Proceedings
of the lnternationalSymposiumon SlopeStabilityEngineering-IS-Shikoku'99,
Matsuyama,Shikoku,Japan.pp. 757-762.November8-I 1,1999
Slope Stability Engineeing, Yagi, Yamagami & Jiang@ 1999 Balkema, Rotterdam, ISBN 90 5809 079 s
shearstrengthof anunsaturated
Unconfinedcompression
silty soil subjected
to high totalsuctions
TNishimura
AshikagaI nsrituteof Technolog.v,Tochigi.J apan
D.G.Fredlund
Universityof Saskatchewan,Saskatoon.Sask.,Canada
ABSTRACT TheTedoes not appear to be data availablethat shows the relationship
b e t w e e n t h e s o i l - r v a t e r c h a r a c t e r i s t i cc u r v e a n d e x p e r i m e n t a l s h e a r s t r e n g t h b e y o n d t h e
r e s i d u a l s t a t e . T h i s p a p e r d e s c r i b e s t h e s h e a r s t r e n g t h o f a c o m p a c t e d u n s a t u r a t e ds i l t y
This study involved performing unconfined
soil beyond residual conditions
c o m p r e s s i o n t e s t s o n a c o m p a c t e d u n s a t u r a t e ds i l t y s o i l s u b j e c t e d t o h i g h t o t a l s u c t i o n
T h e s o i l - w a t e r c h a r a c t e r i s t i cc u r v e s a l s o m e a s u r e d o v e r a u ' i d e r a n g e o f s u c t i o n s . T h e
h i g h e s t t o t a l s u c t i o n w a s m a x i m u m 9 3 , 6 0 0 k P a c o r r e s p o n d i n gt o a r e l a t i v e h u m i d i n , o f
50 oh. The relationshipbetweenshearstrengthand total suction for the siltv soil shows
an essenlialll' horizontal failure surface beyond residual conditions
Prior to the soil
reachingresidual conditions,the failure envelopeis non-linear.
I
INTRODUCTION
Unsaturated natural soils and artificially
compacted unsalurated soils near the
ground surface can have hi_gh negative
pore-water pressure due to evaporation
The ground surfaceis a dynamic boundary,
which
is
controlled largely by
the
environment or
climatic
conditions.
G e o t e c h n i c a le n s i n e e r sa r e w e l l a w a r e t h a t
e v a p o r a t i v e e , v ' e n t sc a n g r e a t l ) , e x c e e d f o r
infiltration events in many regions of the
world.
Recent
have
studies
evaluated
evaporative rates from
soil surfaces.
Silvestri, Soulie. Lafleur, Sarkis and
Bekkouche(1990) showedthat clays were
strongly
potential
influenced
by
evaporation and result in
settlement
problems
on
lightweight
structures.
Sattler and Fredlund (1989) demonstrated
that heave and settlement for expansive
clay soils are influenced by evaporation.
Barton
(1979)
soil
suggested that
e v a p o r a t i o n m a 1 ,b e e s t i m a t e d o n t h e b a s i s
of the humiditt and water content of the
near surface soil
Granger (1989) stated
that evaporation from unsaturated soil
surfaces is a function of the actual vapor
p r e s s u r ea t t h e s o i l s u r f a c e .
T h e c o n c e p t o f s t r e s ss t a t e v a r i a b l e st o
d e s c r i b e t h e b e h a v i o r o f u n s a t u r a t e ds o i l s
IVas
introduced
Fredlund
bv
and
M o r g e n s t r e n( 1 9 7 7 )
An empirical,
analytical model was developed to predict
the shear strength in terms of soil suction
u s i n g a s o i l - w a t e r c h a r a c t e r i s t i cc u r v e a n d
saturated
parameter
shear
strensth
( V a n a p a l l i ,e t a l ( 1 9 9 6 ) )
A typical soilw a t e r c h a r a c t e r i s t i cc u r v e h a s o n e c u r v e f o r
drying and one curve for the wetting of a
soil.
Different saturation stages can be
defines through the desaturation process
due to increasing soil suction. The first
future is the air entry value. At large
increasesin suction, there is a relativelv
small change of water content at the
residual zone stage (i.e., residual water
content condition).
Beyond residualsoil suction conditions,
changes in the shear strength of an
u n s a t u r a t e ds o i l h a v e n o t b e e n w e l l d e f i n e d
The change in shear strength beyond
residual soil suction conditions (i.e,
residualzone stage)may depend on the soil
Laboratory tests are required in
type
757
t
o r d e r t o e s t i m a t et h e s h e a r s t r e n e t h a n d
beyond residual water cont;t
in
u n s a t u r a t esdo i l m e c h a n i c s .
100
90
sgo
2 . P U R P O S EO F T H I S S T U D Y
Shear strength tests for a soil beyond
residual conditions have not been
a d e q u a t e l ys t u d i e d . T h i s p a p e r d e s c r i b e s
t h e s h e a rs t r e n g t hb e h a v i o ro f a c o m p a c t e d
u n s a t u r a t esdi l t y s o i l b e y o n dr e s i d u a w
l ater
contentconditions. Large total suctions
w e r e c r e a t e di n a c o m p a c t e ds i l t y s o i l b y
controlling
t h e r e l a t i v eh u m i d i t yi n t h e s o i l
This was done in a relative humidity
c h a m b e r . U n c o n f i n e d c o m p r e s s i o nt e s t s
were conducted on unsaturated soil
s p e c i m e n si n t h e r e s i d u a l w a t e r c o n t e n t
range
The relationshipbetween total
s u c t i o na n d s h e a rs t r e n g t hi s e v i d e n ti n t h e
t o t a l s u c t i o nr a n g e f r o m 4 l k P a t o 9 3 , 6 0 0
kPa
tr
10
100 1000 100001000001E+06
Totalsuction kPa
Fig.1 Relativehumidityversustotal
suclionrelationshiD
Table1 Summaryof unconfinedcompression
test results
Relative Totalsuctron
humrdityo/o
kPa
3 T E S TP R O C E D U R E
A siltv soil was usedin this test program
( i e . , a f i n e - g r a i n e d c o h e s i o n l e s ss o i l )
The statically compacted silty soil
s p e c i m e n hs a d a h e i g h t o f 1 0 0 m m a n d a
diameterof 50 mm.
I n i t i a l p h-vhsai dc a l
p r o p e r t i e so f t h e s i l t y s o i l s p e c i m e n s
a
water content of 9.6 Yo, a void ratio of
0 . 9 4 7 a n da d e g r e eo f s a t u r a t i o no f 2 7 o / o .
A l l s p e c i m e nw
s e r e p l a c e dd i r e c t l yi n t o a
temperature and
relative
humidity
c o n t r o l l e dc h a m b e ri n o r d e r t o a p p l y a h i g L
t o t a l s u c t i o n T h e c h a m b e rc o u l d c o n t r o
t h e r e l a t i v eh u m i d i t y i n a r a n g e f r o m 2 0 % ; o
t o 9 0 o , / oa t a t e m p e r a t u r eo f 3 0 d e g r e e s .
T h e r e i s a r e l a t i o n s h i Db e t w e e n r e l a t i v e
humidity and soils suction (i.e.. total
s u c t i o n )a s s h o w n i n F i g l
Fig t is
plotted using the theoretical model
( F r e d l u n da n d R a h a r d j o( 1 9 9 3 ) ) T h e t e s t
program selectedrelative humidifies of
8 8 % , 8 0 % , 7 0 % , 6 0 o / oa n d 5 0 o / o E a c h
s i l t y s o i l s p e c i m e nw a s s u b j e c t e dt o t h e
relativehumidity for a long time. Total
suction values correspondingto each
r e l a t i v eh u m i d i t y a r e s h o w ni n T a b l e l .
S o i l w a t e r l e a v e s t h e s o i l s u r f a c ea s
r e s u l t o f e v a p o r a t i o n . D e s a t u r a t i o no f a
s o i l o c c u r sa s t h e d r i e s W h e n t h e w e i e h t
o f e a c hs o i l s p e c i m e nu n d e r w e n n
t o furthler
toi
0
Unconfined
Axialstraina1
compresive
failureVo
strengthkPa
88
17260
254
v.zo
80
30129
324
0.12
70
60
48158
38.8
019
68972
583
015
c3.l
032
41
288
uof,
In caseof "lnitialcondition",
suctionmeansmatric
suctron.
change, it was assume that the soil had
come to equilibrium at the selectedrelative
humidity. Each soil specimen was in a
residual condition
After soil specimen
had reached equilibrium, an unconfined
c o m p r e s s i o nt e s t w a s c o n d u c t e d a t r e s i d u a l
a rate of axial strain of 0.5 mm/min.
At
the
end
of
the
unconfined
c o m p r e s s i o nt e s t . t h e w a t e r c o n t e n t o f t h e
complete soil specimen was measured in
order
to
evaluate
the
soil-water
characteristic curve
The soil-water
c h a r a c t e r i s t i cc u r v e i s a m e a s u r eo f t h e
availablesoil water at a particularsoil
s u c t oi n .
T h e s o i l - w a t e rc h a r a c t e r i s t i c u r v e f o r
t h e s i l t y s o i l w a s e v a l u a t e du s i n g a p r e s s u r e
p l a t ea p p a r a t u(si . e . ,p r e s s u r ep l a t e m e t h o d ) ,
g l a s s d e s i c c a t o r sc o n t a i n i n gs a t u r a t e ds a l t
solutions (i e .
vapor
equilibrium
techniquea
) n d r e l a t i v eh u m i d i t y t e c h n i q u e
over the entire soil suction ranqe. The
758
100
100
f90
=80
,70
360
i,50
:40
G
n
s;o
, 7 0
3 6 0
8 5 0
: 4 0
* 3 0
: 2 0
6 1 0
0
igo
'7
zo
o '10
0
o
O
0.2 0.4 0.6 0.8 1
1.2 1.4 1.6
0
0.2 0.4 0.6 0.8 1
1.2 1.4 1.6
Axialstrain %
Fig.3 Stress-strain
curvefor the
unconfinedcompression
testat a relative
humiclity
of 68%
or a totalsuctionof '17,260kPa
Axialstrain %
curyeforlheon
Fig.2 Stress-strain
teslwilhan Inilial
compression
unconfined
of 41 kPa
matricsuction
p r e s s u r ep l a t e m e t h o d m e a s u r e st h e s o i l
w a t e ra t a v a r i e t y o f m a t r i c s u c t i o nv a l u e s
T h e a i r p r e s s u r e i n t h e p r e s s u r ep l a t e
apparatuw
s a s i n c r e a s e du n t i l a m a x i m u m
The water content
of 182 kPa.
c o r r e s p o n d i n gt o h i g h e r v a l u e s o f t o t a l
s u c t i o n w a s d e t e r m i n i n gu s i n g b o t h t h e
vapor equilibrium technique and the
relativehumidity technique. Small soil
samples were placed into each glass
desiccators, and water contents were
thetotalsuction
m e a s u r e d . c o r r e s p o n dtion g
e s t a b l i s h eidn t h e d e s i c c a t o r s .
100
o90
9Bo
9,70
860
i;50
o-40
E30
7' Z0
oio
0
0 0.2 0.4 0.6 0.8 I 1.2 '1.4 1.6
Axialstrain %
Fig.4Stress-strain
curveforthe
compression
teslat a relalive
unconfined
humidity
of 80%
of 30.129
kPa
or a lotalsuctron
4 LABORATORYTEST RESULTS
G e o t e c h n i c ael n g i n e e r so f t e n r e q u i r e d a n
e s t i m a t i o no f t h e s h e a rs t r e n g t ho f s o i l s a t
low water contents. Previous research
work on unsaturated soils has not
p e r f o r m e ds h e a r s t r e n g t h t e s t s a t r e s i d u a l
water content conditions.
This study
reports the
unconfined
results of
c o m p r e s s i otne s t sa t l o w w a t e r c o n t e n t so n
a s i l t y s o i l . F o r c o m p a r i s o np u r p o s e ,t h e
i n i t i a l l y c o m p a c t e ds i l t y s o i l w i t h a m a t r i c
suction of 41 kPa, was tested in an
u n c o n f i n e dc o m p r e s s i o tne s t .
S t r e s s - s t r a i nc u r v e s o b t a i n e d f r o m t h e
u n c o n f i n e dc o m o r e s s i o nt e s t sa r e s h o w n i n
F i g s 2 , 3 , 4 , 5, 6 a n d 7 . T h e s t r e s s - s t r a i n
c u r v ef o r t h e i n i t i a l c o m p a c t e ds i l t y s o i l i s
shown in Fig 2.
tabte I provides a
s u m m a r yo f t h e u n c o n f i n e d c o m p r e s s r o n
t e s t r e s u l t s . T h e c o m p a c t e ds i l t y s o i l
i n d i c a t e sa s m o o t h s t r e s s - s t r a i nc u r v e a s
s h o w ni n F i g . 2 . T h e m a x i m u m d e v i a t o r
s t r e s si s r e a c h e da t a n a x i a l s t r a i no f 0 . 6 5 %
T h e c o m p a c t e ds i l t y s o i l s p e c i m e n w
s ith a
h i g h t o t a l s u c t i o ns h o w sa d i s t i n c t p e a k o n
t h e s t r e s s - s t a i cnu r v e . A f t e r r e a c h i n gt h e
m a x i m u m d e v i a t o r s t r e s s ,t h e s t r e s s - s t r a i n
c u r v e d e c r e a s e sr a p i d l y . F a i l u r e s o c c u r
s u d d e n l y i n t h e s p e c i m e n sw i t h a h i g h
s u c t i o n T h e a x i a l s t r a i na t f a i l u r e f o r t h e
d r i e d s p e c i m e n si s I o w e r t h a n t h a t o f t h e
i n i t i a l l y c o m p a c t e ds i l t y s o i l . T h e v a l u e
o f t h e s t r a i na t f a i l u r e v a r i e sw i t h t h e w a t e r
c o n t e n tc o n d i t i o n . T h e s h e a rs t r e n g t ho f a
c o m p a c t e ds i l t y s o i l i n c r e a s e ss l i g h t l y a t
hightotalsuctions.
5 . D I S C U S S I O NO F R E S U L T S
T h e s h e a rs t r e n g t ho f a n u n s a t u r a t e sd o i l i s
r e l a t e d t o s o i l - w a t e r c h a r a c t e r i s t i cc u r v e .
The
soil-water characteristic curve
relationship between
describes the
a v a i l a b l ew a t e r i n t h e s o i l a n d t h e s o i l
s u c t i o n ,f o r d r y i n g a n d w e t t i n g . T h e s h e a r
759
100
90
{x 87 00
froo
9 5 0
3 + o
0
';: 3 zu
4 1 0
0
o
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Axialslrain o/o
Fig.5 Stress-strain
curveforthe
unconfinedcompression
test at a relative
humidityof 70%
or a totalsuctionof 48,158 kpa
100
6
Q
n
x d u
n 7 0
p 6 0
i;50
:
b 4 0 a
6 3 0
: 2 0
d 1 0 oU a-
0
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Axialstrain%
Fig.6 Stress-slrain
curvefor the
unconfinedcompression
testat a relative
humidityof 60%
or a totalsuctionof 68,972kpa
100
f 9 0
? 8 0
3 7 0
9 6 0
i ; 5 0
b 4 0
E 3 0
it 20
o 1 0
0
0
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Axialstrain %
Fig.7 Stress-strain
curvefor lhe
unconfinedcompression
test at a relative
humidityof 50%
or a lotatsuctionof 93,590kpa
s t r e n g t h o f a n u n s a t u r a t e ds o i l i s r e l a t e d t o
the amount of water in the void of the soil
The soil-water characteristiccurve for the
silty soil is shown Fig 8
Several soil-water characteristiccurve
m o d e l s h a v e b e e n p r o p o s e dt o e m p i r i c a l l y
p r e d i c tt h e p e r m e a b i l i t ya n d s h e a rs t r e n g t h
f u n c t i o nf o r a n u n s a t u r a t e sdo i l . T h e s o i l w a t e r c h a r a c t e r i s t i cc u r v e m o d e l c a n b e
written as an equation as proposed by
F r e d l u n da n d X i n g ( 1 9 9 4 )( F i g 8 ) . M o d e l
parameters for the best-fit soil-water
characteristic urve for the silty soil are
shownin Fig. 8
A silty soil has an arr
entry value of 30 kPa. Beyonda suction
of 200 kPa, the soil enters the residual
s t a te .
I t i s w e l l - k n o w nt h a t t h e r ea r e d i f f e r e n r
s t a g e so f d e s a t u r a t i o d
n e f i n e db y t h e s o i l w a t e r c h a r a c t e r i s t i c u r v e . V a n a p a l l i ,e t
al. ( I 996) suggested four stages as
following: boundaryeffect stage, primary
t r a n s i t i o ns t a g e ,s e c o n d a r yt r a n s i t i o ns t a g e
a n d r e s i d u a ls t a g e . T h e s o i l i s e s s e n t i a l l y
s a t u r a t e di n t h e b o u n d a r ye f f e c t s t a g e . A l l
the soil poresare filled with water. The
s o i l s t a r t s t o d e s a t u r a t ei n t h e p r i m a r v
t r a n s i t i o ns t a g e . T h e w a t e r c o n t e n ii n t h e
s o i l r e d u c e ss i g n i f i c a n t l yw i t h i n c r e a s i n gi n
s u c t i o n . T h e a i r - e n t r yv a l u e f o r t h e s o i l
I i e s b e t w e e nt h e b o u n d a r ye f f e c t s t a g ea n d
the primary transition. In the secondary
t r a n s i t i o n s t a _ s e ,t h e a m o u n t o f w a t e r
between the soil particle or aggregate
c o n t a c t sr e d u c e sa s d e s a t u r a t i o n
continies.
T h e w a t e r m e n i s c u sa r e ai n c o n t a c tw i t h t h e
s o i l p a r t i c l eo r a q s r e g a t ebse g i n st o b e c o m e
d i s c o n t i n u o u s . T h e r a t e o f d e c r e a s ei n
w a t e r c o n t e n t ,t o a c h a n g ei n s u c t i o ni n t h i s
stage, is less than that in the primary
t r a n s i t i o ns t a g e . T h e r e i s l i t t l e w a t e r l e f t
i n s o i l p o r e s w h e n t h e s o i l r e a c h e st h e
r e s i d u a ls t a t e . T h e w a t e r c o n t e n t o f t h e
u n s a t u r a t esdo i l r e m a i n sr e l a t i v e l yc o n s t a n t
i n t h e r e s i d u a ls t a g e . A i r a l m o s i o c c u p i e s
a l l t h e s o i l p o r e s . T h e w a t e r m e n i s c u ii n
contact with the soil Darticles is not
c o n t i n u o u sa n d m a y b e v e r y s m a l l . T h e r e
i s a l i t t l e w a t e rl e f t i n s o i l p o r e s .
F i g . 9 s h o w st h e r e l a t i o n s h i pb e t w e e n
the shear strength (i.e, unconfined
compressive
s t r e n g t h )a n d t o t a l s u c t i o nf o r
t h e r e s i d u a lc o n d i t i o n i n t h e u n s a t u r a t e d
s il t y s o i l .
The shear streneth has a
s l i g h t l y i n c r e a s ei n s t r e n g t hw i t l i i n c r e a s i n g
of total suction. The ratio of the increase
i n s h e a r s t r e n g t h t o a n i n c r e a s ei n t o t a l
s u c t r o n t r a n s l a t e st o a n a n e l e o f 0 . 0 2
d e g r e e s . T h e r e i s a n e g t i g i b l i i n c r e a s ei n
s h e a rs t r e n g t hb e c a u s et h e a m o u n to f w a t e r
i n t h e s o i l p o r e si s v e r y s m a l l . T h e e f f e c t
o f t o t a l s u c t i o n o n t h e s h e a r s t r e n q t hi s
760
100
t l
s
o
o
o
3
O Measuredwatercontent(Vaporequilibrium
technioue)
A Measuredmter content(Pressureplate
melhod)
O Measuredmter content(Relativehumidity
equilibriumtechnioue)
I
fgo
I
5 8 0
E70
'a
45 lI
40 F-35 l-- :*
ao .nF525 4
Pamamerer
Water contentat saturation= 31 o/o,
Air entryvalue= 30 kPa
Total sucttonat residual= 200 kPa,
Best-fitsoitparameterstor Fredtund
a n d X i n g( 1 9 9 4 )m o d e l .
Zol_-+-a=38, n=9' m=085
, A :
15
3so
5lo
830
E
zo
o
ru
I
10
0
3
20000 40000 60000 80000 1oo0o0
Totalsuction kpa
100
1000
10000 100000 1000000
Totalsuctln kPa
Fig.g Relationship
betweenunconfined
compresstve
strengthand
soilsuctionin the residualstate
Fig.8 Soil-water characlerislic curve
t o r t h e s i l t ys o i l
n e g l i g i b l e . I t i s c o n c l u d e dt h a t t h e s h e a r
strength for a residual water in the
u n s a t u r a t e ds i l t y s o i l , r e m a i n r e l a t i v e l y
conslant.
The shear strength envelope is
p o s t u l a t e di n F i S 1 0 f o r t h e i n i t i a l l y
c o m p a c t e sd i l t y s o i l a t a l o w m a t r i cs u c t i o n
up the 41 kPa. Before the soil sucrion
r e a c h e s. t h e a i r - e n t r y v a l u e , t h e s o i l i s
e s s e n t i a l l yi n a s a t u r a t e d s t a t e . T h e
f a i l u r ee n v e l o p er v i l l b e t a n g e n t o a n a n g l e
o f i n t e r n a l f r i c t i o n f o r t h e s a t u r a t e ds i l t y
s o i l . T h e a n g l eo f i n t e r n a lf r i c t i o n o f s i l t y
soil used in this studv was 43 deerees.
Beyond the air-entry ualres, the effJct of
s o i l s u c t i o n t r a n s l a t i n gt o s h e a r s t r e n g t h
d e c r e a s e s .A n o n - l i n e a ri n c r e a s ei n s h e a r
s t r e n g t h i s s h o w n i n F i g .1 0 .
Gan,
Fredlund and Rahardjo ( I 988) observed
n o n - l i n e a r l yi n t h e f a i l u r e e n v e l o p ew i t h
r e s p e c t o m a t r i c s u c t i o nf o r a c o m p a c t e d
g l a c i a l t i l l w h e n u s i n g m u l t i s t a g ed i r e c t
s h e a rt e s t s . T h e t a n g e n t o f t h e f a i l u r e
e n v e l o p ed e c r e a s e s i g n i f i c a n t l ya t m a t r i c
s u c t i o n si n t h e r a n e eo f 5 0 - 1 0 0k P a . T h e
a n g l ew i t h r e s p e c t o m a t r i cs u c t i o nr e a c h e s
a fairly consianrvalue when the matric
s u c t i o nr e a c h e s5 0 0 k P a
Since the shear strength versus total
s . u c t i o nr e l a t i o n s h i p* u s . o m p u t e d a s 0 0 2
o e g r e e si n F i g . 9 , t h e f a i l u r e s u r f a c e
g 100
P
e o
o
o
> o u
'6
o
o"
E { U
0 ) t O
c - '
.E
a
l
Air entryvalueof 30 kPa
^
0
20
40
60
80
100
Soilsuctionkpa
Fig.1
0 Relationship
between
unconfined
compresive
strength
andmatricsuction
indicatesa horizontal relationshipwith
totalsuction.
6 CONCLUSIONS
paper
This
presents
unconfined
compression test
results and
the
measurement of
the
soil-water
characteristiccurve for a comoacted
u n s a t u r a t e sdi l t y s o i l
C h a n g ei n s h e a r
strength under residual conditions are
76'1
d i s c u s s e d . T h e c o m p a c t e du n s a t u r a t e d
silty soil was brought to equilibriumat
r e l a t i v e h u m i d i t i e so f 8 8 % . 8 0 % . 7 0 % ,
60 Yo and 50 oh.
T h e d e v i a t o r s t r e s sf o r t h e s o i l u n d e r
r e s i d u a l c o n d i t i o n s ,r e a c h e dt o m a x i m u m
value at a low axial strain. After the
m a x i m u m d e v i a t o r s t r e s sw a s r e a c h e d ,t h e
s t r e n g t hs u d d e n l yd e c r e a s e d . B e f o r e t h e
t o t a l s u c t i o n r e a c h e di t s r e s i d u a ls t a t e .t h e
silty soil indicated a non-linearfailure
envelope. The shear strengthremained
c o n s t a nu
t n d e rr e s i d u a lc o n d i t i o n s .
REFERENCES
B a r t o n ,I J 1 9 7 9 A p a r a m e t e r i z a t i oonf t h e
e v a p o r a t i o nf r o m n o n - s a t u r a t e ds u r f a c e .
J o u r n a lo f A p p l i e d M e t e o r o l o g yV, o l l 8 ,
pp 43-47.
F r e d l u n dD
, . G a n d M o r g e n s t e r nN,. R . 1 9 7 7 .
Stress state variablesfor unsaturated
soils. Journal of the Geotechnical
E n g i n e e r i nD
g i v i s i o n ,A S C E , 1 0 3 ( G T 5 ) ,
pp 447-466.
F r e d l u n d ,D G . a n d R a h a r d j o H
, l99l Soil
M e c h a n i c sf o r U n s a t u r a t e dS o i l s .J O H N
W I L E Y & S O N S ,I N C 5 1 7 p p
1994
F r e d l u n d , D .G . a n d X i n g , A
soil-water
Equation
for
the
Canadian
characteristic
curve
G e o t e c h n i c aJl o u r n a l , V o l . 3 l , p p 5 2 1 532.
G a n , J - K . M . , F r e d l u n d ,D . G . a n d R a h a r d j o ,
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H y d r o l o g yV
, ol I I l. pp.2l-29.
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t h e r m a lc o n d u c t i v i t ys e n s o r st o m e a s u r e
matric suction in the laboratory.
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pp491-498.
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d r o u g t s .l : R a i n f a l l d e f i c i t s i n M o n t r e a l
(1930-1988) Canadian Geotechnical
J o u r n a l ,Y o l . 2 7 , p p . 2 8 5 - 2 9 3
Vanapalli,S K., Fredlund,D G., Pufahl,
D . E a n d C l i f t o n , A . w 1 9 9 6 .M o d e l f o r
762
the predictionof shear strengthwith
respect to soil suction Canadian
G e o t e c h n i c a Jl o u r n a l , V o l . 3 3 , p p 3 7 9 5YZ.