c o n o m y o f e x p e ri r i m e n t , h e n ce c e t o w a r d s t h e s im i m p li li f i c a t i o n o f p h e n o m e n o l o g i c a l i n v e s t i g a t i o n s (F R EU E U D E N TH TH A L , 1 9 50 50 ). ). A t t h i s s ta t a g e , a s u r v e y o f t h e m e c h n i c a l p r o p e r t i e s o f so so i ls ls m u s t , t h e r e f o r e , s t r ik i k e a c o m p r o m i s e : w h i le le p r e s e n t i n g , w h e n e v e r p e r t i n e n t , r e l a t e d p h y s i c a l aspects, it will mostly have to discuss empirical relations keeping irrelevant p a r t i c u l a rs r s a t a m i n i m u m a n d e m p h a s i z i n g , i f p o s s ib i b l e , u n i fy f y i n g tr tr e n d s . T h u s i t w i ll l l p r o v e n e c e s s a r y , q u i t e e a r l y i n o u r d i s c u s si si o n , t o t r e a t s a n d s a n d c l a y s s e p a r a t e l y b u t t h e r e w o u l d b e s c a r c e l y a n y p r o f i t in i n d w e l li l i n g o n t h e r e s u l ts t s o f c u r v e f i tt t t in in g which, alas, form s the subject of so m uc h o f the published literature. DESCRIPTION AND CLASSIFICATION

S o i ls ls , a s o b s e r v e d b e f o r e , a r e

p a r t i c u l a t e m e d i a , i. i . e .,. , s u b s t a n c e s h a v i n g a

s k e l e t o n o f e a s i ly l y s e p a r a b l e p a r t i c le le s w h i c h e n c l o s e i n t e r c o n n e c t e d a n d i r r e g u l a r l y s h a p e d v o i d s . T h e v o i d s p a c e m a y b e w h o l l y o r p a r t l y f i ll l l ed e d w i t h a l iq iq u i d , g e n e r a l l y water containing salts in solution. T h e so s o - c a ll l l e d v o l u m e - w e i g h t r e l a t io io n s h i p s

s e rv r v e t o e s ta t a b l is i s h a d e s c ri r i p ti ti v e

v o c a b u l a r y i n s o il i l m e c h a n i c s : t h e y a r e b a s e d o n a s c h e m a t i c r e p r e s e n t a t i o n o f so s o il il i n w h i c h it it s t h r e e c o m p o n e n t s a r e

lum pe d

a s s h o w n in i n F ig i g . 1 , w h i c h a ls l s o i n c lu lu d e s

t h e c u s t o m a r y d e f i n it i t io i o n s . A b a s i c c h a r a c t e r i s t i c o f th t h e s o i l s k e l e to t o n i s th th e s i z e a n d s h a p e o f i ts t s c o n s t i t u e n t p a r t i c le le s : i n s a n d s t h e y a r e b u l k y a n d r e l a t i v e l y l a r g e ( re r e p r . s iz iz e 0 . 5 m m ) i n c l a y s t h e y a r e p l a t e - - o r n e e d l e - - s h a p e d a n d q u i t e s m a l l ( c o l l o i d a l s iizz e . B o t h s i z e a n d s h a p e i n f l u e n c e t h e i m p o r t a n t s o i l p r o p e r t y o f s pe p e c if i f ic i c s u r f ac a c e w h i c h m a y r a n g e f r o m s e v e ra ra l h u n d r e d s q u a r e m e t r e s p e r g r a m f o r c e r t a in i n c l a y s t o a f r a c t i o n o f a s q u a r e m e t r e p e r g r a m f o r s a n d s. s. G r a i n s iz i z e i s e x p r e s s e d i n t e r m s o f a n e q u i v a l e n t d i a m e t e r w h i c h , f o r si s i ze ze s l a r g e r t h a n 7 4 I t ( B . S . o r A . S . T . M . S i e v e n o . 2 0 0 ) , i s d e t e r m i n e d b y s i ev ev i n g a n d b e l o w t h a t size by elutriation methods based on Stokes' Law. The grain size distribution of a soil is usually represented by a cumulative curve such as shown in Fig.2, from w h i c h v a r i o u s d i s t r ib ib u t i o n p a r a m e t e r s m a y b e d e t e r m i n e d . O n e o f t h e m o s t w i d e l y used is the un ifo rm ity coefficient defined as Cu = d6o/dlo. S i n c e t h e s o i l w a t e r c o n s i d e r a b l y i n fl f l u e n c e s t h e b e h a v i o u r o f c l ay ay s , a n u m b e r Earth-Sol. Rev. 6 ( 1970 1970)) 54 9

 

8

I. ALPA N / - o l u r ne ~

~l e~ahls

I LIn/~ A r e a ~ ,q ,q , n b o l a n d

Ter m

f.

Un / t

-Oef'/n/(/on

Po ro i~/

e.

k / O / C /P /P a t ~ o

.~

P e r c e , ~ - / c , ~ , e R z r l / o lu lu m e

~/~

e

a= vo v

c*/*~

~ ~/~

~*/,



A a 3 ( = A c z ) . L e t t h e st s t re re s s

t r ip i p l e t in in q u e s t i o n b e r e p r e s e n t e d b y t h e p o i n t P i n F i g . 9 b ; i t c a n o b v i o u s l y b e r e a c h e d b y a v a r i e t y o f s t re r e s s p a t h s o f w h i c h t h e f o l l o w i n g a r e s h o w n a s e s p ec e c i a ll ll y significant: (1) OA-AP.

with

AO

2

=

a l l - r o u n d p r e s s u r e f o l l o w e d b y t h e a p p l i c a t i o n o f sh s h e a r s t r es es s

A ir ir 3 h e l d c o n s t a n t .

r e s s r a t i o , K = A t r 3 /A /A a I = c o n s t a n t . ( 2 ) O P : t h e s t re tr e s s c h a n g e d u r i n g w h i c h t h e ( 3 ) O B - B P : a l l - r o u n d p r e s s u r e f o l l o w e d b y a s tr

Earth-ScL Rev., 6 (1 970) 5M-9

 

THE GEOTECHNI GEOTECHNICAL CALPROPERTIES PROPERTIESOF OF SOILS

19

f i rs rs t s t r e s s i n v a r i a n t , A I 1 = A a ~ + A a 2 + A a 3 i s h e l d c o n s t a n t . B P i s f r e q u e n t l y term ed the pa th of

pu re dev iatoric load ing

( KL K L A U SN S N E R , 1 96 9 6 4) 4) .

T h e r e m a r k s a b o v e a p p l y , n a t u r a l l y , t o t o t a l a s w e l l a s ef e f fe f e c ti t i v e s t re re s s p a t h s depending upon the conditions investigated. T h e b a s i c o b j e c t o f s t r e s s - s t r a i n i n v e s t i g a t io i o n s i n so so i l m e c h a n i c s a p p e a r s , t h u s , t o b e t h e s t u d y o f ef e f f ec e c t iv i v e s t re re s s p a t h s a n d t h e c o n c o m i t a n t c h a n g e s o f volume, shape or both. I n t h e g e n e r a l c a s e o f t r i a x i a l s t r e s s a p p l i c a t i o n ( A ax a x > A ~r ~ r2 :

Aa3) we m ay

w r i t e SKEMPTON, 1954): Au

=

B[A a 3

A(Aa~

Aa 3 ) ]

(14)

a n d , b a s e d o n c o n c e p t s b y S KE KE MP M P TO TO N a n d B IS IS H O P ( 1 9 54 54 ) :

AV Vo

C ~ A a 3 / 1 _ B + Sd _ B A) [ Aa l

1]~

Aa

]

[

15)

w h e r e A i s a p o r e p r e s s u r e c o e f f ic ic i e n t a n d S d i s d e f i n e d a s a s t r u c t u r a l p a r a m e t e r . A t fu fu l l s a t u r a t i o n w i t h d r a i n a g e p r e v e n t e d , B =

1 a n d , s in i n c e A V / V o = O,

we find that: Sd = A

(16)

F o r a l l - r o u n d c o m p r e s s i o n , w i t h A a l = A O -z -z = A o -3 -3 = A p , e q . 1 4 a n d 1 5 b e c o m e , o f c o u r s e , id i d e n t i c a l w i t h e q . 9 a n d 1 3. 3. I t m a y b e n o t e d , i n p a s s i n g , t h a t e q . 1 6 a p p e a r s t o c o n f i r m t h e s o - c a ll ll e d

A m eric an

hypothe sis

r e ga g a r di d i .n .n g t h e s h e a r

s t r e n g t h o f n o r m a l l y c o n s o l i d a t e d c l a y s (S ( S KE K E M PT PT ON O N a n d B I s H o P , 1 9 5 4 , p . 4 73 73 ) . Consolidation

A s m e n t i o n e d b e f o r e , t h e p r o c e s s o f d r a i n a g e i n a fu f u l ly ly s a t u r a t e d s a m p l e i s a c c o m p a n i e d b y th t h e d i s s ip i p a t i o n o f t h e p o r e w a t e r p r e s su s u r e , (A (A u ~ 0 ) ,

and by

v o l u m e c h a n g e s r e s u l t i n g f r o m t h e s i m u l t a n e o u s c h a n g e s i n e ff f f e ct c t iv i v e s tr t r e ss ss . I t i s o b v i o u s t h a t t h e r a t e o f t h is i s p r o c e s s m u s t d e p e n d , i n th t h e f ir i r st s t p l a c e , u p o n t h e s o il il permeability. In clays, the process, termed consolidation, is in most cases a very s l o w o n e a n d h a s , f o r t h is i s v e r y r e a s o n , f o r m e d t h e s u b j e c t o f e x t e n si s i v e s tu tu d i e s o v e r f o r t y y e a r s s i n c e t h e c l a s s i c a l i n v e s t i g a t i o n s o f T E R ZA Z A G H I ( 1 9 2 3 , 1 9 24 24 ) a n d , l a t e r , o f B l O T ( 1 9 4 1 ) a n d T A Y L O R ( 1 9 4 2 ). ). T h e c o n v e n t i o n a l a n a l y s is i s o f s a t u r a t e d c o n s o l i d a t i o n , i n b ri r i e f es e s t o u t li li n e , is as follows (cf., GmSON and LUMm 1953): L e t t h e v o i d r a t i o e , b e a f u n c t i o n o f t h e a p p l i e d e f f e c t iv i v e s t re r e s s , i. i . e. e. : e =

e(a ) =

e(a - u)

17)

then:

1970) 0) 54 9 Earth-Sci. Rev., 6 197

 

20

I. ALPAN

d e = _ _3 _3 e d a ' = _ _3 _3 e ( d a -

Oa

Oa

du)

(18)

If, as usual, the applied total stress remains constant during the process, and the stress interval is sufficiently small: 0e --

-

= av = the cons tant

0t7'

c o e f f i c ie ie n t o f c o m p r e s s i b i l i t y .

H o w e v e r , f o r l a r g e r s t re r e s s i n t e rv r v a l s a p p l i e d to to

no rm ally-c ons olida ted

( 19 19 ) c l a y s, s , i .e .e . ,

clays being consolidated under a pressure never exceeded in their past, the following relationship holds: Cc log (a /a o)

e = eo -

where Cc = constant

(20)

com pression index .

It follows that, for this case: 0e

2.3 ( C d a ) .

-

Off'

(21)

T h e t i m e r a t e o f c h a n g e o f th t h e v o i d r a t i o c a n b e w r i t te te n a s : 0e

Ot

-

0u

av-

22)

Ot

A s s u m i n g t h e v a l id i d i ty t y o f D a r c y ' s r u le le , t h e a p p l i c a t i o n o f th th e l a w o f m a s s c o n servation yields: 3

1

k~

Yw

0 2u ~

i=1

-

av 1 +

0U e

23)

at

and, for a homogeneous and isotropic soil: CV 2/ /-

0U

(24)

Ot wh ere the c

-

c o e f f i ci ci e n t o f c o n s o l i d a t i o n : k(1 + e ) ~w

25 )

av

m a y b e a s s u m e d a s s e n s ib i b l y in i n d e p e n d e n t o f t h e a p p l i e d e f fe f e c ti t i v e s tr t r e ss ss . T h e a n a l y s is i s , o u t l i n e d a b o v e , w h i l e f o r m i n g t h e b a s i s o f p r a c t i c a l l y al al l w o r k o n t h e c o n s o l i d a t i o n p r o b l e m , f a il i l s to t o a c c o u n t f o r t he h e r e l a ti ti v e m o v e m e n t o f t h e soil skeleton and the extruded water during the process. An attempt to include t h i s a s p e c t w a s p r e s e n t e d b y Z AS AS L AV AV SK SK Y( Y( 1 9 6 4 ) , u l t i m a t e l y l e a d i n g t o t h e f o l l o w i n g expression: Earth-Sci. Rev. 6 ( 1 9 7 0 ) 5 4 9

 

THE GEOTECHNI GEOTECHNICAL CALPROPERTIES PROPERTIES OF SOILS

k.V

21

( y u~ + z ) = ~ - ~3 [ l n ( 1 + e ) ] + q s . V [ l n ( 1 + e ) ]

(26)

w h e r e q s = a v e r a g e v e l o c i t y v e c t o r o f t h e s o il i l p a r t i c l e s r e la la t i v e t o a f i x e d c o o r d i n a t e s y s te t e m . A n o t h e r a p p r o a c h , c l a im i m i n g g r e a t e r g e n e ra r a l it it y , h a s b e e n p r o p o s e d b y M IK IK A SA SA ( 19 1 9 6 5) 5) , w h o f o r m u l a t e s t h e c o n s o l i d a t i o n p r o c e s s i n t e r m s o f a l o g a r i th t h m i c v o i d r a t i o f u n c t i o n a s f o l lo lo w s ( m o d i f i e d h e r e t o c o r r e s p o n d t o e q . 24) : c

V2e -

& at

(27)

where: e - -- - -I - I n . . . +. e o l+e

( 28)

H o w e v e r , a s a l r e a d y i n d i c a te t e d , e q . 2 4 r e p r e s e n t s th t h e g e n e r a l ly ly a c c e p t e d f o r m u l a t i o n o f th t h e t h e o r y o f c o n s o l i d a t i o n a n d i ts ts s o lu l u t io i o n s , f o r v a r io io u s b o u n d a r y c o n d i t i o n s , f o r m t h e b a s i s o f s e t tl tl e m e n t p r e d i c t i o n s i n e n g i n e e r i n g p r a c t i c e . O f t h e s e s o l u t i o n s w e s h a ll l l b r i e f l y c o n s i d e r t h e a x i a l - s y m m e t r i c a l c a s e, e , i .e . e ., ., t h a t o f v e r t i c a l a n d r a d i a l d r a i n a g e o f w a t e r f r o m a s a t u r a t e d c y l i n d r i c a l s o il i l v o l u m e (C (C A R R IL IL L O, O, 1942; G I BSO N an d H EN K EL, 1954 1954)) . L e t Uo U o b e t h e i n i ti ti a l, l , u n i f o r m l y d i s t r ib ib u t e d , p o r e w a t e r p r e s s u r e i n a s a t u r a t e d c y l in i n d r i c al al c l a y s a m p l e p r i o r t o t h e s t a r t o f d r a i n a g e a n d u t ) t h e a v e r a g e p o r e pressure in the sample at a time t after drainage has started. The average degree of consolidation is then defined as: U = 1 --

U

(29)

Uo

I f d r a i n a g e t a k e s p l a c e b o t h i n t h e v e r ti t i c a l a n d r a d i a l d i re r e c t io io n , t h e a v e r a g e d e g r e e o f c o n s o l i d a t i o n is is s h o w n t o b e : U -- 1 -- (1 -- Uz)(1 -

U r)

( 30)

where: U z = 1 - - -z

31)

UO

and:

U r

1

( 32)

~/r Uo

H e r e , Uz is t h e s o l u t i o n o f t h e o n e - d i m e n s i o n a l c o n s o l i d a t i o n e q u a t i o n : Earth-Sci. Rev., 6 (1970) 5-49

 

22

I. ALPAN 92/ I

0u

cz ~z ~ = -O t

33)

a n d Ur t h a t o f t h e r a d i a l c o n s o l i d a t i o n e q u a t i o n :

F02. + _ 2u ]

Cr[~?

F OF

0u

= 5t

34)

F o r a c y l i n d ri r i c a l s p e c i m e n o f h e i g h t h a n d r a d i u s R , w i t h o n l y v e r t ic ic a l d r a i n a g e t h r o u g h b o t h e n d s u r fa f a c e s , t h e s o l u t i o n o f eq e q . 33 3 3 i n t r o d u c e d i n e q. q . 31 3 1 f u r n is is h e s : 8 Uz = 1 -- -;

l

exp

- 1

+ 2n 2-

n=0

7~ 2 7~2

4

Cz

t

35)

with H = h/2, the longest drainage path; whereas for radial drainage, the solution o f e q . 3 4 i n t r o d u c e d i n e q . 3 2 y i e ld ld s :

Ur = 1 - 4

~ -e x p

Cr

-

o, ~

t

36)

On

n=l

w h e r e o ) , is is t h e n t h r o o t o f t h e z e r o o r d e r B e s s e l f u n c t i o n , J o I n m o s t c a s e s , d u e t o s t r a t i f i c a t i o n , c r / c z = ~ > 1 e .g. ABOSHt a n d M O N D E N ,

tO

I

U=SO

i

.o

i

i[ /

?

.7

4

~

=

6

Cr/C

5

7

S

9

tO

z

F i g .1 .1 0 . T h e i n f l u e n c e o f a n i s t r o p y o n t h e s p e e d o f c o n s o l i d a t i o n .

1 9 60 60 , 1 9 61 61 ; M c K I N L A Y , 1 96 96 1 ) a n d t h e i n f l u e n c e o f t h i s c o n d i t i o n i s i l l u s t r a t e d i n Fig.10 for 50 ~ averag e consolidation, where ~ = 0 represents one-dim ensional vertical) consolidation, the time for this case being taken as reference. Earth-Sci. Rev.

6 1 9 70 70 ) 5 4 9

 

THE

GEOTECHN1CAL

PROPERTIES

OF

3

SOILS

Elastic theory concepts R e v e r t i n g t o o u r g e n e r a l t o p i c o f s t re r e s s - s t r a i n r e l a ti ti o n s , o n e w o u l d e x p e c t t o fi f i n d a c o n s i d e r a b l e a m o u n t o f r e s e a r c h c o n c e r n e d w i t h a t t e m p t s t o e x p re r e s s t h e se se r e la l a t io io n s i n t e r m s o f c o n v e n t i o n a l p a r a m e t e r s s u c h a s Y o u n g s m o d u l u s , P o i s s o n s r a t i o e t c .,., m a i n l y a s a re r e s u l t o f a n u n f o r t u n a t e d i l e m m a . F o r , w h i le l e e v e r y b o d y is is a w a r e o f t h e n o n - l i n e a r c h a r a c t e r i s t i c s o f s o il i l s, s , t h e a n a l y t i c a l t o o l s u s e d i n th th e m a j o r i t y o f d e f o r m a t i o n p r o b l e m s in i n s o il i l e n g i n e e r i n g a r e b a s e d o n r e s ul u l ts ts f r o m l i n e a r c o n t i n u u m m e c h a n i c s e .g . g ., . , t h e p r o b l e m o f th t h e s t r es e s s d i s t ri r i b u t i o n i n s o il il m a s s e s . S t il il l, l, i f u n w a r r a n t e d e x t r a p o l a t i o n s a r e a v o i d e d , v e r y u s e fu fu l r e s u l t s a r e available. A s a t y p i c a l a n d i n t e r e s t i n g e x a m p l e , t h e w o r k o f JA JA KO KO BS BS O N ( 1 95 95 7 ) o n s a n d s c a n b e c i te t e d . F i g . 1 1, 1, b a s e d o n h i s r e s u lt lt s , s h o w s t h e v a r i a t i o n o f E a n d v a s f u n c t i o n s o f t h e e f f e c ti ti v e s tr t r e s s r a t i o K = a 3 / a ~ a p p l i e d in in t h e t r i a x i a l a p p a r a t u s . S i m i l a r l y , t h e f u n c t i o n K / I +K ) i s s h o w n w h i c h , i n e l a s t i c t h e o r y , c o r r e s p o n d s t o z e r o l a t e r a l s t r a i n . T h e i n t e r s e c t i o n s o f t h i s f u n c t i o n w i t h t h e v - l in in e s o f t h e t e s t e d s a n d s w o u l d t h e n r e p r e s e n t t h e s o c a l l e d K o c o n d i t i o n ( e .g .g . , A L P A N , 1 9 6 7 a) a) a n d Q7

06

.-

--

.

.~ O .~ .~

~

-

0. 4

-

f

7 ~O ~O O

_

--

2aO0

/ O t

_

/

7

_ __

500

o 0

02

0.4

06

O0

fO

Fig.l 1. 1. Elastic co ns tan ts for sa nd s. (After (After JaKOBS JaKOBSON, ON,1957. 1957.)) i t a p p e a r s t h a t t h e v a l u e o f K o, o , a s d e t e r m i n e d f o r t h e s p e c if i f ic i c te te s t i n g c o n d i t i o n s i m p o s e d , i s g r e a t e r i n t h e l o o s e r s a n d , c o n t r a r y t o r e s u l ts ts o b t a i n e d i n c o n v e n t i o n a l o e d o m e t e r t e s ts t s . O n t h e o t h e r h a n d , t h e e v i d e n c e o f F ig i g .1 .1 1 i n d i c a t e s a n i n c r e a s e o f P o i s s o n s r a t i o w i t h d e n s i ty t y , i n a g r e e m e n t w i t h a te te n t a t i v e i n t e r p r e t a t i o n o f certain dynamic tests on sands (ALPAN, 1967b).

Earth-Sci. Rev., 6 (1970) 5-49

 

24

i. ALPAN T h e i n i t ia ia l p o r t i o n o f a t y p i c a l s t r e s s - s t r a i n c u r v e i s, s, i n g e n e r a l , s u f f ic i c i e n tl tl y

l i n e ar a r t o p e r m i t t h e d e t e r m i n a t i o n o f a r e a s o n a b l y c o n s t a n t m o d u l u s f o r th t h is is r a n g e , u s u a ll l l y t e r m e d t a n g e n t m o d u l u s , E ~. ~ . T h e v a r i a t i o n o f t hi h i s m o d u l u s w i th th o v e r b u r d e n p r e s s u r e i s s h o w n i n F i g . 1 2 ( c f . , T ~ R Z A C H I a n d P E C K , 1 9 67 67 , a r t . 1 5 ); ); a l s o 500O

J

/q 2 ~/rn~r ~/rn~r

o

5

tO

Z~ePfh

L~O of

,~

~ erL~JrDCen

40

5t9

m

Fig.12. Fig. 12. Tan gen t m odu lus vs. vs. overburde overburden. n.

Af ter TERZAOH[ and PEck, 1967.)

s h o w n , f o r c o m p a r i s o n p u r p o s e s , i s a c u r v e f o r a sa s a n d a t 7 0 ~ r e la l a t iv i v e d e n s i ty ty c o m p u t e d f r o m d a t a g i v e n b y W I LS L S O N a n d S U T TO T O N ( 1 94 9 4 8 ) e x h i b i t in i n g a s i m i la la r trend. T h e p r o b l e m o f t h e l in i n e a r i ty t y ra r a n g e , m e n t i o n e d a b o v e , h a s b e e n r e c e n tl tl y i n v e s t i g a t e d b y S O U TO T O S IL IL VE V E IR IR A ( 1 9 6 7 ) w h o d e f i n e s t h e

line arity perc en t

as that

6'5

I

/ 7o/~/u.re

Co/7/ enz

:~/

(O/o)

Fig.13. Linear deformation range of a soil. (After SOLrTOSILVEIRA 1967.) Earth-Sci. Rev. 6 (1970 ) 5-5--49 49

 

25

THE GEOTEC HNI C AL P R OP ER TIES TIES OF S OI LS

f r a c t i o n o f t h e f a i lu l u r e s tr tr e s s w h i c h c o n s t i t u t e s t h e u p p e r l i m i t o f t h a t r a n g e . A s e v i d e n t i n F i g .1 . 1 3 , t h i s p a r a m e t e r i s se s e e n t o d e c r e a s e w i t h in in c r e a s i n g m o i s t u r e content and the all-round consolidation pressure in the triaxial cell.

Soil stren strength gth In the preceding parag rap h,

t h e f a il i l u r e s tr t r e ss ss a p p e a r s a s a c o n v e n i e n t

r e f e r e n c e s tr t r e ss s s a n d i t i s a p p r o p r i a t e , a t t h is is s t ag ag e , t o c o n t i n u e o u r d i s c u s s i o n o f s t r e ss s s - s tr t r a i n r e l a t io i o n s h i p s w i t h a s o m e w h a t d e t a i le le d t r e a t m e n t o f t h e p r o b l e m o f strength and failure in soils. S o il i l s, s , s t r a i n e d i n s h e a r b e y o n d a c e r t a i n l i m i t o f r e s is i s t a n ce ce , a r e c o n s i d e r e d a s h a v i n g f a i l e d a n d t h u s s t r e n g t h m a y b e d e f i n e d as a s r e s i st s t a n c e t o e x c e s si si v e s h e a r deformations. A typical triaxial compression test curve, corresponding to the stress path

A P o f F i g .9 . 9 b , i s s h o w n i n F i g . 1 4 w i t h th th e c u s t o m a r y f a i l u r e c o n d i t i o n a t t h e maximum principal stress difference. ~-~

[

too

I

I

\

Ic

I

F i g . 1 4. 4. T r i a x i a l s t r e s s - s t r a i n c u r v e .

O n c e t h e a l l o w a b l e l im im i t o f d e f o r m a t i o n h a s b e e n s t ip i p u l a te t e d , t h e s t a te te o f f a i l u r e c a n b e d e s c r i b e d b y a r e l a ti t i o n s h i p i n v o l v i n g st s t re r e s s es es a n d m a t e r i a l p a r a m e t e r s ; such a relationship constitutes a failure criterion. F o r i s o t r o p i c m a t e r i a l s , f a i lu lu r e is i n d e p e n d e n t o f o r i e n t a t i o n , h e n c e , a c c o r d i n g t o t h e g e n e r a l m a t h e m a t i c a l p r i n c i p l e s o f i n v a r i a n c e , a s c i e n ti t i f ic ic a l ly ly c o r r e c t failure criterion must contain the three principal stresses in a cyclic-symmetrical arrangement B R I N C H - H A N S E N a n d L U N D G R E N , 1960 1960,, p. 39 ; IRMA Y , 1968 1968)) . F a i l u r e c r i t e r i a f o r s o il il s w o u l d e v i d e n t l y b e e x p r e s s e d i n t e r m s o f e f f ec e c t iv i v e s tr t r e ss s s e s. s. T h u s , t h e g e n e ra r a l ly l y a c c e p t e d M o h r - C o u l o m b f ai a i lu l u r e c r it i t e ri ri o n m a y b e f o r m u l a t e d a s ( D RU CK ER a n d PRA G ER, 1952) 1952):: Earth-Sci. Rev. 6 1 9 7 0 ) 5 ~ - 9

 

26

i. A LP A N ~( A llf -

3Au f) +

V/[ -

A/d 2]f = k

(37)

where: A l l f = 3 ( A 6 oc oc t ) f = A a ~ r +

38)

4-

Ao-3f

-

A o 3 f ) 2 -~ - ( A o 3 f

AO'2f

and: lai d2 ] --

_ 3~ ( A r o , ) f2 =

f

~[(A O- lf

--

A o 2 f ) 2 -1 - ( A o ' 2 f

(39)

- - A O ' lf ) 2 ]

a n d c~ c~ a n d k a r e m a t e r i a l p a r a m e t e r s . I n m o r e c o n v e n t i o n a l n o t a t i o n , t h e f a il i l u r e c o n d i t i o n i n t r ia ia x i a l c o m p r e s s i o n , (AO -l'f >

A o ';f

~ ----

/~ O ' if ) , r ead s :

AO lf = N 0, Ao-3f + 2 c a / N O, O, with the

(40)

flow value

N 0, -

sin qS'

1 1

(41 )

sin qS'

-

w h e r e q S ' d e n o t e s t h e e f f e c ti t i v e a n g l e o f s h e a r i n g r e s i s ta t a n c e a n d c ' t h e e f fe f e c t iv iv e c o h e s i o n i n t e r c e p t . I n t e r m s o f t h e e ff f f e c ti t i v e n o r m a l a n d s h e a r i n g s t r e s se s e s o n th th e f a i l u r e p l a n e ( i n c li li n e d b y 0 r t o t h e m a j o r p r i n c i p a l p l a n e ) t h e f a i l u r e c o n d i t i o n reads: A~-f = c ' + Ao-'nf a n ~b'

(42 )

where: Ao- nf = (1 -

sin qT)A a'lf -

c ' c o s q S' S' = ( 1 + s i n ~ b ) A o 3 f + C ' C O S q ~

(43)

T h e f a i l u re r e c o n d i t i o n s e x p r e s s e d b y e q .3 . 3 7 , 4 0 a n d 4 2 a re r e s h o w n i n F i g .1 .1 5 f o r a s oi oi l o f g i v e n s t r e n g t h p a r a m e t e r s . W e s h a l l c o n t i n u e i n d i sc sc u s s i n g t h e s t r e n g t h c h a r a c t e r i s t i c s o f s a n d s a n d clays separately. S a n d s d o n o t e x h i b i t a c o h e s i o n i n t e r c e p t , i .e . e .,. , c ' = 0 , k = 0 . C o n s e q u e n t l y , t h e i r s h e a r i n g r e s i s ta t a n c e i s c o m p l e t e l y d e f i n e d b y t h e p a r a m e t e r q~' w h i c h d e p e n d s , in general, on the following physical properties (BR1NCH-HANSEN and LUNOGREN, 1960): ( 1) 1 ) G r a i n s h a p e : t h e c h a n g e i n ~b ~ b ' b e t w e e n t h e e x t r e m e s o f v e ry ry a n g u l a r a n d v e r y r o u n d g r a i n s is is o f t h e o r d e r o f 6 ° . ( 2) 2 ) G r a i n s iz i z e: e : f o r t h e r a n g e s a n d - g r a v e l a c h a n g e i n $ ' m a y b e o f th th e o r d e r o f 2 ° . T h e r e a p p e a r s , h o w e v e r , t o b e a m a r k e d i n fl f l u e n ce ce o f g r a d a t i o n : t h u s , u n i form

ma terials

e x h ib ib i t a m u c h

l a rg rg e r

change

than

well-graded

ones, nam ely

o f th t h e o r d e r o f 1 0 ° f o r a r a n g e o f m a x i m u m p a r t i c le l e s iz i z e f r o m 0 .2 .2 t o 2 0 m m . ( H EN N ES , 1 9 5 2 ) . Earth-Sci. Rev., 6 (1970) 5-49

 

THE GEOTECHNICALPROPERTIES GEOTECHNICALPROPERTIES OF SOIL SOILS S

27

3~0

~o

.//

zo

,.

No.O,, c/;,~c~

to /.O

lifo

,3 .0

4.0

. o .0 .0

i

1i

' role

~;r

~m~

I r- a ~ u r Jme

Fig.15. Failure conditions. 3 ) G r a i n s iz i z e d i s tr t r i b u t i o n a s e x p r e s se se d , f o r e x a m p l e , b y t h e u n i f o r m i t y c o e f f ic ic i e n t C , = d 6 o / d x o . 4 ) D e n s i t y o f p a c k i n g , c o m m o n l y e x p r e s s e d b y th t h e v o i d r a t i o , e. e. T h e i n f lu l u e n c e o f t h e l a s t t w o p r o p e r t i e s i s i l lu l u s t r a te te d b y t h e e m p i r i c a l c u r v e s s h o w n i n F i g .1 . 1 6 w h i c h a r e b a s e d o n t h e f o l l o w i n g r e l a t io i o n s h i p f o u n d t o e x p r e ss ss <

/ 0

~

o N kN',

0.4

02

O .. .. r

ZnitlUI

04

VOid

05

rotlO

Oa

02

08

o9

Io

iI

eo

Fig.16. The influence of void ratio and grading on the shearing resistance of sands. a d e q u a t e l y t h e v a r i a t i o n o f s h e a r i n g r e s i st st a n c e w i t h v o i d r a t i o

C A QU QU O T a n d

K~RISEL, 1966; WINTERKORN , 1966): Earth-Sci.

Rev.,

6 197 1970) 0) 54 9

 

28

L ALPAN e ta n ~b ~b'' = ks

(44)

w h e r e t h e p a r a m e t e r k s i s s h o w n t o d e p e n d p r i m a r i l y o n g r a di d i n g . T o s o m e e x t en en t k s d e c r e a s e s w i t h i n c r e a s i n g e f f e c t i v e c o n f i n i n g p r e s s u r e ( c f . , T A Y L O R , 1 94 9 4 8 , c h . 1 4: 4: T e s t s o n O t t a w a s a n d ) . T h e i n t e r e st s t i n g f a c t o f a n a p p a r e n t u p p e r l i m i t o f s tr tr e n g t h i n g r a n u l a r m a t e r i a l s h a s b e e n d i s c u s s e d t h e o r e t i c a l l y b y I RM R M A Y ( 1 96 9 6 8 ). ). I f t e s t e d iinn s h e a r a s a n o p e n s y s t e m , s a n d s e x h i b i t v o l u m e c h a n g e s w h i c h d e p e n d , i n t h e fi f i r st s t i n s t a n c e , o n t h e i n i t ia i a l s t a t e o f p a c k i n g : d e n s e s a n d s d i l a te te , l o o s e s a n d s a r e c o m p r e s s e d . T h i s t e n d e n c y a f f ec ec t s t h e b e h a v i o u r o f s a t u r a t e d s a n d s w h e n s h e a r e d a s a c lo l o s e d s y s te te m : i n d e n s e s a n d s t h e p o r e w a t e r p r e s s u r e diminishes while it increases in loose sands. A n a d d i t io i o n a l f a c to t o r , g o v e r n i n g th th e v o l u m e c h a n g e i n s a n d s u n d e r g o i n g s h e a r , i s t h e i r e f f e c ti t i v e s t a t e o f st st r e s s a n d i t s c h a r a c t e r . I n d e e d , r e c e n t r e s e a r c h s u p p o r t s t h e v i e w t h a t , u p t o a c e r t a in i n l e v el el , p u r e d e v i a t o r i c l o a d i n g d o e s n o t a p p e a r t o p r o d u c e s i g n i f ic i c a n t v o l u m e c h a n g e s ( F RY R Y D M A N , 1 96 9 6 8) 8 ) . I n a n y e v e n t , i t is is r e a s o n a b l e t o p o s t u l a t e th t h e e x is i s t e nc nc e o f a

critical

s t a te t e o f d e n s i ty ty a n d c o n f i n i n g

pressure in which sands do not exhibit volume changes in shear (for a thorough d i s c u s s i o n s e e T A YL Y L O R, R , 1 94 9 4 8) 8) . T h e c r i t i c a l v o i d r a t i o , e , , d e c r e a s e s w i t h i n c r e a s i n g c o n f i n i n g p r e s s u r e , P er er , a n d t h is is r e l a t i o n s h i p d e t e r m i n e s t w o r e g i o n s o f p o t e n t i a l v o l u m e c h a n g e i n a ( e, e , p ) - p l a n e a s s h o w n i n F i g . 17 17 . I f , n o w , a s a t u r a t e d s a n d i s ~ F

ll

g o n l ra c l ~ n Z o n e

Ca

U n i o rr n lt L l £ o e f~ f~ /c~ / c~ n /

c r /Y / Y / c ~ l c ~ // // ~7 ~ 7 in in y P r ~ u z - e

Fig. 17. C ritical void rati o an d pressure. e x p o s e d t o a n a p p l i c a t i o n o f s h e a r in i n g s t r es e s s es es , q u i c k e n o u g h f o r n o d r a i n a g e t o o c c u r , t h e p o r e w a t e r p r e s s u r e w i ll ll c h a n g e a c c o r d i n g t o t h e z o n e r e p r e s e n t i n g t h e state of the sand. Acco rding for exam ple to eq.40 the factor of safety o f the sand again st shear failure can be written as F = N o, (0 3 --/ / )/ (0 1 --/ / ) ~ 1, fro m which t h e c h a n g e i n s a f e ty t y d u e t o a c h a n g e i n p o r e w a t e r p r e s s u r e i s e a s il il y d e r i v e d a s (1970) 54 9 Earth-Sci. Rev. 6 (1970)

 

THE GEOTE CHNIC

29

L PROPERTIE S OF SOI SOILS LS

h a v i n g th th e f o r m d F =

-a

du, where the constant a >

c o n d i t i o n s . It I t f o l lo l o w s t h a t f ai a i l u re re m a y o c c u r i n t h e

0 r e p r e s en e n t s t h e i n it i t ia ia l

co ntra ctio n

zone, provided

the sand in question exists in the corresponding state. That this may not be so is s i m i l a r ly ly s h o w n i n F i g . 1 7 i n w h i c h t h e r e l a t i o n s h i p s o f F i g . 1 6 h a v e b e e n q u a l i t a t i v e l y i n t r o d u c e d t o s h o w t h a t i n c r e as as i n g u n i f o r m i t y o f g r a d i n g e n h a n c e s t h e d a n g e r o f l i q u e f a c t i o n , a t e r m c o m m o n l y u s e d f o r t h e t y p e o f f a il i l u r e d e s c r ib ib e d a b o v e . T h e f a c t o r s i n f lu l u e n c i n g t h e s h e a r i n g r e s i st st a n c e o f c l a y s a p p e a r t o b e t o o n u m e r o u s a n d , i n p a r t , n o t a d e q u a t e l y c la la r if i f ie i e d t o a l lo l o w a u n i f ie i e d tr tr e a t m e n t o f t h e p r o b l e m . T h u s , i t i s m o s t i n s t ru r u c t i v e t o s t u d y th t h e l is is t o f f u n d a m e n t a l a n d i n t e r r e l a t e d f a c t o r s g i v e n b y T A Y L O R ( 19 1 9 4 8 , s e c t i o n 1 5. 5.2 ) i n o r d e r t o a p p r e c i a t e the complexities involved. Accordingly, our discussion will have to be limited to those basic aspects which, while far from exhausting the subject, still a fforda s u f f ic i c i e n tl tl y c o h e r e n t v i e w o f it . I n l i m i t in i n g a t t h e o u t s e t o u r t r e a t m e n t t o f u l l y s a t u r a t e d c l a y s, s, a c o n d i t i o n most often encountered, we shall postulate as significant the following three f a i l u r e c o n d i t i o n s ((cc f . B R IN IN C H - H A N S E N a n d L U N D G R E N , 1 9 60 60 , p a r a . l . 4 2 ) , r e l e v a n t e q u a t i o n s b e i n g f o r m u l a t e d f o r d i r e c t s h ea ea r :

the

( / ) T r u e f a i l u r e: e : d e t e r m i n e d b y t h e e f f e c ti t i v e s tr t r e ss ss e s a t a g i v e n v o i d r a t i o ( o r m o i s t u r e c o n t e n t ) r e g a rd r d l e s s o f t h e s tr t r e ss s s h i s t o r y o f th t h e m a t e r ia ia l . T h u s i n t h e relation: Azf = C + Aa ',f ta n 4~r

(45)

t h e t r u e s t r e n g t h p a r a m e t e r s c r a n d C r a r e c o n s i d e r e d u n i q u e f u n c t i o n s o f th th e m o i s t u r e c o n t e n t a t f a il i l u r e . I n a r i g o r o u s s e n se s e , t h e s tr t r e ss s s h i s t o r y o f a c la la y s h o u l d s h o w t h e v a r i a t i o n w i t h t i m e o f t h e e f f e c ti t i v e s t re re s s t e n s o r a p p l i e d t o i t f r o m i ts ts f o r m a t i o n t o t h e t i m e o f t e st s t in i n g . I n a c t u a l f a c t, t , h o w e v e r , a c o m p a r i s o n o n l y is is ma de between the m axim um

e f fe fe c ti t i v e s tr t r es es s e v e r e x p e r i e n c e d b y t h e c l a y i n

q u e s t i o n , a n d t h e e f f e c ti t i v e s tr t r e ss s s u n d e r w h i c h i ts ts p r o p e r t i e s a r e b e i n g i n v e s t i g a t e d : if bo th are equa l the clay is said to be

n o r m a l l y c o n s o l i d a t e d , i f a l a r g e r e f f ec e c t iv iv e

s tr t r e ss s s h a s b e e n e x p e r ie i e n c e d in i n th t h e p a s t, t , t h e c l ay ay is t e r m e d ( c f. f. o u r d i s c u s s i o n o f c o n s o l i d a t i o n ) .

ove r-conso lidated

( 2 ) E f f e c ti t i v e f a i lu l u r e : d e t e r m i n e d b y t h e e f f e c ti t i v e s tr t r e ss ss e s a t v a r i o u s m o i s t u r e contents. Its formal expression has been given in eq. 42: Azf = c' + Aa'nftan ¢ ' w h e r e t h e e f f e ct c t i v e s t r e n g t h p a r a m e t e r s c ' a n d ¢ ' a r e i n f lu l u e n c e d b y s t re re s s h i s t o r y . O b v i o u s l y , t h e t w o f a i l u re r e c o n d i t io io n s p r e s e n t e d a b o v e i m p l y t h e p o r e w a t e r pressure at failure to be known. ( 3) 3 ) A p p a r e n t f a i l u re r e : d e t e r m i n e d w i t h r e s p e c t to t o t h e t o t a l a p p l i e d s t re r e s s es es : AZf :

C q- Acrnf ta n q5

( 46) Earth-Sci. Rev.

6 (1970) 5-49

 

30

i. AL P AN

w h e r e t h e s t r e n g t h p a r a m e t e r s c a n d ~b ~b d e p e n d , a m o n g s t o t h e r th t h i n g s , o n s t re re s s history and drainage conditions. C o n s i d e r a s a t u r a t e d c l a y , n o r m a l l y c o n s o l i d a t e d u n d e r a n e f f ec e c ti ti v e a l l - r o u n d c o n s o l i d a t i o n p r e s s u r e a ¢, ¢ , a n d s u b s e q u e n t l y b r o u g h t t o f ai a i lu l u r e in i n t ri r i a x ia ia l s h e a r with no drainage allowed. Its true cohesion intercept is found to be linearly related to the consolidation pressure (GmSON, 1953; HvogSLEV, 1960): C = xa~

(47)

w h e r e ~ is t e r m e d t h e

c o h e s i o n f a c t o r , a n d t h e fa f a i lu lu r e c o n d i t i o n m a y b e w r i t t e n

a s f o l l o w s : ( S K EM E M P TO TO N a n d B I S H O P , 1 9 5 4 ) : ½(A o.I __ __ Ao.3)f = xoxo-ee co s 4b 4brr -I-I- (a e - - A u f)s in q$r sin ~ 1

(4 8 )

with ac = Aa3 f S i n c e n o r m a l l y c o n s o l i d a t e d c l a y s d o n o t e x h i b i t a n e f f ec e c t iv i v e c o h e s i o n i n t e rrcept, the corresponding failure condition reads (cf. eq.40): sin 4b' ½ A f f l - - A 6 3 ))ff - - -1 - sin 46' ( t i c -

A u f) f)

( 49 49 )

I t i s a n e x p e r i m e n t a l f a c t t h a t f o r c la la y s , n o r m a l l y c o n s o l i d a t e d u n d e r v a r i o u s a m b i e n t p r e s s u re r e s a n d th t h e n s h e a r e d w i t h o u t d ra r a i n a g e , t h e s o - ca c a l le le d un dra ine d

conso lidated-

f a i lu l u r e c o n d i t i o n i n t e r m s o f t o t a l s t re r e s s es e s c a n b e e x p r e s s e d as as :

l( A o ' l -

s i n ~b¢ i 1 is t h e

ove r-

c o n s o l i d a t i o n r a t i o , a q u a n t i t a t i v e p a r a m e t e r o f st s t re re s s h is i s t o r y a n d d e f in i n e d as as t h e r a t i o o f m a x i m u m e f f e ct c t iv i v e s tr t r e ss s s e v e r e x p e r i e n c e d t o t h a t a p p l i e d i n t h e t e st st . SELECTED SPECIAL TOPICS

U n d e r t h i s h e a d i n g w e s h a ll l l d is i s c u ss s s b r i e f ly ly s o m e a s p e c t s o f o u r s u r v e y w h i c h , a l t h o u g h i m p o r t a n t , h a v e b e e n t h e o b j e c t o f r a t h e r s p e c ia i a l iz i z e d in i n q u i ri r i es es . Swelling soils

T h e s p o n t a n e o u s i n t a k e o f m o i s t u r e b y c o h e s i v e s o il i l s i s, s, i n g e n e r a l , a s s o c i a t e d w i t h v o l u m e i n c r e a se s e o r , i f t h e l a t te t e r i s p r e v e n t e d b y a p p r o p r i a t e c o n f i n in in g c o n d i ti t i o n s , w i t h t h e d e v e l o p m e n t o f p r e s su su r e . The swelling processs in clays may be viewed as due, essentially, to osmotic forces (WARKENT1Na (WARKENT1N a n d S CH C H O FI FIE LD L D , 1 9 62 62 ), ), t h e e x t r e m e l y f i n e c a p i l la la r i e s f u n c t i o n i n g a s a s e m i - p e r m e a b l e m e m b r a n e . A b r o a d c l a s s i fi f i c a t io i o n o f t h e f a c t o r s in in f l u e n c i n g t h e s w e l li l i n g c h a r a c t e r i s t ic i c s o f c l a y - w a t e r s y s t e m s w o u l d b e a s f o l lo l o w s (A (A L P A N , 1 9 6 5 b) b) : Qualitative factors: Ty pe o f clay mineral T e x t u r e o f c la la y ( c o m p o s i t i o n ) S t r u c t u r e o f c l a y ( p a rt r t ic ic l e a r r a n g e m e n t ) Q u a n t i t a ti t i v e f a c t o r s: s: Electrolite content of soil water Exchange capacity (cation exchange) Colloid content Density Moisture content D e g r e e o f s a t u r a t io io n A s o m e w h a t s i m p l e m o d e l , a s s u m i n g a r e g u l a r a r r a y o f c l a y p l a t e le le t s , w a s a n a l y s e d b y W A RK R K Er E rq T IN IN ( 1 96 9 6 2 ) w h o e x p r e s s e d t h e s w e l li li n g p r e s s u r e i n t e r m s o f t h e c la l a s si s i c al a l V a n ' t H o f f e q u a t i o n i n t o w h i c h t h e c a t i o n a n d s a lt lt c o n c e n t r a t i o n s i n t h e pore water were introduced. This equation may be written as follows: Ps = a wo + b) -2 + c

58) Earth-Sci. Rev., 6 ( 1970 1970)) 54 9

 

34

|. ALPAN

in w hich Wo is the initial water con ten t a, b an d c are consta nts for a given clay. Fo ur extreme poin ts of the experimental curve of Fig.20

i

K A SS S S IF IF F a n d Z EI EIT LE LE N, N,

i

• Colr'z~oc'ediC/~'f,

~-xt~r/me~tfc,/ / ( U n o t , ~ / u r ~ o C l ~ fJ fJ - 1

I I

--

(

~v ~

)

-

Fig.20. Sw elli elling ng pressure vs. initi initial al m oisture content.

After KAS KASSI SIFF FFan d ZEITLEN, ZEITLEN,1961.)

1 9 6 1 ) w e r e u s e d t o c a lc l c u l a t e t h e c o n s t a n t s a p p e a r i n g i n e q .5 . 5 8 a n d t h e t r en en d o f t h e resulting curve appears to be in fair agreement with empirical evidence, including tests on com pa cte d clay

W t S E M A N a n d Z E 1T 1T LE LE N , 1 9 6 0 ) .

E x p e r i m e n t a l e v i d e n c e s h o w s t h e t im i m e c u r v e s o f t h e sw sw e l l i n g p r e s s u r e t o b e similar to th ose of con solid atio n

N A L E Z N Y a n d L I , 1 9 6 7 ; B A K E R a n d K A S S tF tF F ,

1968) and may, therefore, be expressed by a function analogous to eq.35:

P s= P o

1-

M - ~ e xp xp

-

~

t

59)

n=

with M

=

~ 1 +

2 n ) / 2 , Cp Cps t h e a p p r o p r i a t e c o e f fi f i c ie ie n t o f s w e l l i n g p r e s s u r e a n d

L a l e n g t h r e p r e s e n t at a t i v e o f t h e f lo l o w - p a t h g e o m e t r y . T h e t i m e - r a te t e o f s w e l l in in g pressure becomes, therefore:

ddp~s = 2 p o LC~Ps P s ~~ e x p - M 2 ~c-w t ) n

60)

O

I n p r a c t ic i c e , t h e t i m e r a t e o f s w e l l in i n g p r e ss s s u r e is i s i n d e e d a m o n o t o n o u s l y d e c r e a s in in g Earth-Sci. Rev. 6 1970) 5 4 9

 

35

THE GEOTECHNICAL PROPERTIES OF SOILS

f u n c t i o n o f t i m e p a s s i n g t h r o u g h z e r o w h e n , a s i s o f t e n t h e c a s e , t h e s w e l l in in g p r e s s u r e e x h i b i t s a p e a k v a l u e A L P A N , 1 9 57 57 ). ). A s y n o p t i c p i c t u r e o f t h e i n fl f l u e n c e o f v a r i o u s f a c t o r s o n t h e s w e l li li n g p r e s s u r e

~0

¢ I t O

II t.

-~

- tsa..'o / */ */,. ,.~~

\

1

0

i'o

~o

.3o

arnit/o/

-¢o

~o

~o

7 0

P o r o a / ~ 17o o~)

Fig.21. Fig. 21. Fac tors affecting sw elling pressur pressure. e. A fter KASSlFF et al., al., 1968.)

o f r e p r e s e n t a t i v e I s r a e l c l a y s is i s a f f o r d e d b y t h e e m p i r i c a l c u r v e s i n F i g .2 .2 1 ( K A S S I F F e t a l. l. , 1 96 9 6 8, 8 , p . 1 1 0 ) w h i c h m a y b e c o n v e n i e n t l y e x p r e s s e d a s f o l lo lo w s :

- - -dps Ps

[ dwo - dwl)f no) + ~dno]

61)

w h e r e f no) i s a l i n e a r f u n c t i o n o f th t h e i n i t ia ia l p o r o s i t y , n o , a n d p o s i t i v e p r o v i d e d n o > 6 0 ~ ; W o i s t h e i n i ti t i a l m o i s t u r e c o n t e n t ; w~ t h e l i q u i d l i m i t o f t h e c l a y ; a n d ~x a p o s i t i v e c o n s t a n t . I t is i s e v i d e n t t h a t t h e s w e l l in in g p r e s s u r e d e c r e a s e s w i t h i n creasing moisture content and porosity and increases with the liquid limit, which m a y b e v i e w e d a s a n o v e r - a l l i n d e x o f t h e p h y s i c o - c h e m i c a l c h a r a c t e r i s t ic ic s o f a clay. Additional empirical evidence, supporting the relationship expressed by e q . 6 1 , h a s b e e n p r e s e n t e d b y D A NI N IL O V 0 9 6 4 ) a s s h o w n i n F i g .2 .2 2 . I f w e a s s u m e t h a t c l a y s o f e q u a l s w e l li l i n g p o t e n t i a l a r e r e p r e s e n t e d i n t h i s f ig ig u r e b y l in i n e s p a r a l le le l to the zone boundary, these may be expressed as: Earth-Sci. Rev., 6 ( 1 9 7 0 ) 5 - 4 9

 

36

T

ALPAN

fO

fo 80

1

m

~o

cloys.

I

4o ~

4

30

4 5

fO 2O

4O

Zn/~/c ,l

Poro.. e/7

q

- no

{ I .)

Fig.2 2. Iden tification of sw elling clays. A fter DAN DANIILO LOV~ V~1964).

dWl = q wl dn 0

62)

a n d c o m p a r e d w i t h th t h e c o n d i t i o n o f n o c h a n g e i n sw s w e l li li ng n g p r e s s u r e a n d i n it i t ia ia l moisture content imposed on eq.61: 63)

dwl = [~/f(no)]dno

I f v o l u m e e x p a n s i o n d u r i n g w a t e r in i n t a k e i s p e r m i t t e d , t h e p r o c e s s m a y b e v i ew ew e d , ph eno m eno logic ally, as reversed con solidatio n

T E R z A C H I , 1 94 9 4 3, 3 , p . 2 7 1 ). ). S i n c e

the flow gradient during swell is directed into the clay, the pore water pressure increases during the process and would be governed, for example in the oned i m e n s i o n a l ca ca s e , b y t h e a n a l o g o u s e q u a t i o n Cszz Cs

dZu ~z 2

-

3u ~t

c f. f . e q . 3 3 ): ): 64 )

w h e r e c sz sz = c o e f f i c i e n t o f s w e l l in in g . E x p e r i m e n t a l s w e l li l i n g t i m e c u r v e s h a v e , i n d ee ee d , t h e s a m e a p p e a r a n c e a s c o n s o l i d a t i o n c u r v e s e . g . , D U B O S E , 1 9 5 2 ; W IIS S EM EM A N a n d Z E IT IT L E N , 1 9 60 60 ). ). S i n c e t h e e f f e c ti t i v e s t re re s s es e s i n t h e c l a y d e c r e a s e d u r i n g t h e s w e l l in i n g p r o c e s s , i ts ts v o l u m e c h a n g e c h a r a c t e ri r i s ti t i c s a r e o b v i o u s l y t h o s e o f a n o v e r c o n s o l i d a t e d c la l a y . E x p r e s s in in g t h e change in void ratio, in analogy with eq.20, as: Ae = -

C~ log(a'/ a'o)

65) Earth-Sci. Rev., 6 1970 1970)) 54 9

 

 T HE GEOTECHNICALPROPERTIES GEOTECHNICALPROPERTIES OF SOI SOILS LS

37

where Cs denotes the swelling index, it is reasonable to assume the index to be influenced by the degree of overconsolidation. E x p e r i m e n t a l e v i d e n c e p e r m i ts t s , i n d e e d , a c o r r e l a t i o n b e t w e e n t h e i n d i c es es f o r n o r m a l l y o v e r c o n s o l i d a t e d c l ay a y s in i n t e r m s o f th th e o v e r c o n s o l i d a t i o n r a t i o (ALPAN, 1966): 0. 1 l og R 0.1 w h e r e , f o r p l a s t iicc c l ay a y s , th t h e c o n s t a n t k h a s a v a l u e o f th t h e o r d e r o f 0 .2 .2 . CJC c ~ k

( 66)

Thixotropy and sensitivity

Practically all cohesive soils are known to exhibit, after remoulding, a s t r e n g t h i n c r e as a s e w i t h t i m e . A s i m i la la r p h e n o m e n o n , c h a r a c t e ri r i s ti t i c o f c o l lo lo i d a l suspensions, is that of thixo trop y defined as the isothermal, reversible gel-sol

( -F/z -s/ 5oli /f/dc'~'/'aM /f/dc'~'/'aM

~/- 9uefachon .

a. P e r f e c t

.

.

.

Tht xo

rop y

I/r n~,

/I/. >

b. .Zm per foc/

Th/xo/ Th/ xo/ro, ro,o f

~)77e

Fig.23. Thixotropi Thixotropicc behaviour. (After Bm uc , 1962.) transformation produced in the suspensions by a mechanical disturbance (VON E N GE G E LH LH A R DT D T , 1 9 4 3 ; M I T C H E L L, L , 1 9 61 61 ). ). I n f ig ig . 2 3 t i m e c u r v e s f o r p e r f e c t a n d i m p e r f e c t t h i x o t r o p y a r e s h o w n ( B IL I L L IG IG , 19 1 9 62 6 2 ). ). S i n ce c e m a n y c l a y s l o o s e a c o n s i d e r a b l e p o r t i o n o f th t h e i r s t re re n g t h u p o n r e moulding, it appears logical to assume a close connexion between this property, t e r m e d s e n si s i ti t i v it it y , a n d t h i x o t r o p i c b e h a v i o u r . B y d e f i n i t i o n SKEMPTONa n d NORTHLY,1 95 9 5 2) 2 ) , th t h e T h i x o t r o p i c R e g a i n i s: s: Rt

-

ct -

cr

67 )

¢r

Earth-Sci. Rev., 6 (1970) 5~,9

 

38

1. ALPAN

whe re Cr is the re m ou lde d streng th and ct the strength m easu red after a certain t i m e o f s t o r ag ag e . D e n o t i n g b y cu c u t h e u n d i s t u r b e d s t r e n g t h , t h e q u a n t i t a t i v e e x p r e s s i o n f o r s e n si s i t iv iv i t y is: S t

68)

C ~ uu

Cr a n d t h e R e m o u l d i n g L o s s , L , c a n b e d e fi f i n e d a s: s: Lr -

c u - cr

_

St

_

1

69)

C r

A t h i x o t r o p i c r e c o v e r y f u n c t i o n c a n n o w b e d e f in in e d , w h i c h i n c o r p o r a t e s t h e t h i x o t r o p i c t i m e e f fe fe c t s a s w e l l a s t h e l o s s i n s t r e n g t h d u e t o t h e c h a n g e s i n t h e c l a y s tr tr u c t u r e c a u s e d b y r e m o u l d i n g : fe t)- -L ,-

-- 1

S t-

1)

7 0) 0)

The recov ery function evidently ranges from zero to u nity

for perfectly thixo-

t r o p i c m a t e r i a l s ). ) . I n g e n e r a l , h o w e v e r , c t < c . a n d t h u s t h e l i m i t in in g v a l u e f R o ~) ~) < 1 i s a m e a s u r e o f t h i x o t r o p i c i m p e r f e c t i o n . I t a p p e a r s , t h e r e f o r e , t h a t thixotropy cannot be considered as the cause of, at least, high sensitivity as e v i d e n t f r o m t h e t r e n d o f r e l e v a n t r e c o v e r y f u n c t i o n s S KE K E M PT PT ON O N a n d N O RT RT HE H E Y, Y, ~ ft7

r

O g 0

8

I

I

r

Okuram ur~

_

r ii ll

]

l~y

_

i

i

- P/ii i

Io

3fo, -/~

r

oL7

7 7; 7 ; 7 7 ee- d o u ~

Fig.2 4. Typic al thixotro pic reco very . A fter YAMAGU YAMAGUCH CHII, 1959.) 1 95 9 5 2 ). ). F o r c l a y s o f l o w o r m e d i u m s e n s i t i v i ty t y s a y , f o r S t ~< ~< 8 ) t h e t r e n d o f . f R O i n d i ca c a t e s c o m p l e t e st s t r e n g t h r e c o v e r y w i th th t i m e a s s h o w n i n F i g . 2 4 b a s e d o n d a t a reported by YAMAGUCm 1959). Earth-Sci. Rev., 6 1970) 5-49

 

THE GEOTECHNICALPROPERTIES GEOTECHNICALPROPERTIES OF SOILS

39

Plasticity, on the other hand, seems intimately related to thixotropy, both b e i n g s i m i l a r l y i n f l u e n c e d b y c h a r a c t e r i s ti ti c s o f t h e c l a y - l i q u i d s y s t e m s u c h a s s p ec e c if i f ic i c p a r t i c le l e s u r fa fa c e , m i n e r a l c o m p o s i t i o n , t y p e a n d c o n c e n t r a t i o n o f t h e s o l u t i o n i o n s a n d t h e t y p e o f t h e li l i q u id id c o m p o n e n t . B u t w h e r e a s , w i t h r e s p e c t t o t h e g e o m e t r y o f t h e c l a y p a r ti t i c le le s , t h i x o t r o p y i s a l i n e a r f u n c t i o n o f o n l y t h e s p e c i f ic ic s u r f a c e , t h e l e v e l o f p l a s t i c i t y is is a ls ls o i n f l u e n c e d b y p a r t i c l e s h a p e

VON

PLA TEN TEN an d WI N K LER 1958). 1958). C o n c e r n i n g t h e in i n f lu lu e n c e o f t h i x o t r o p y o n s t r e n g t h a n d d e f o r m a t i o n c h a r a c te t e r is i s t ic ic s t h e fo f o l l o w i n g d a t a t a k e n a t r a n d o m f r o m a c o n s i d e ra ra b l e a m o u n t o f e x p e r i m e n t a l w o r k , m u s t s u ff f f ic i c e a s i l lu l u s t r a t io i o n s o f t y p i c a l tr tr e n d s : N A LE L E ZN Z N Y a n d L I 1 9 6 7 ) r e p o r t a r e d u c t i o n o f th t h e a m o u n t o f s w e l li li n g a n d o f s w e ll l l in i n g p r e s s u r e w i t h s t o r i n g t i m e o f c o m p a c t e d c la l a y s . T h e y a t t r ib i b u t e t h is is b e h a v i o u r t o t h e r e - f o r m a t i o n o f i n te t e r p a r t ic i c l e b o n d s d u r i n g t h e t h i x o t r o p i c h a r d e n i n g w i th th t h e c o n c o m i t a n t s t r e n g t h i n c r e a s e o p p o s i n g s w e l l c f . M I TC T C H E L L, L , 1 96 9 6 1) 1) . I t m a y b e r e c a l l e d t h a t a s i m i la l a r r e l a t i o n s h i p c o n n e c t s t h e K o - c o e f fi f i c ie ie n t w i t h s h e a r i n g resistance. S E ED ED a n d C H A N 1 9 57 5 7 ), ) , w o r k i n g o n c o m p a c t e d c l a ys ys , e x a m i n e d t h e p r o b l e m o f th t h e i n f l u e n c e o f t h i x o t r o p i c h a r d e n i n g a t d i f f e r e n t s t r a i n le l e v e ls ls a n d m o i s t u r e c o n t e n t s . F i g . 2 5 s h o w s t h e v a r i a t i o n o f t h e s t re re s s r a t i o P t / P o w i t h a x i a l s t r a i n a t ~D

X8 / 7

/ 6

N~

/ 4

f~

Z/

~ x i a l S rct n

~o

Fig.25. Thixotrop ic hardening of a com pacted cla y. After SEED SEED and CHAN, 1957.) h i g h a n d l o w m o i s t u r e c o n t e n t s , w h e r e P o i s t h e s t re re s s a p p l i e d i m m e d i a t e l y a f t e r c o m p a c t i o n a n d P t t h e s t re r e s s a p p l ie i e d a f t e r s t o r i n g - - b o t h s tr t r e ss ss e s p r o d u c i n g a n equal axial strain. T h e p h y s i c a l b a s i s o f s e n s it i t i v it it y d o e s n o t , a s y e t , a p p e a r t o b e w e l l u n d e r s t o o d ; a l l t h e s a m e , a ffee w s p e c u l a t i v e o b s e r v a t i o n s a r e i n o r d e r . R e m o u l d i n g i m p a r t s t o c l a y p a r t i c le le s a c e r t a i n d e g r e e o f p r e f e r e n t i a l o r i e n t a t i o n a n d t h e l a r g e r t h e Earth-Sei. Rev. 6 1970 1970)) 54 9

 

40

i. ALPAN

d i f f er er e n c e i n o r i e n t a t i o n b e t w e e n t h e u n d i s t u r b e d a n d r e m o u l d e d s t a t e o f a c l a y , t h e h i g h e r i t s s e n s i t i v i t y M I T C H E L L , 1 9 5 6 ) . Y A M A GU G U C HI HI 1 9 59 59 ), ), a p p l y i n g t h e t h e o r y o f r a t e p r o ce c e s s e s , a r r iv i v e d a t a n e x p r e s s io i o n s h o w i n g t h e s e n s i ti t i v i ty ty o f a c l a y t o i n c r e a s e e x p o n e n t i a l l y w i t h t h e d i f f e re re n c e b e t w e e n t h e u n d i s t u r b e d a n d remoulded activation energies. T h e p r a c t i c a l u s e f u ln ln e s s o f t h e t h e o r y o f r a t e p r o c e s s e s i n t h e s t u d y o f t h e m e c h a n i c a l p r o p e r t i e s o f c l a y s a p p e a r s t o m e a s n o t y e t e s t a b li li s h e d , a l t h o u g h s e v e r a l r e l e v a n t c o n t r i b u t i o n s h a v e b e e n m a d e i n t h i s d i r e c t i o n c f. f. M IT I T C H EL EL L , 1964;; MUR AVAMA 1964 AVAMA an d SHI SHIB B ATA, 19 66 ; MITC HELL et al., 1968 ). Sim ilarly, th e f r a c t u r e o f ro ro c k s h a s b e e n a n a l y s e d u s i n g t h e c o n c e p t o f a c t i v a t i o n e n e r g y h e u r i s t ic i c a l l y K t JM JM A R , 1 9 68 68 ). ). I t c o u l d b e a r g u e d t h a t , s i n c e c h a n g e s i n p a r t i c l e o r i e n tation can be reasonably connected with changes in entropy, the observed dependence of sensitivity on orientation might lead, in conjunction with the activation energy relations postulated by YAMAGUCHI 1959), to a more consistent thermod y n a m i c f o r m u l a t i o n o f s en e n s it i t iv i v i ty ty . F u r t h e r m o r e , a s t h e ir i r p a r a ll ll e l a r r a n g e m e n t corre spo nds to a stab ler con ditio n of the clay particles MITCHELL, 1956), a s p o n t a n e o u s r e t u r n t o a n o r i g in i n a l ly l y r a n d o m s t r u c tu t u r e w i t h a c o rr r r e s p o n d i n g s t re re n g t h i n c r ea e a s e s e em e m s u n l i k e ly ly . C o n s i d e r a t i o n s o f t h e k i n d o u t l i n e d a b o v e w o u l d a p p e a r , t h e n , p r o m i s i n g i n e x p l a i n i n g t h e r e l a t io i o n b e t w e e n s e n s i ti t i v i ty ty a n d t h i x o t r o p y . D y n a m i c s o i l p r o p e r ti ti e s T h e f o l l o w i n g d i s c u s s io i o n is is c o n c e r n e d w i t h t h e r e s p o n s e o f so s o i ls ls t o d y n a m i c

s t i m u l i , i. i . e. e . , t h e w a y t h e i r d e f o r m a t i o n c h a r a c t e r i s ti t i c s a r e a f f e c te te d b y t h e a p p l i c a t i o n o f r a p i d l y c h a n g i n g f o rc r c e s . T h e s e m a y b e o f s h o r t d u r a t i o n s h o c k s ), ) , ir ir r e g u l a r l y f l u c t u a t i n g e a r t h q u a k e - a n d b l a s t - in i n d u c e d tr tr e m o r s ) o r p e r i o d i c a l l y c h a n g i n g vibrations). The kinetic energy, imparted to the soil during rapid loading, is partly lost i rr r r e ve v e r si s i bl bl e d e f o r m a t i o n s , h e a t ) a n d p a r t l y r a d i a t e d i n t o t h e s u r r o u n d i n g m e d i u m f o r e x a m p l e a s w a v e s ). ). F r o m t h e v i e w p o i n t o f e n e r g y t r a n s f e r i t a p p e a r s c o n v e n i e n t t o c l a s s i f y t h e d y n a m i c r e s p o n s e o f s o il il s a c c o r d i n g t o t h e l e v e l o f t h e i r e n e r g y s t a t e s a s f o l l o w s S L A O E, E, 1 9 54 54 ): ): 1) A high energy state in which changes in the average soil characteristics occur; these are, essentially, changes in porosity. 2 ) A m e d i u m e n e r g y s t a te t e , c h a r a c t e r i z e d b y i r re r e v e r s ib ib l e l o c a l c h a n g e s i n t h e s o i l s t r u c t u r e ; h o w e v e r , w i t h o u t s i g n i fi fi c a n t c h a n g e s i n p o r o s i t y . 3) A low energy state in which the structural changes are reversible, i.e., elastic bu t no t necessarily linear. E a c h o f t h e s e e n e r g y s t a t e s is is a s s o c i a t e d w i t h a c h a r a c t e r i s ti ti c t y p e o f s o i l response. Thus, the high energy state may result in compaction, rarefaction or flow. In the medium state, energy is lost by dissipation or a process resembling diffusion. In the low energy state a soil mass may be treated as an elastic contin u u m , p r o v i d e d t h e a n a ly l y s i s p r o c e e d s f r o m a n e l e m e n t a r y v o l u m e o f s u i ta ta b l e Earth-Sci. Rev. 6 1970) 5-49

 

THE GEOTECHNI GEOTECHNICAL CALPROPERTIES PROPERTIES OF SOILS

41

d i m e n s i o n s a s c o m p a r e d w i th t h a g i v e n w a v e l e n g t h o n t h e o n e h a n d a n d p a r t ic i c l e s iz iz e on the other. T h e d y n a m i c r e s p o n s e o f s o il il s d e p e n d s , i n p r i n c i p l e , o n t h e r e l e v a n t c h a r a c t e r is i s t ic i c s o f i ts t s c o n s t i t u e n t s ( s o li l i d s a n d p o r e f lu l u i d ), ), t h e i r r e l a t iv iv e m o b i l i t y o r d e g r e e o f c o u p l i n g ( c f. f. P AT A T ER E R SO S O N , 1 95 9 5 6) 6) a n d o n b u l k p a r a m e t e r s s u c h a s p o r o s i t y , d e g r e e o f s a t u r a t i o n , t h e s t r u c t u r e o f t h e p a r t ic i c l e s k e l e t o n , e tc tc . I n a d d i t i o n , t h e response appears to be influenced by intergranular pressure and the type and d u r a t i o n o f t h e a p p l i e d l o a d i n g . I t is is , t h e r e f o r e , n o t s u r p r i s i n g t h a t t h e c o m p l ex e x i ti ti e s o f t h e p h e n o m e n a i n v o l v e d h av a v e , s o f a r, r, p r e c l u d e d t h e f o r m u l a t i o n o f a r e a s o n a b l y i n t e g r a t e d t h e o r y f o r r e a l so so il i l s. s. A l l t h e s a m e , t h e s t u d y o f s i m p l if if i e d m o d e l s o n t h e o n e h a n d a n d e x t e n s iv i v e e m p i r i c a l i n v e s ti t i g a t io io n s o n t h e o t h e r , h a v e l ed e d t o v a l u a b l e i n si s i g ht h t s a n d m a n y i m p o r t a n t p r a c t ic i c a l c o n c l u s io io n s . T h u s , f o r e x a m p l e , W IN IN TE T E RK R K O RN R N ( 1 95 95 4 ) a p p l i e d c e r t a i n c o n c e p t s f r o m t h e p h y s i c s o f t h e l i q u i d s t a t e t o g r a n u l a r a s s e m b l i e s a t t h e i r c ri r i t ic ic a l v o i d r a t i o , p r e d i c ti t i n g t h e i r b e h a v i o u r u n d e r t h e e n e r g y i n p u t a s s o c i a te t e d w i t h v i b r a ti ti o n s . L ' H E R M IT IT E ( 1 94 94 9 ) c o n s i d e r e d t h e g r a i n s t o b e h a v e a s s i m p l e r e s o n a t o r s a n d v i e w e d t h e r e s p o n s e o f a g r a in in a s s e m b l y i n t e r m s o f a v e l o c i t y s p e c t r u m w i t h r e s p e c t t o t h e m a s s o f t h e i n d i v i d u a l g r a in in s . A n a l y s i n g a s a t u r a t e d m o d e l a g g r e g a t e o f s p h e r e s , B RA R A N DT D T ( 1 9 5 5) 5) d e r i v e d a n e x p r e s s i o n s h o w i n g s o u n d v e l o c i t y t o i n c r e a s e w i t h i n c r e a s i n g e ff f f e c ti t i v e s t re re s s a n d d e c r e a s i n g p o r o s i t y , a t r e n d i n a c c o r d a n c e w i t h t h e e x p e r i m e n t a l f i n d i n g o f H A R D IN IN a n d R IC I C H A R T ( 19 1 9 6 3 ). ). Rheological models are often used to render complex material properties a m e n a b l e t o a n a ly l y s is i s a n d t h e s o - ca c a l le le d

K elvin-V oigt bo dy

substance) has been found adequate in this respect

( o r f i rm rm o - v i s c o u s

HARDINan d SCO TT, 1966 1966)) .

W e s h a ll l l u s e it i t h e r e to t o i l l u st s t ra r a t e th th e c o n n e x i o n b e t w e e n d e f o r m a t i o n a n d t h e r a t e o f l o a d a p p l i c a ti ti o n . T h e m o d e l c o n s is is ts ts , a s is w e l l k n o w n , o f a

spring

and a

das h-p ot

c o u p l e d i n p a r a l l e l a n d i ts t s r h e o l o g i c a l e q u a t i o n ( s ay a y , in i n a x i a l s tr tr e ss s s ) is is :

~r = Ee + 24

(71 )

w h e r e E = e l a st s t ic i c m o d u l u s ; 2 = T r o u t o n ' s c o e ff f f i c ie ie n t o f v i s c o u s t r a c t i o n . C o n s i d e r a s tr t r es e s s, s , a o, o , a p p l ie ie d i n s t a n t a n e o u s l y a n d k e p t c o n s t a n t . W e c a n t h e n d e f i n e t h e s t a t i c s ti t i f fn f n e s s , S ~, ~, a s t h e r a t i o b e t w e e n t h e st s t rree s s a n d t h e t i m e dependent strain, which yields: S~ -

ao _

E 1 - e x p ( - t/Tret

(72)

w i t h Tr e = 2 / E = t h e r e t a r d a t i o n t im im e . Let, in a dynamic test, the applied stress and the resulting strain be periodic functions o f the form:

Earth-Sci. Rev., 6 (1970) 5-49

 

42

n. ALPAN = a0 sin cot e = e0 sin(ogt - - ¢p) ¢p)

a n d l e t , a g a i n , th th e

(73)

d y n a m i c s ti t i f fn fn e s s

b e d e f i n e d i n t e r m s o f t h e s t re re s s a n d s t r a i n

amp litudes as: Sd = a 0/e 0 S u b s t i t u t i n g t h e s e e x p r e s s io i o n s i n t h e r h e o l o g i c a l e q u a t i o n y i el e l d s: s:

(74)

Sd = E[L +

(75)

2nTret/T)2] ~

w h e r e T = 2 rc rc /~ /~ o = v i b r a t i o n p e r i o d . W e can now define the

s t i ff ff n e s s r a t i o , ¢ , a s :

~P = S d /S s = [ 1 - - e x p ( - - t / T r e , )] )] [ 1 +

2nTr~ t/T)2] ~

(76)

a n d t h is i s c o m p a r a t i v e p a r a m e t e r e v i d e n t ly l y in i n c r e a s es e s t h e l o n g e r th t h e s t a t ic i c t e s ti ti n g time, t, and the shorter the vibration period. Furthermore, as far as the intrinsic m a t e r i a l p r o p e r t i e s , a s e x p r e s s e d b y T r~ r~ , a r e c o n c e r n e d , t h e i n c r e a s e w i l l b e t h e

jLU Io

io

3 f ~t t~

Io J

I lo d~

l e .,., ,~ ,~

off

0 4

.Z-I~,s //c/~q ,

Fig.26. Dynamic and static moduli of elasticity. m o r e p r o n o u n c e d t h e m o r e c o m p r e s s i b l e t h e m a t e r i a l a n d t h e s t r o n g e r it it s v i sc sc o u s c o m p o n e n t . T h e e m p i r i c a l c u r v e s o f F i g .2 . 2 6 s u p p o r t t h e f o r e g o i n g a n a ly l y s i s. s. T u r n i n g n o w t o t h e c l o s el e l y r e l a t e d a s p e c t o f s t r e n g th th , i t s h o u l d b e n o t e d t h a t t h e r e e x i st s t t w o o p p o s e d t e n d e n c i e s a s f a r a s t h e e f fe f e c ts ts o f d y n a m i c l o a d i n g a r e c o n c e r n e d . O n t h e o n e h a n d , a s p o i n t e d o u t e l s ew e w h e r e in i n th th i s p a p e r , t h e s h e a r i n g r e s i s t a n c e o f s o il i l s i n c r e a se s e s w i t h t h e t i m e r a t e o f s tr tr a i n . O n t h e o t h e r , t h e a p p l i c a t i o n o f d y n a m i c f o r c e s, s , n o t a b l y v i b r a t i o n s , t e n d t o r e d u c e t h e r e s is i s t a n c e to to s h e a r o f s o i ls ls . F i g . 2 7 , b a s e d o n r e s u l t s r e p o r t e d b y S Z A FR F R A N ( 1 96 9 6 4 ), ), s h o w t h e s t r e n g t h Earth-Sci. Rev., 6 (1970) 5-49

 

T H E G E O T E C H N IC I C A L P R O P E R T IE IE S O F S O IL IL S

43

~0

r -,, k

f o

¢ormol

f 5

PreSSu ~

~o

/~

~.5

- kq/It m

z

F i g . 2 7 . T h e e f f e c t o f v i b r a t i o n o n t h e s t r e n g t h d e c r e a s e o f a c l a y . A f t e r SZAFRAN 1 9 6 4 . ) 00

~

Q

:~

Dr',/~a,.~

to

t~

¢

I o0

500

z OO O O0

30o o

F i g . 2 8 . T h e e ff ff e c t o f v i b r a t o r y a c c e l e r a t i o n o n t h e s t r e n g t h d e c r e a s e o f a d r y s a n d . M O G A M I a n d K u B o , 1 9 5 3 .) .)

After

decrease after vibration, As, relative to the pre-vibration strength, So, as a function o f no rm al press pressure. ure. Simil Similarly arly,, Fig.28, prepared fro m data for a sand reported reported b y MO6AMI MO6A MI and K uB o (1953), sho ws the influence influence o f accele accelerati ration, on, the strength strength being measured during the vibrat vibratory ory m otio n. Qualitativel Qualitat ively, y, the latte latterr results results may be expla ined on th e basis basis o f the conc ept of

exp ans ion pressure pressure , pos tulate d by L'HE L'HERMI RMITE TE (1949) for fresh concrete an d Earth-Sci. Rev. 6 1 9 70 70 ) 5 4 9

 

44

1. ALPAN

appl ied by BA applied BA~ANT (196 (1967) 7) to sands, s ands, accordi acc ording ng to which the shea shearr resis resistance tance of a vibrated granular medium is practically zero below a certain limiting value of confining pressure equal to the above-mentio above -mentioned ned expansion press pressure ure.. The expansion pressure depends, amongst other things, on the kinetic energy supplied to the medium, a conclusion conclus ion evidently suppor supported ted by the tes tests ts reported by MOGAM and an d KU KUBO BO (1953). The dynamic model o f a grain assembl assembly y consisting consisting of individual individual resonators respo re spondi nding ng with w ithin in a given ba band nd wid width th to exc excita itatio tion n (L'HER (L'HERMI MITE TE an and d TOURNON, 1948; 194 8; L'HE L'HER~ R~aI aITE TE,, 1949 1949)) impl implies ies a thre thresho shold ld value va lue for f or the inpu input, t, below which w hich the shearing strength should remain practically unaffected. Recent vibration experiments on sands (ST6TZNER, 1965) show, indeed, such threshold to exist at given frequencies, velocities and accelerations. We shall shall conclude conc lude our dis discus cussio sion n of dynamic dynam ic soil soil properties with some remarks regarding their damp damping ing chara characte cteris ristic tics. s. Damp Damping ing in soil soilss is is determi determined, ned, in many cases, by observing the decay of wave amplitudes with the distance from the point poin t of o f excitation. Part of the decr decreas easee in amplitudes is, is, of cours course, e, due to the increasing volume excited as the waves radiate outward from the source, but in part the dissipative properties of the material are responsible. In the case of surface waves, waves, for example example,, the following followin g relationship may be derived from the variation of energy density density with with dist distance: ance: Ar - V r ~ e x p [ - 2 ( r A0

r0) 1

(77,

where Ar Ar and Ao are the wav wavee amplitudes at a t distances r and a nd ro from the excitation ex citation source and # is the "abs orptio n coefficient" coefficient" of the medium. The absorption coefficient is, for many materials, dependent upon the wave frequency. This dependence is shown in Fig.29, prepared from reported amplitude /.¢= 3 . I 3

~1o 4 To.zs

j L

: i

4

0

I

1:5

2

0

2

5

d O

d

5

~0

Fig.29. Ene Energy rgy dissipation dissipat ion in seismic waves. (Afte (Af terr IS ISSHtKIet al, 1962.) Earth-Sci. Rev.

6 (1970) (1970) 549

 

45

THE GEOTEC HNI C AL P R OP ER TIES TIES OF S OI LS

m e a s u r e m e n t s o f tr t r e m o r s p r o d u c e d b y t h e e ru r u p t i o n o f a v o l c a n o I s S H I K I et al., 1962). In the laboratory, the methods used for measuring damping are mostly b a s e d o n t h e m o d e l o f a l i n e a r r e s o n a t o r . T h u s , H A L L a n d R IC I C H A R F ( 1 96 96 3 ) m e a s u r e d t h e d e c a y i n a m p l i t u d e o f s a n d s p e c i m e n s c o m i n g t o r e s t in i n f r e e v i b r a t io io n . T h e d a m p i n g w a s e x p re re s s e d i n t e r m s o f t h e

l o g a r i t h m i c d e c r e m e n t , 6, 6 , d e f in in e d

as follows: A(t)/A(t + T ) = exp(6 )

(78)

t h e r a t i o b e i n g t h a t o f a m p l i t u d e s a t t im i m e s d i f fe fe r i n g b y a p e r i o d . T h e l o g a r i t h m i c decrement appears from the reported results to be amplitude-dependent, and may be expressed as: ( 79)

6 = mA

A s i m i la l a r t r e n d i n c l a y s w a s r e p o r t e d b y K O N DN D N ER E R a n d K R IZ I Z E K ( 1 96 96 5 ) a n d w e a r e l e d t o t h e c o n c l u s i o n t h a t t h e s t r e s s - s t r a i n c h a r a c t e r i s ti t i c s o f th t h e t e s t e d s o il il s m a y have deviated from linearity. CONCLUDING REMARKS

I t h a s b e e n s a i d o f s o m e b o o k s t h a t t h e y a r e n e v e r f in i n i sh sh e d b u t h a v e t o b e a b a n d o n e d b y t h e i r a u t h o r s . I a m a f r a i d t h a t t h is i s a p p l ie i e s w i t h e q u a l j u s ti ti c e t o papers such as the present. Quite a few topics I would consider significant and interesting have been left out, and probably many more considered as such by o t h e r w o r k e r s i n t h e f ie ie ld ld . A l l t h e s a m e , t h e s u r v e y p r e s e n t e d h e r e s h o u l d a f f o r d s o m e i n s i g h t in in t o t h e f u n d a m e n t a l p r o b l e m s o f t h e s t u d y o f t h e m e c h a n i c a l p r o p e r t ie i e s o f so s o i ls ls a n d g i v e a n a c c o u n t o f th t h e m e t h o d s a p p l i e d i n t h e i r a t ta ta c k . N o a p o l o g y iiss o f fe fe r e d f o r t h e u n e v e n e m p h a s i s p l a c e d o n t h e v a r i o u s t o p i c s n o r f o r a l t o g e t h e r o m i t t i n g a d i s cu c u s s io i o n o f th t h e t h e r m a l c o n d u c t i v i t y o f s oi o i ls ls , f o r e x a m p l e . O n t h e o t h e r h a n d , t h e c o n t r o l o f so s o il i l p r o p e r t i e s o r f ie i e ld ld a n d l a b o r a t o r y t e s t in i n g a r e d e f i n i t e ly l y s u b j e c ts ts w h o s e i n c l u s i o n w o u l d h a v e e n h a n c e d t h e u s e f u l n e s s o f t h e p a p e r . H o w e v e r , a t o l e ra ra b l y a d e q u a t e t r e a t m e n t w o u l d h a v e b e e n p r o h i b i t iv iv e w h i c h b r i n g s u s b a c k t o t h e o p e n i n g s e n t e n c e o f t h e s e r e m a r k s .

R EF ER ENC ES A B OS OS Ia Ia l,l, H . a n d M O N D EN E N , H . , 1 96 96 0. 0. A n e x p e r i m e n t a l m e t h o d t o d e t e r m i n e t h e h o r i z o n t a l c o e f fi f i c ie i e n t o f c o n s o l i d a t i o n i n f i n e g r a i n e d s o il i l s. s . Proc . R e g. C onf. Soil M e c h. Found. Eng . A s i a 1 st st N e w D e l h i 1 2 p p . A B o s m , H . a n d M O N D EN E N , H . , 1 96 9 6 1. 1. T h r e e - d i m e n s i o n a l c o n s o l i d a t i o n o f s a t u r a t e d c l a y . Proc . Intee rn. Int rn. Conf. Soil M e c h. Found. Eng . 5th Paris p p . 5 5 9 - 5 6 2 . A L PA P A N , I .,. , 1 95 95 7. 7. A n a p p a r a t u s f o r m e a s u r i n g t h e s w e l l i n g p r e s s u r e i n e x p a n s i v e s o il il s. s . Proc .

hlte rn. Conf. Soil M e c h. Found. Eng . 4th L ondon p p . 3 - 5 . Earth-Sc i. Re v . 6 1 9 70 70 ) 5 4 9

 

46

I. ALPAN

A L P A N , I . , 1 9 6 5 a . E f f e c t i v e s t r e s s e s i n p a r t l y s a t u r a t e d s o i ls ls . I n : D . A B I R , F . O LL LL EN EN DO DO RF RF F a n d M . R E IN IN E R ( E d i t o r s ) , T opic s in Applie d M e c hanic s. E l s e v i e r , A m s t e r d a m , p p . 2 3 5 - 2 4 4 . ALP AN, I . , 1965b. T he Nature and M e asure m e nt o f Volum e Change Change s due to to M oisture Vari Variat ation ion in Soils. T h e s i s , I s r a e l I n s t . T e c h n . , H a i f a , 6 6 p p . ( u n p u b l i s h e d ) . ALPAN, I., 1966. The use of empirical relationships in evaluating the pore pressure coefficient A. Bull. Inte rn. Inst. Se ismology Earthquak e Eng., 3 : 3 9 - 5 1 . A L P A N , I . , 1 9 6 7 a . T h e e m p i r i c a l e v a l u a t i o n o f t h e c o e f f i c i e n t K o a n d Kog. Soil Found., 7 (1): 31-40. ALP AN, I . , 1967b. Notes on Soil Engineering. I n t e r n . I n s t . S e i sm sm o l o g y E a r t h q u a k e E n g . , T o k y o , 147 pp. B A KE KE R , R . a n d K A SS S S IE IE F, F , G . , 1 9 68 68 . M a t h e m a t i c a l a n a l y s i s o f s w e ll ll p r e s s u r e w i t h t i m e f o r p a r t l y s a t u r a t e d c l a y s . Can. Geotech. J . , 5 ( 4 ) : 2 1 7 - 2 2 4 . B A ~A ~ A N T , Z . , 1 96 96 7. 7 . D y n a m i c s t a b i l i t y o f s a t u r a t e d s a n d i n s u b s o i l b e n e a t h d a m s . Proc. Intern. Congr. L arge Dams, 9th, lstanbul, 4 : 1 4 9 - 1 6 0 . BEAR, J., ZASL ZASLAVSKY, AVSKY, D . an d IRMAY, S., 1968. Phy sic al Princ iple s of W ate r Pe rc olation and Se e page . U N E S C O , P a r i s , 4 6 5 p p . BERNATZIK, W ., 1947. B a u g r u n d u n d P h y s i k . S . D . V . , Z u r i c h , 3 1 0 p p . B IL I L L IG IG , K . , 1 9 6 2 . T h i x o t r o p i c c l a y s u s p e n s i o n s a n d t h e i r u s e i n c i v i l e n g i n e e r i n g , 2 . Civil Eng. P u b l i c W o r k s R e v . , 57 ( 666) : 101- 105. B L OT OT , M . A . , 1 94 94 1. 1. G e n e r a l t h e o r y o f t h r e e - d i m e n s i o n a l c o n s o l i d a t i o n . J . Appl. Phy s., 12 (2): 155-164. B IS IS HOP , A. W . , 1959. The pr in c ip le of e f f e c tive str e ss. TeA. Ukeblad, 3 9 : 8 5 9 - 8 6 3 . B Is I s H oP oP , A . W . a n d B L I G H T, T, G . E . , 1 9 6 3 . S o m e a s p e c t s o f e f f ec e c t i v e s t r e s s in in s a t u r a t e d a n d p a r t l y s a t u r a t e d s o i l s . G~otechnique, 1 3 : 1 7 7 - 1 9 7 . B IS IS HO HO P, P , A . W . a n d E L DI D I N , G . , 1 95 95 0. 0. U n d r a i n e d t r i a x i a l t e s ts t s o n s a t u r a t e d s a n d s a n d t h e i r s ig ig n i f i c a n c e i n t h e g e n e r a l t h e o r y o f s h e a r s t r e n g t h . Gkotechnique, 2 : 1 3 - 3 2 . B IS IS HOP , A. W . a n d HENKEL, D. J. , 1962. T he M e asure m e nt o f Soil Prope rtie s in the T riax ial T e st. st. 2 r id id e d . , A r n o l d , L o n d o n , 2 2 8 p p . B O LT LT , G . H . a n d M IL I L L ER ER , R . D . , 1 95 95 8. 8. C a l c u l a t i o n o f t o t a l a n d c o m p o n e n t p o t e n t i a l s o f w a t e r i n soil. Trans. Am. Geophys. Union, 3 9 ( 5 ) : 9 1 7 - 9 2 8 . B RA R A N DT DT , H . , 1 95 95 5. 5. A s t u d y o f t h e s p e e d o f s o u n d i n p o r o u s g r a n u l a r m e d i a . J . Appl. M e c h., 7 7 : 479486. B R I NC H-HANS H-HANS EN, J. a n d LUNDGR EN, H. , 1960 1960.. Hauptproble me de r Bode nme c hanik . S p r i n g e r , Berlin, 282 pp. B U CK CK IN IN G HA HA M , E . , 1 9 07 07 . S t u d i e s o n t h e m o v e m e n t o f s o i l m o i s t u r e . U.S. De pt. Agr., Bur. Soils, Bull., 3 8 : 6 1 p p . CAQUOT, A . a n d KI~ KI~RIS RISEL, EL, J., 1966. Trait~ de Mkcanique des Sols. 4 t h e d . , G a u t h i e r V i l la l a r s , P a ri ri s , 506 pp. CARRILLO CARRI LLO N . 1 94 94 2. 2. S i m p l e tw tw o - a n d t h r e e - d i m e n s i o n a l c a s e s i n t h e t h e o r y o f c o n s o l i d a t i o n o f soils. J . M a t h . P h y s . , 21 ( 1) : 1- 5. CASAGRA CAS AGRANDE NDE A . 1 9 4 8 . C l a s s i f i c a t i o n a n d i d e n t i f i c a t i o n o f s o i l s . T rans. rans. A m . So c . C iv il Engrs., 113: 901-930. CASAGRANDE A . a n d W I LS LS ON O N , S . D . , 1 95 95 1. 1. E f f e c t o f r a t e o f l o a d i n g o n t h e s t r e n g t h o f c l a y s a n d s h a le l e s a t c o n s t a n t w a t e r c o n t e n t . G~otechnique, 2 : 2 5 1 - 2 6 3 . CASAGRANDE L. 1 9 5 2 . E l e c t r o - o s m o t i c s t a b i l i z a t i o n o f s o i l s . J . Boston Soc . Civ il Eng., 39 ( l) 51-83. C O LE LE M AN AN , J . D . a n d M A R SH S H , A . D . , 1 96 96 1. 1. A n i n v e s t i g a t i o n o f t h e p r e s s u r e - m e m b r a n e m e t h o d f o r m e a s u r i n g t h e s u c t i o n p r o p e r t i e s o f s o i l . J . Soil Sc i., 1 2 ( 2 ) : 3 4 3 - 3 6 2 . COOLING COOLI NG L. F . 1 94 94 5. 5. D e v e l o p m e n t a n d s c o p e o f s o il i l m e c h a n i c s . I n : The Principl Principles es and App lication i l E n g r s .,. , L o n d o n , p p . l - 3 0 . o f S o i l M e c h a n i c s . I n s t . C i v il DANILOV DANIL OV A. I . 1 96 96 4. 4. D i a g r a m f o r d i v i d i n g s o il il s i n t o o r d i n a r y , s l u m p i n g a n d s w e l li li n g . S o i l M e c h . Found. Engrs., 5 : 3 2 4 - 3 2 6 ( T r a n s l . C o n s u l t a n t B u r e a u ) . DER ES ES IEWI IEWIC C Z, H. , 1958 1958.. M e c h a n ic s of gr a n ul a r m a tte r . I n: H. L. DR YDEN a n d T. VON KAR KARM M .~ .~ N ( E d i t o r s ) , Adv anc e s in Applie d M e c hanic s. A c a d e m i c P re r e s s, s, N e w Y o r k , N . Y . , 5: 233-306. DORSEY, DORSE Y, N . E ., 1940. Prope rtie s o f Ordi Ordinar naryy W ate r-Substanc e . R e i n h o l d , N e w Y o r k , N . Y . , 6 7 3 p p .

Earth-Sc i. Re v ., 6 ( 1 9 7 0 ) 5 - 4 9

 

THE GEOTEC HNI C AL P R OP ER TIES TIES OF S OI LS

7

D R U C K ER ER , D . C . a n d P R A G E R, R, W . , 1 9 52 52 . S o i l m e c h a n i c s a n d p l a s t i c a n a l y s i s o r l i m i t d e s i g n . ): 1 5 7 - 1 6 5 . Q u a r t . A p p l . M a t h . , 1 0 ( 2 ): D UB U B OS O S E, E, L . A . , 1 95 95 2. 2. E v a l u a t i n g t a y l o r m a r l c l a y f o r i m p r o v e d u s e i n s u b g r a d e s . T e x as Eng. Expt. Sta., Res. Rept., 3 5 : 1 7 p p . F OR SLI SLIND, ND, E. , 1952 1952.. A th e o r y o f wa te r . Sv e nsk a Forsk Forsk nings ningsins inst. t. Ce m e nt Be ton g V id Kg L T e k . Hogskol. Stockholm, Handl., 1 6 :4 3 p p . FREUDENTHAL FREU DENTHAL,, A. M .. 1950. The Inelast Inelastic ic Behavi Behaviour our o f Enginee Engineering ring Ma terials an d Structu res. Wiley, New Yo rk, N .Y., 700 pp. FRYDMAN, S., 1968. T h e E f f e c t o f S t r e s s H i s t o r y o n t h e S tr tr e s s - D e fo fo r m a t i o n B e h a v io io u r o f S a n d. d. Thesis, Israel Inst. Tech., Haifa, 170 pp. (un published). G IB IB SO S O N , R . E . , 1 95 9 5 3. 3. E x p e r i m e n t a l d e t e r m i n a t i o n o f t h e t r u e c o h e s i o n a n d t r u e a n g l e o f i n t e r n a l f r i c t i o n i n c l a y s . Pro c. Int Intern. ern. Con f. Soil M ech . Found. Eng ., 3rd, Zur ich, l : 1 2 6 - 1 3 0 . G m s o y , R . E . a n d H E NK NK EL E L , D . J . , 1 9 54 54 . I n f l u e n c e o f d u r a t i o n o f t e s t s a t c o n s t a n t r a t e o f s t r a i n o n m e a s u r e d d r a i n e d s t r e n g t h . G~otechnique, 4 : 6 - 1 5 . G IB IB SO S O N , R . E . a n d L U M a, a, P . , 1 95 9 5 3. 3. N u m e r i c a l s o l u t i o n o f s o m e p r o b l e m s i n t h e c o n s o l i d a t i o n o f c la y. Pro c. Inst. Inst. Civil Eng rs., 1 ( 5877) : 182- 198. H A B IB IB , P . e t S O EI EI R O , F . , 1 9 57 57 . L e s m o u v e m e n t s d e l e a u d a n s l e s s o l s s o u s l i n f l u e n c e d e l a t e m p e r a t u r e . Cahiers Rech. 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J . , 1 9 6 0. 0. P h y s i c a l c o m p o n e n t s o f t h e s h e a r s t r e n g t h o f s a t u r a t e d c l a y s . A m . S o c . Civil Eng rs., Res . C onf., Colorado, p p . 1 6 9 - 2 7 3 . IR M AY AY , S . , 1 9 6 8 . F a i l u r e c r i t e r i a o f p l a s t i c s o l i d s i n t h e s p a c e o f s t r e s s i n v a r i a n t s . Israel J. Tech., 6 ( 4) : 165- 173. I SS SS HIKI HIKI , N. , KU NO , H. , M I NAKAM I , T. a n d I WAS AKI, AKI, I . , 1962. O - S im a V olc a no . Intern. Syrup. Volcanol.. (In st. Ar chite cts Eng rs., Inte Volcanol Intern. rn. Union Geodesy Geo phy s.), T o k y o , p p . 7 0 - 8 4 . JA KO KO BS BS O N, N, B . , 1 9 57 57 . S o m e f u n d a m e n t a l p r o p e r t i e s o f s a n d . Proc . Inte Inte rn. rn. Conf. Soil M e c h. Found. Eng. 4th, L ondon, 1: 167- 171. J EN EN N IN IN G S, S, J . E . a n d B U R LA LA N D , J . B . , 1 9 62 62 . 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(Received May 7, 1969)

Earth-Se i. Re v ., 6 ( 1970) 5~ 19