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Analysis of shear-induced anisotropy in leda clay
d
Research Council of Canada
705
lational de recherches du Canada
ANALYZED
-'
ANALYSIS OF SHEAR-INDUCED ANISOTROPY
IN
LEDA CLAY
__
.
-.
---
by
K. T. Law and Kwan Y. Lo
4
FEB
14
1977
Reprinted from
Numerical Methods in Geomechanics
Blacksburg, Va., June 1976
Proceedings, Engineering Foundation Conference on
held at Virginia Polytechnic Institute and State University
Vol. 1, p. 329-344.
g-4
5s3Q
DBR Paper No. 705
Division of Building Research
Une mdthode des dldments finis est mise au point pour I'analyse du comportement, al I'dtat non draind, d'un remblai reposant sur des argdes tendres et sensibles ayant comme caractdristiques une anisotropic produite par cisaillement et un ramollissement au-dell d'une certaine charge. La mdthode se fonde sur I'observation des discontinuitds dues au cisaillement qui sont mobilisdes lorsque l'argile est ddformde au-dell de sa rdsistance maximale. Des dtudes en laboratoire des conditions de cette mobilisation indiquent que la pression de consolidation en est le facteur ddterminant inddpendamment de la vitesse de ddformation, de l'inclinaison de I'dchantdlon et du genre de chargement. A l'aide de donndes typiques, l'analyse est appliqude
A
la construction des remblais afin d'dtudier I'dtreinte latdrale artificielle, la profondeur de l'assise rocheuse, le regime de contrainte initiale, la rigiditd du remblai et la resistance audelal d'une certaine charge maximale. On dvalue dgalement I'analyse dlastique ordinaire en fonction de la mdthode proposde.I
T "
III~I~IIIII~II
IIIIIIII[I~I~!~II
-
-809
002
-9
-
ANALYSIS OF SHEAR-INDUCED ANISOTROPY IN LEDA CLAY
By K.T.
awl
andK.Y.
LO,^
A.M. ASCEINTRODUCTION
Many field observations involving deformation or failure in earth structures have revealed that there are regions of induced shear or strain discontinuities within the soil mass. In a number of landslide records (e.g., refs. 3, 10, 12) the failure mass moved monolithically along a thin zone of soil underlain by a relatively unsheared or undisturbed soil mass. Similar discontinuities have also been observed in embankment construction (e.g. ref. 8) and such discontinuities have even been found outside the sliding surface (17). Because of the many uncertainties, little work has been done on the stress-strain analysis of problems involving these discontinuities.
The complexity is further aggravated when work-softening behavior
is involved. The associated problems have been discussed (6, 11).
An
important advance was brought about by Lo and Lee (16) and by Desai (7). A particular solution of the problem in undrained behavior under embankment loading, however, still requires further attention.
An attempt has been made to define the conditions favorable to the development of shear-induced discontinuities in the laboratory and a model has been developed for the post-peak behavior. The proposed method has been applied to the study of embankments founded on a soft sensitive clay.
LABORATORY STUDY
Block samples and 12.7-cm diameter Osterberg samples (18) of Leda clayweretaken from two locations in Ottawa, Ontario to study the conditions under which discontinuities arise. This clay is noted for its brittleness, high sensitivity and compressibility. A general
description of the deposit has been given by Crawford (4) and Bozozuk
and Leonards (1). Additional specific geotechnical data are given in
Table 1.
Research Officer, Division of Building Research, National Research Council of Canada, Ottawa, Ontario.
Professor, Faculty of Engineering Science, The University of Western Ontario, London, Ontario.
330
NUMERICAL METHODS IN GEOMECHANICSTable 1. Summary of So11 Properties
Table 2. S m a r y of Laboratory Tests
Location
Gloucester
"
"
Heron Rd
'I1 i = angle between axis of specimen and the vertical
('I 0;
-
vertical consolidation pressure; P = in sit" overburden pressure 13' 0; = horizontal consolidation pressureSr = post-peak strength; Sp = peak strength VS = vertical splitting; SP = shear plane
Test Type UU on vertical specimens UU an inclined specimens 1') 1;30'.90' CAU on vertical speclrnens CIU on ~nclined specmens 1=30°-go0 CIU, different
":
CAU, different depths CAU, plane straln different depths CAU, plane straln stress controlled UU an vertical specimens UU on inclined specimens i=309-90' CAU Constant ( 8 ' + 0 1 ) 1 3 drained test No. of Tests 5 4 3 4 4 5 5 2 7 5 4 I Straln rats. % / m m . 0.43-0.0001 0.0093 0.017-0.0001 0.017 0.017 0.017 0.017 0.56-0.0001 0.013 0.084-0.0001 0.00023 i2) o;/Po 1.27 1 .O 2.18-5.45 1.0 1.0 1.0 0 0 1 11
Sr'Sp 0.74-1.08 0.71-1.00 0.66 0.67-0.79 0.56-0.79 0.66-1.00 0.58-0.16 0.55-0.62 1 3 ) o ' l o ' h v 1 1 0.70 1.0 1.0 0.5 0.5 0.5 1 1 0.5 0.5 Mode of failure I shear plane angle i5) VS+SP, 56°-570 VS+SP, 50°-560 SP, 56' SP, 56O-57' Bulging SP, 54'-60' SP. 5S0-60' SP, 56' VS+SP, 55'-57° VS+SP, 54'-57' SP, 56O-58' SP.56'SHEAR INDUCED ANISOTROPY 33 1
The e x p e r i m e n t a l program c o n s i s t e d mainly o f c o n v e n t i o n a l t r i a x i a l u n d r a i n e d t e s t s c o n s o l i d a t e d a t d i f f e r e n t p r e s s u r e s and s h e a r e d under d i f f e r e n t s t r a i n i n g r a t e s r a n g i n g from 0 . 5 % p e r min t o 1 % p e r week. P l a n e s t r a i n t e s t s , b o t h s t r a i n and s t r e s s c o n t r o l l e d , t e s t s under c o n s t a n t a v e r a g e e f f e c t i v e p r e s s u r e and t e s t s on i n c l i n e d specimens were a l s o performed.
A summary o f some 50 t e s t s i s g i v e n i n T a b l e 2. For a l l t e s t s , t h e major p a r t o f t h e p r e - p e a k s t r a i n i n g g e n e r a l l y r e s u l t s i n a r e a s o n a b l y uniform l a t e r a l d e f o r m a t i o n w i t h o u t t h e development o f any d i s c o n t i n u i t i e s . F a i l u r e s t r a i n s a r e u s u a l l y s m a l l (about 1 % ) e x c e p t when t h e c o n s o l i d a t i o n p r e s s u r e i s h i g h ( 2 x Po, where Po = e f f e c t i v e overburden p r e s s u r e ) . Work-softening b e h a v i o r g e n e r a l l y p r e v a i l s w i t h t h e r a t i o o f t h e p o s t - p e a k t o peak s t r e n g t h r a n g i n g from 0 . 5 5 t o 1 . 0 . I t i s a p p a r e n t from T a b l e 2 t h a t t h e v a l u e o f t h e c o n s o l i d a t i o n p r e s s u r e i s t h e f a c t o r t h a t governs t h e mode o f f a i l u r e . A t h i g h p r e s s u r e s , ' a b u l g e - t y p e f a i l u r e i s t h e predominant f e a t u r e . A t low p r e s s u r e s , however, f o r u n c o n s o l i d a t e d u n d r a i n e d t e s t s (UU t e s t s ) v e r t i c a l s p l i t t i n g o c c u r s around t h e peak d e v i a t o r i c s t r e s s and i s f o l l o w e d by s h e a r p l a n e s upon f u r t h e r s t r a i n i n g . S p l i t t i n g h a s been a s c r i b e d t o t h e e f f e c t o f end r e s t r a i n t s which might g i v e r i s e t o t e n s i l e s t r e s s ( 5 , 9 ) . T h i s view i s s u p p o r t e d h e r e by t h e r e s u l t s o f t h e c o n s t a n t e f f e c t i v e s t r e s s t e s t i n which t h e specimen f a i l s w i t h o u t s p l i t t i n g . A t t h e i n t e r m e d i a t e p r e s s u r e (below o r s l i g h t l y above P o ) , s h e a r p l a n e s o r d i s c o n t i n u i t i e s a r e i n v a r i a b l y t h e p r e v a i l i n g mode of f a i l u r e . T h i s b e h a v i o r i s found t o be independent o f t h e f o l l o w i n g : 1) t h e r a t e o f s t r a i n ; 2) t h e i n c l i n a t i o n a t which t h e specimen was trimmed from t h e block sample; 3 ) t y p e o f l o a d i n g c o n d i t i o n , i . e . p l a n e s t r a i n o r t r i a x i a l s t a t e .
I n many e n g i n e e r i n g o p e r a t i o n s i n Leda c l a y i t i s common
f o r u n d r a i n e d l o a d i n g t o s t a r t from i n s i t u s t r e s s e s . L o c a l i z e d s h e a r d i s c o n t i n u i t i e s s h o u l d be a n t i c i p a t e d and a n a l y s i s i n c o r p o r a t i n g t h e p e r t i n e n t b e h a v i o r i s e s s e n t i a l i f t h e s a f e t y f a c t o r i s m a r g i n a l . NUMERICAL FORMULATION
A f i n i t e element method i s proposed i n t h e a n a l y s i s o f s o i l - s t r u c t u r e i n t e r a c t i o n , i n p a r t i c u l a r , f o r s o i l showing w o r k - s o f t e n i n g and s h e a r d i s c o n t i n u i t i e s when s t r a i n e d beyond t h e peak. In t h i s method, which i s an e x t e n s i o n o f t h e method u s e d by Lo and Lee ( 1 6 ) , a l i n e a r e l a s t i c b e h a v i o r i s assumed i n t h e pre-peak s t a t e . When t h e s o i l f a i l s l o c a l l y , two s e p a r a t e p r o c e s s e s a r e a p p l i e d t o m a i n t a i n s t r e s s and s t r a i n c o m p a t i b i l i t y . F i r s t l y , a s t r e s s t r a n s f e r t e c h n i q u e (21) i s employed t o g e n e r a t e a new s e t o f n o d a l f o r c e s f o r t h e subsequent i t e r a t i v e s o l u t i o n . Secondly, an a p p r o p r i a t e s t i f f n e s s m a t r i x is f o r m u l a t e d , which r e a l i s t i c a l l y d e s c r i b e s t h e p o s t - p e a k d e f o r m a t i o n a l c h a r a c t e r i s t i c s o f t h e s o i l .
The p r e s e n t method d i f f e r s from t h e p r e v i o u s a n a l y s i s (16) i n two r e s p e c t s : it d e a l s mainly w i t h t h e s h o r t - t e r m l o a d i n g c o n d i t i o n ( t h e p r e v i o u s one i s concerned w i t h excavated s l o p e s under t h e long-term s i t u a t i o n ) , and i t e x p l i c i t l y t r e a t s t h e problem o f s h e a r d i s c o n t i n - u i t i e s , t h e f o r m u l a t i o n o f which i s p r e s e n t e d i n t h e f o l l o w i n g .
f a i l u r e p l a n e , a s w e l l a s i t s a n a l o g y , i s shown i n F i g . 1. The system c o n s i s t s of two i n t a c t masses s l i d i n g r e l a t i v e t o each o t h e r and hence a n a p p a r e n t a n i s o t r o p y i s i n t r o d u c e d . C o n s i d e r i n g t h e s t r e s s - s t r a i n b e h a v i o r i n t h e d i r e c t i o n s p a r a l l e l and normal t o t h e f a i l u r e p l a n e , t h e c o m p r e s s i o n a l moduli f o r b o t h d i r e c t i o n s (Ep and En) can be d e r i v e d w i t h t h e h e l p of t h e analogy of two systems of s p r i n g s , one connected i n p a r a l l e l and t h e o t h e r i n s e r i e s ( F i g s . l b and l c ) . The r e s u l t i n g e x p r e s s i o n s a r e :
and
where
E1/E2 = r a t i o o f modulus o f t h e i n t a c t t o t h a t o f t h e s o f t e n e d s o i l , and
t / h = r a t i o o f t h e t h i c k n e s s of t h e s o f t e n e d t o t h a t o f t h e i n t a c t s o i l .
E x i s t i n g d a t a i n d i c a t e t h a t t / h i s u s u a l l y l e s s t h a n 0 . 1 % and t h a t E1/E2 seldom exceeds 10 (14). The r a t i o s o f E /E P 1 and En/E1 a r e p l o t t e d i n F i g . 2. For a l l p r a c t i c a l p u r p o s e s b o t h Ep and En can b e t a k e n a s e q u a l t o El, t h e modulus o f t h e o r i g i n a l i n t a c t m a t e r i a l . I t was found i n a s i m i l a r manner t h a t t h e e f f e c t i v e P o i s s o n ' s r a t i o , v , of t h e system c o n t a i n i n g a s h e a r p l a n e i s e q u a l t o t h a t o f t h e i n t a c t m a t e r i a l .
The s h e a r modulus a l o n g t h e f a i l u r e p l a n e however s h o u l d b e c o n s i d e r e d s e p a r a t e l y . Assuming a m o n o t o n i c a l l y i n c r e a s i n g l o a d , once f a i l u r e i s r e a c h e d , t h e r e i s no s h e a r r i g i d i t y t o p r e v e n t f u r t h e r r e l a t i v e d i s p l a c e m e n t between t h e i n t a c t masses. T h e r e f o r e t h e s h e a r modulus i s e s s e n t i a l l y z e r o , which was a l s o n o t e d by'Lo (15) b u t from a d i f f e r e n t v i e w p o i n t .
Consequently t h e s e l f - i m p o s e d composite system can be f u n c t i o n a l l y t r e a t e d a s a g r o s s l y a n i s o t r o p i c m a t e r i a l with p r i n c i p a l p l a n e s l y i n g p a r a l l e l and normal t o t h e s h e a r p l a n e . The e l a s t i c i t y m a t r i x
[D']
w i t h r e s p e c t t o t h e s e d i r e c t i o n s i s w r i t t e n a s f o l l o w s f o r t h e p l a n e s t r a i n c o n d i t i o n :
R e f e r e n c e t o t h e g l o b a l c o o r d i n a t e s i s o b t a i n e d v i a t h e t r a n s f o r - mation m a t r i x [TI ( 2 0 ) , and g i v e s :
SHEAR INDUCED ANISOTROPY P O R T I O N F O R S P R I N G A N A L O G Y I L L U S T R A T I O N ( a ) S C H E M A T I C D I A G R A M O F A S O I L S A M P L E A F T E R F A I L U R E FIGURE 1
Modeling of soils, failing with a shear plane
u x I b l S T R E S S P A R A L L E L T O F A I L U R E P L A N E
t
"Yt
Y ( c ) S T R E S S N O R M A L T O F A I L U R E P L A N E 1 0 0 . 0 \ I I I I I [ l -Y&
\'\,
'--.?l\n = 0 . 0 0 0 5j
-
-
,
..
0 . 0 0 1 0-
8.
.
Z - '\\p*.
-
d 0 0 0 5 ** * % W --
\..
-
C -** FIGURE 2 Y \ 9 9 . 5 - \-
Typical values of the o
-
-
E I E'
0 . 0 0 1 0modulus of deformation
-
----
P 1"<
- E " ' E l of the composite CL-
\-
W system'.
\-
'.
-
- \ 2 0 6 8 10Assembly o f t h e combined s t i f f n e s s m a t r i x c o m p r i s i n g a l l e l e m e n t s a t d i f f e r e n t s t a g e s o f l o a d i n g can t h e n b e accomplished. Coupled w i t h t h e g e n e r a t e d nodal f o r c e s from l o c a l l y f a i l e d e l e m e n t s , i t e r a t i o n c a n be performed u n t i l s t r e s s - s t r a i n c o m p a t i b i l i t y i s s a t i s f i e d .
APPLICATION TO EMBANKMENTS FOUNDED ON SOFT CLAYS
The proposed method was used t o s t u d y t h e performance of an embankment founded on s o f t c l a y s . Some o f t h e symbols and p a r a m e t e r s a r e d e f i n e d i n F i g . 3 ; a d d i t i o n a l d a t a a r e a s f o l l o w s : K = 0 . 5 = c o e f f i c i e n t o f e a r t h p r e s s u r e a t r e s t ; D / H = 5 = r a t i o of bedrock d e p t h t o embankment h e i g h t ; 0 = Sr/S = 1 . 0 = r a t i o o f p o s t - p e a k t o peak s t r e n g t h s o f s u b s o i l ; P L/B = 5 = r a t i o o f l e n g t h o f l a t e r a l g e o m e t r i c confinement t o h a l f b a s e width o f embankment. An a b r u p t d r o p t o p o s t - p e a k s t r e n g t h s i m i l a r t o t h e t r e a t m e n t by Lo and Lee (16) was assumed. I t should be n o t e d t h a t t h i s i s n o t a r e s t r i c t i o n t o t h e a p p l i c a t i o n o f t h e proposed method.
Two s t r e n g t h p r o f i l e s , c a s e s L and H ( F i g . 3 ) , a r e c o n s i d e r e d . The c o n v e n t i o n a l f a c t o r s o f s a f e t y computed by t h e s i m p l i f i e d B i s h o p ' s method a r e , r e s p e c t i v e l y , 1 . 3 6 and 2 . 3 2 . Except when a c e r t a i n v a r i a b l e was under i n v e s t i g a t i o n , t h e s e d a t a were m a i n t a i n e d t h r o u g h o u t t h e s t u d y .
The c o n s t r u c t i o n p r o c e d u r e was s i m u l a t e d by i n a c t i v a t i n g and r e a c t i v a t i n g e l e m e n t s r e p r e s e n t i n g t h e embankment. I n a c t i v a t i o n c o n s i s t s o f s e t t i n g t h e s t i f f n e s s o f t h e i n a c t i v e e l e m e n t s t o a n e a r z e r o v a l u e and p r e s c r i b i n g z e r o d i s p l a c e m e n t t o t h e i n a c t i v e nodes. During r e a c t i v a t i o n , i . e . , s i m u l a t i n g t h e a d d i t i o n o f a new l a y e r o f embankment m a t e r i a l , t h e a p p r o p r i a t e i n a c t i v e e l e m e n t s and nodes a r e r e s t o r e d t o t h e i r o r i g i n a l b e h a v i o r . F u r t h e r d e t a i l s a r e g i v e n i n r e f . (14). The t o t a l number o f nodes and c o n s t a n t s t r a i n t r i a n g u l a r e l e m e n t s used a r e , r e s p e c t i v e l y , 234 and 407.
DETERMINATION OF THE DISTANCE OF LATERAL CONFINEMENT
A f i n i t e dimension o f t h e problem must b e s p e c i f i e d i n t h e f i n i t e element method. I t would be p r e f e r a b l e t h a t t h i s s h o u l d conform c l o s e l y t o f i e l d c o n d i t i o n s . U n f o r t u n a t e l y , f o r embankment c o n s t r u c t i o n i n an open f i e l d , t h e l a t e r a l e x t e n t i s u s u a l l y t o o l a r g e t o b e accommodated i n t h e a n a l y s i s . Placement of a n a r t i f i c i a l l a t e r a l g e o m e t r i c
confinement a t a s u f f i c i e n t d i s t a n c e (L) i s g e n e r a l l y r e q u i r e d . From F i g . 4 , which shows t h e v a r i a t i o n o f t h e s u r f a c e s e t t l e m e n t a t t h e c e n t r e (6VC) and t h e h o r i z o n t a l d i s p l a c e m e n t a t t h e t o e (6HT) w i t h d i f f e r e n t assumptions o f l a t e r a l c o n f i n e m e n t , it would seem t h a t a v a l u e o f L/B e q u a l t o o r g r e a t e r t h a n 5 i s a d e q u a t e . S e t t l e m e n t p r o f i l e s w i t h d e p t h a l o n g t h e c e n t r e l i n e and t h e e x t e n t of t h e zone of
SHEAR INDUCED ANISOTROPY
LATERAL GEOMEtRIC CONFINEMENT
SUBSOIL EMBANKMENT
-
PARAMnER
SYMBOL
SYMBOL
VALUE
COHESION Su AS SHOWN C f 0.05 kglcm2 ON RIGHT FRICTION ANGLl #, "f 35" DENSITY 7, 1.7btlm3 y , 2.0tlrn3 MODULUS E 240 kglcm2 Ef 240 k g k m 2 POISSON'S u s 0.49 v f 0.40 RATIO - C FIGURE 3
Basic p a r a m e t e r s and symbols employed i n t h e numerical a n a l y s e s
0 0 2 4 6 8 10 LENGTH O F CONFINEMENT. L I B I I I __oC-- 9-
-
..*I\
-,*
8,,/H. C A S E L-
-
z/Oe
-
-
0--
A d --
B H T I H , C A S E H-
I I I I I I I I I FIGURE 4E f f e c t o f l a t e r a l geometric confinement on computed deformations
t h e peak s t r e n g t h ) have been examined. The r e s u l t s a l s o s u b s t a n t i a t e t h e same L / B v a l u e . I t i s o f i n t e r e s t t o n o t e t h a t t h i s c o n d i t i o n h a s seldom been imposed i n s i m i l a r numerical a n a l y s e s .
EMBANKMENT
I
D I H-
10----
8---
5. . . .
.
.
.
.
.
..
2 FIGURE 5 Zones of l o c a l f a i l u r e a t d i f f e r e n t bedrock depths (case L) D I H FIGURE 6Surface s e t t l e m e n t s a t v a r i o u s value of bedrock depths (case
EFFECT OF BEDROCK DEPTH
Figure 5 d e p i c t s t h e r e l a t i v e e x t e n t of
t h e
Z.L.F. under v a r i o u s D/H r a t i o s . With g r e a t e r depth t o bedrock, a l a r g e r Z.L.F. r e s u l t s .The surface settlement
at
t h e centre f o r t h e v a r i o u s valuesof
D/H i s shown i n F i g . 6. It i s s i g n i f i c a n t t o n o t e that f o r a low s a f e t yfactor t h e settlement at D/H = 10 is 4.5 times greater than
when
O / H = 2. This clearly illustrates t h e j o i n t e f f e c t
of
t h e thickness ofSHEAR INDUCED ANISOTROPY
COEFFICIENT OF EARTH PRESSURE AT REST, KO
FIGURE 7
Embankment performance a t d i f f e r e n t KO (Case L)
EFFECT OF KO
The v e r t i c a l s t r e s s and t h e assumed v a l u e o f KO c o n t r o l t h e i n i t i a l s h e a r s t r e s s e s i n t h e f i e l d . Coupled w i t h t h a t induced by t h e imposed l o a d , t h e r e s u l t a n t s h e a r w i l l d e t e r m i n e t h e e x t e n t o f t h e Z . L . F . The a n a l y s e s i n d i c a t e t h a t when KO d e c r e a s e s o r t h e i n i t i a l s h e a r i n c r e a s e s , t h e Z.L.F. s p r e a d s a p p r e c i a b l y , p a r t i c u l a r l y i n t h e downward d i r e c t i o n . T h i s may have a s t r o n g i n f l u e n c e on t h e immediate g e n e r a t i o n of p o r e w a t e r p r e s s u r e and i t s subsequent d i s s i p a t i o n , which i n t u r n i n f l u e n c e s t h e t i m e r a t e o f s e t t l e m e n t and change o f s o i l r e s i s t a n c e .
F i g u r e 7 shows t h e r e l a t i v e magnitudes o f Z.L.F., hVC, and hHT a s normalized by t h e q u a n t i t i e s computed w i t h KO = 1 . The a p p a r e n t e f f e c t o f KO i s c l e a r l y d e m o n s t r a t e d .
TRAPEZOIDAL LOADING 0 . 6 0 . 4
"*
0. 2 ( a ) VERTICAL SIRESSES r 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 FIGURE 8xlB
D i s t r i b u t i o n o f induced E t l E S s t r e s s e s a t t h e embankment--
s u b s o i l i n t e r f a c e ( c a s e H) 0. 1.
.
.
.
. . . .
1.0EFFECT OF EMBANKMENT RIGIDITY
Embankment r i g i d i t y g e n e r a l l y s e r v e s t o s p r e a d t h e v e r t i c a l l o a d on t h e f o u n d a t i o n ( F i g . 8 a ) . The t r a p e z o i d a l d i s t r i b u t i o n r e p r e s e n t s t h e l o a d i n g s i t u a t i o n w i t h z e r o embankment r i g i d i t y . In a l l o t h e r c a s e s , some o f t h e s t r e s s e s a r e t r a n s f e r r e d towards t h e t o e . Thus s h e a r s t r e s s i s i n t r o d u c e d a t t h e i n t e r f a c e ( F i g . 8 b ) . No
s i g n i f i c a n t d e v i a t i o n from t h i s o b s e r v a t i o n can be d e t e c t e d with d i f f e r e n t v a l u e s f o r P o i s s o n ' s r a t i o o f t h e embankment m a t e r i a l .
Concern o v e r t h e p o s s i b i l i t y of induced t e n s i l e s t r e s s e s and hence t e n s i o n c r a c k s , h a s been e x p r e s s e d ( e . g . r e f . 1 3 ) . T h i s concern stems from t h e o b s e r v a t i o n o f t e n s i l e s t r a i n a t t h e i n t e r f a c e
( e . g . r e f . 1 9 ) . To p u r s u e t h i s p o i n t , t h e d i s t r i b u t i o n o f t h e e x t e n s i o n s t r a i n and t h e r e s u l t a n t minor p r i n c i p a l s t r e s s e s a t t h e i n t e r f a c e have been s t u d i e d . In s p i t e o f t h e p r e v a l e n t e x t e n s i o n s t r a i n which v a r i e s from about 0.15% t o 0.05% from t h e c e n t r e l i n e t o n e a r t h e t o e , t h e minor p r i n c i p a l s t r e s s e s remain compressive
t h r o u g h o u t . The a d v e r s e p o s s i b i l i t y o f t e n s i o n c r a c k s w i l l n o t a r i s e i n t h e s e c a s e s .
The v a l u e s o f bVC and bHT a t d i f f e r e n t embankment r i g i d i t i e s a r e shown i n F i g . 9. In g e n e r a l t h e d e v i a t i o n i s s m a l l and l i e s w i t h i n 10%.
SHEAR INDUCED ANISOTROPY
I-
G V C I H . E f l E S-
0 7. 6 DISPLACEMENT 3.0 2 . 8 6. 8 2 . 2 1 10 100 FIGURE 9 E f f e c t o f embank- ment r i g i d i t y on t h e computed d e f o r m a t i o n s ( c a s e L)EFFECT OF POST-PEAK STRENGTH
R e s u l t s o f a n a l y s e s o f t h e r a t i o s o f p o s t - p e a k t o peak s t r e n g t h s e q u a l t o 0 . 7 5 , 0 . 9 and 1 . 0 show t h a t t h e r e i s a tendency f o r t h e zone t o s p r e a d l a t e r a l l y w i t h lower p o s t - p e a k s t r e n g t h ( F i g . 1 0 ) . A
d e c r e a s e i n p o s t - p e a k s t r e n g t h o f 25% may i n c u r a change o f 50% t o 90% i n t h e computed d e f o r m a t i o n and a r e a of Z.L.F.
PROPOSED METHOD VERSUS ELASTIC METHOD
The o r d i n a r y e l a s t i c f i n i t e element method ( e . g . r e f . 2 ) i s i n a c c u r a t e when t h e f a c t o r o f s a f e t y i s low ( c a s e L, F i g . 3 ) . I t i s o f i n t e r e s t , t h e r e f o r e , t o a s s e s s t h e e r r o r s r e s u l t i n g from t h e u s e o f such a method.
F i g u r e 11 shows t h e change o f t o t a l v e r t i c a l and h o r i z o n t a l s t r e s s e s a l o n g t h e c e n t r e l i n e computed by t h e proposed and t h e o r d i n a r y e l a s t i c methods. The same s e t o f i n p u t d a t a was used i n b o t h a n a l y s e s e x c e p t t h a t peak and p o s t - p e a k s t r e n g t h s were g i v e n i n t h e proposed method. The v e r t i c a l s t r e s s e s a g r e e c l o s e l y n e a r t h e t o p b u t d e v i a t e s l i g h t l y a t g r e a t e r d e p t h s . The h o r i z o n t a l s t r e s s e s computed by t h e proposed method however a r e a p p r e c i a b l y h i g h e r t h r o u g h o u t t h e Z.L.F. T h i s i s u n d e r s t a n d a b l e a s , when t h e change o f v e r t i c a l p r e s s u r e i s r e l a t i v e l y i n s e n s i t i v e t o t h e s t r e n g t h p r o f i l e , t h e h o r i z o n t a l p r e s s u r e i s l a r g e l y c o n t r o l l e d by t h e a v a i l a b l e p o s t - p e a k s h e a r r e s i s t a n c e . T h e r e f o r e t h e lower t h e r e s i s t a n c e , t h e h i g h e r w i l l be t h e h o r i z o n t a l s t r e s s . S u r f a c e s e t t l e m e n t s a t t h e c e n t r e l i n e and h o r i z o n t a l d i s p l a c e m e n t a t t h e t o e a r e compared i n F i g u r e 12. The l a r g e d i s c r e p a n c y (up t o 400%; f o r a d e c r e a s e o f 25% i n t h e p o s t - p e a k s t r e n g t h from t h e peak should be n o t e d .
2.0 1 1 1 1 1.8
-
Ln Y-
+-
1.6- C Z u 3 0 a 1.4- W C 3...
'\
CL 5'..
\ \z
...
\ 0 1 . 2 -...
\-
U Y o QUANTITIES (NORMALIZED o-
BY THOSE FROM S I S = 1) 1.0- C r P 4w
-
AREA OF ZONE OF LOCAL FAILUREFIGURE 10 Performance o f f o u n d a t i o n a t v a r i o u s v a l u e s o f p o s t - p e a k s t r e n g t h s ( c a s e L) HORIZONTAL MOVEMENT AT TOE
.
. .
.
.
. .
k 8t
---
SURFACE SEITLEMENT AT CENTRE1
CONCLUSIONSA f i n i t e element method i s proposed t h a t t a k e s i n t o account
s h e a r - i n d u c e d a n i s o t r o p y and w o r k - s o f t e n i n g c h a r a c t e r i s t i c s . The f o r m u l a t i o n i s based on t h e o b s e r v a t i o n o f t h e development o f a f a i l u r e p l a n e when s t r e s s e d beyond t h e peak. The method h a s been a p p l i e d t o t h e s t u d y o f embankments founded on such s o i l s and t h e f o l l o w i n g o b s e r v a t i o n s may be made:
1. The geometric confinement u s e d i n a f i n i t e element a n a l y s i s should c o v e r a d i s t a n c e n o t l e s s t h a n 5 t i m e s t h e h a l f b a s e width o f t h e embankment i f it i s t o s i m u l a t e f i e l d c o n d i t i o n s .
2 . The deeper t h e bedrock, t h e l a r g e r i s t h e zone o f l o c a l f a i l u r e and t h e more s e v e r e t h e d e f o r m a t i o n .
3. For an embankment c o n s t r u c t e d a t a low f a c t o r o f s a f e t y ( 1 . 3 ) , lower KO g i v e s a l a r g e r zone o f l o c a l f a i l u r e and h i g h e r d e f o r m a t i o n s .
4 . The e f f e c t o f embankment r i g i d i t y i s small f o r t h e c a s e s s t u d i e d . I t t e n d s t o s p r e a d t h e v e r t i c a l l o a d more e v e n l y and i n t r o d u c e s s h e a r s t r e s s a t t h e embankment-subsoil i n t e r f a c e . No t e n s i l e s t r e s s e s a r e d e t e c t e d a t t h e i n t e r f a c e .
SHEAR INDUCED ANISOTROPY C H A N G E OF T O T A L S T R E S S , A o l y . H
---
ELASTIC ANALYSIS-
PROPOSED METHOD S IS = 1.0 r P. . .
.
. .
.
PROPOSED METHOD SJS- = 0.75 ' I 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 FIGURE 11 Comparison o f computed s t r e s s e s by d i f f e r e n t m e t h o d ? ( c a s e L)"bAuH
; c 3 . 0p"
{
a Y 5 \ : 1 4. D I I 6 . 0 1 II
- - --~-- - , L -~.
5. P o s t - p e a k d e c r e a s e o f s t r e n g t h b e a r s an i m p o r t a n t e f f e c t on t h e b e h a v i o r o f t h e s u b s o i l , The zone o f l o c a l f a i l u r e , s u r f a c e s e t t l e m e n t and h o r i z o n t a l d e f o r m a t i o n may i n c r e a s e by 50% t o 9 0 % f o r a p o s t - p e a k d e c r e a s e o f s t r e n g t h of 25%. 6. The u s e of an e l a s t i c s o l u t i o n w i t h o u t r e d i s t r i b u t i o n o f s t r e s s e s r e s u l t i n g from l o c a l f a i l u r e w i l l i n t r o d u c e e r r o r s which i n c r e a s e I w i t h lower v a l u e s o f KO and p o s t - p e a k s t r e n g t h s .The main b u l k o f t h e computer a n a l y s i s was performed w i t h t h e CDC 6 4 0 0 system a t t h e U n i v e r s i t y o f Western O n t a r i o u n d e r
Grant No. A7745 from t h e N a t i o n a l Research Council of Canada. The a s s i s t a n c e from t h e t e c h n i c a l and r e s e a r c h s t a f f . ~ a r t i c u l a r l v
SURFACE SETTLEMENT AT CENTRE
L
---
HORIZONTAL DEFORMATION AT TOE1
FIGURE 12
Comparison o f computed deformation by d i f f e r e n t methods ( c a s e L)
0 . 5 0 0. 75 1.00
COEFFICIENT OF EARTH PRESSURE AT REST, KO
M. Bozozuk, of t h e Geotechnical S e c t i o n , D i v i s i o n of B u i l d i n g Research, i s g r a t e f u l l y acknowledged.
T h i s p a p e r i s a c o n t r i b u t i o n from t h e U n i v e r s i t y of Western O n t a r i o and t h e D i v i s i o n of Building Research, N a t i o n a l Research Council o f Canada, and i s p u b l i s h e d w i t h t h e approval o f t h e D i r e c t o r of t h e D i v i s i o n .
APPENDIX 1 . REFERENCES
(1) Bozozuk, M. and Leonards, G . A . , "The G l o u c e s t e r T e s t F i l l , " P r o c e e d i n g s , S p e c i a l t y Conference on Performance of E a r t h - Supported S t r u c t u r e s , ASCE, Purdue Univ., Vol. 1 , P t 1 , 1972, pp. 299-317.
(2) Clough, R . W . , and Woodward, R . J . , 111, "Analysis o f Embankment S t r e s s e s and Deformation," J o u r n a l of t h e S o i l Mechanics and Foundations D i v i s i o n , ASCE, Vol. 93, No. SM4, Proc. Paper 5329, J u l y , 1967, pp. 529-549.
( 3 ) Conlon, R . J . , " L a n d s l i d e s on The Toulnustouc R i v e r , Quebec," Canadian Geotechnical J o u r n a l , Vol. 3, 1966, pp. 113-144. (4) Crawford, C . B . , "Engineering S t u d i e s o f Leda Clay," S o i l s i n
Canada, Royal S o c i e t y Canada, S p e c i a l P u b l i c a t i o n NO. 3 , 1 9 6 1 , pp. 200-217.
(5) Crawford, C . B . , "Cohesion i n an Undisturbed S e n s i t i v e Clay," Geotechnique, I n s t i t u t i o n o f C i v i l E n g i n e e r i n g , London, Vol. 13, No. 2 , 1963,
pp.
132-146.SHEAR INDUCED ANISOTROPY
(6) D e s a i , C . S . , "Overview, T r e n d s , and P r o j e c t i o n s , Theory and A p p l i c a t i o n s o f t h e FE Method i n G e o t e c h n i c a l E n g i n e e r i n g , " P r o c e e d i n g s , Symposium on A p p l i c a t i o n o f FE Method i n G e o t e c h n i c a l E n g i n e e r i n g , Vicksburg, Vol. 1 , 1972, pp. 3-90. (7) D e s a i , C . S . , "A C o n s i s t e n t F i n i t e Element Technique f o r Work-
s o f t e n i n g Behavior," P r o c e e d i n g s I n t e r n a t i o n a l Conference on Computational Methods i n N o n l i n e a r Mechanics, A u s t i n , Texas, 1974, pp. 969-978.
(8) D a s c a l , O . , T o u r n i e r , J . P . , Tavenas, F. and LaRochelle, P . , " F a i l u r e o f an embankment on S e n s i t i v e Clay
,"
P r o c e e d i n g s , S p e c i a l t y Conference on Performance o f E a r t h and E a r t h Supported S t r u c t u r e s , ASCE, Purdue Univ., Vol. 1 , P t . 1 , 1972, pp. 129-158. (9) F i l o n , L.N.G., "On t h e E l a s t i c E q u i l i b r i u m o f C i r c u l a r C y l i n d e r sunder C e r t a i n P r a c t i c a l Systems o f Load," P h i l o s o p h i c a l
T r a n s a c t i o n s o f t h e Royal S o c i e t y o f London, S e r i e s A, Vol. 198, 1902, pp. 147-233.
(10) Gould, J . P . , "A Study o f Shear F a i l u r e i n C e r t a i n T e r t i a r y Marine Sediments," P r o c e e d i n g s , Research Conf. on S h e a r S t r e n g t h o f Cohesive S o i l s , ASCE, Boulder, Colorado, J u n e , 1960, pp. 615-641. (11) Hoeg, K., " F i n i t e Element A n a l y s i s o f S t r a i n - S o f t e n i n g Clay,"
J o u r n a l o f t h e S o i l Mechanics and Foundations D i v i s i o n ,
ASCE, Vol. 9 8 , No. SM1, P r o c . Paper 8650, J a n u a r y , 1 9 7 2 , p p . 43-58. (12) Kenney, T.C. and A l i , M.S., d i s c u s s i o n o f " S t a b i l i t y o f N a t u r a l
S l o p e s i n S e n s i t i v e Clav." by C . B . Crawford and W . J . Eden. ~ o u E n a 1 o f t h e S o i l ~ e c h a n i c s and Foundations D i v i s i o n , ASCE, Vol. 94, No. SM5, S e p t . , 1968, pp. 1185-1190.
(13) Kenney
,
T. C .,
"General Report on Embankments,"
P r e s e n t e d a t t h e 26th Canadian G e o t e c h n i c a l Conference, Toronto, 1973.(14) Law, K.T., "Analysis o f Embankments on S e n s i t i v e C l a y s , " T h e s i s p r e s e n t e d t o The U n i v e r s i t y o f Western O n t a r i o , London, O n t a r i o , i n 1974 i n p a r t i a l f u l f i l l m e n t o f t h e r e q u i r e m e n t s f o r t h e Degree of Doctor o f P h i l o s o p h y .
(15) Lo, K . Y . , "An Approach t o t h e Problem o f P r o g r e s s i v e F a i l u r e , " Canadian G e o t e c h n i c a l J o u r n a l , Vol. 9 , No. 4 , 1972, pp. 407-429. (16) Lo, K.Y. and Lee, C.F., " S t r e s s A n a l y s i s and S l o p e S t a b i l i t y i n
S t r a i n - S o f t e n i n g Clay," Gdotechnique, I n s t i t u t i o n o f C i v i l E n g i n e e r s , London, Vol. 23, March 1973, pp. 1 - 1 2 .
(17) Morgenstern, N.R. and Tchalenko, J . S . , " M i c r o s t r u c t u r a l O b s e r v a t i o n on S h e a r Zones from S l i p s i n N a t u r a l C l a y s , " Proceedings G e o t e c h n i c a l Conference, O s l o , 1967, Vol. 1, pp. 147-152.
(18) O s t e r b e r g , J . O . , "New P i s t o n Tube Sampler," E n g i n e e r i n g News- Record, Vol. 148, 1952, pp. 77-78.
(19) Tavenas, F.A., Chapeau, C . , LaRochelle, P. and Roy, M . , "Immediate S e t t l e m e n t s o f Three T e s t Embankments on Champlain Clay," Canadian G e o t e c h n i c a l J o u r n a l , Vol. 11, No. 1 , Feb. 1974, pp. 109-141.
(20) Zienkiewicz, O.C., and Cheung, Y . K . , The F i n i t e Element Method i n S t r u c t u r a l and Continum Mechanics, McGraw-Hill, London, 1967. (21) Zienkiewicz, O.C., V a l l i a p a n , S . , and King, I . P . , " S t r e s s
A n a l y s i s i n Rock a s a No-Tension M a t e r i a l , " Gbotechnique, I n s t i t u t i o n o f C i v i l E n g i n e e r s , London, Vol. 1 8 , March 1968, pp. 55-66.
APPENDIX 11. NOTATION
The f o l l o w i n g symbols a r e used i n t h i s p a p e r .
B , H = h a l f b a s e width and h e i g h t o f embankment, r e s p e c t i v e l y ; C = c o h e s i o n ;
D = bedrock d e p t h ;
E l , E 2 = moduli o f t h e i n t a c t and s o f t e n e d s o i l s , r e s p e c t i v e l y ; Ep, En = moduli p a r a l l e l and normal t o s h e a r p l a n e s , r e s p e c t i v e l y ;
h , t = t h i c k n e s s e s o f t h e i n t a c t and s o f t e n e d s o i l s , r e s p e c t i v e l y ; KO = c o e f f i c i e n t o f e a r t h p r e s s u r e a t r e s t ; L = l e n g t h of g e o m e t r i c confinement; Sp, Sr = peak and p o s t - p e a k s t r e n g t h s o f s o i l s , r e s p e c s i v e l y ; [Dl, [D'] = e l a s t i c i t y m a t r i c e s w i t h r e f e r e n c e t o t h e g l o b a l and l o c a l c o o r d i n a t e a x e s ; [TI = t r a n s f o r m a t i o n m a t r i x ; y = d e n s i t y ; 6VC = s u r f a c e s e t t l e m e n t a t t h e c e n t r e l i n e ; 6HT = h o r i z o n t a l movement a t t h e t o e ;
