Ministry of education Ministry of agriculture and
and training rural development

water resources university

Nguyen Thi Ngoc Huong Study the effect of the shear strength of
unsaturated soil to the stability of earth
fill dams

Specialization: Geotechnical Engineering
Code number: 62 - 58 - 60 - 01



Critic person 1:
Critic person 2:
Critic person 3: The PhD thesis will be defended at the thesis assessment committee at
the Water Resources University - 175 - Tayson street – Dongda - Hanoi
At……oclock, date/month/year……………………………

The PhD thesis can be obtained: The national library or
The Water Resources University 175 – Tayson – Dongda - Hanoi

- 1 -

INTRODUCTION
I. THE NECESSITY OF THIS STUDY
The properties of unsaturated soil on stress - strain relationship, pore pressure variation, soil
shear strength, and coefficient of seepage are not conformed to the theories of saturated
soil mechanics. In reality the slope in nature (residual) or artificial embankment (local
material dams), are generally a saturated/unsaturated soil system, so all theories for

stability of earthen slopes.
III. SUBJECT AND SCOPE OF THE STUDY
This thesis would try to study some clayey soil and clay loam samples. Except from normal
physical and mechanical properties of soil, this study would mainly concentrate on
important properties of unsaturated soils that related to the stability of earthen slopes, such
as: The relationship between the volumetric water content, coefficient of permeability and
shear strength, then applying for the calculation of dams that are filled by local materials
and natural slopes: representing for the fill soil in North – East area is the Khecat reservoir
(Quangninh province), fill soils that are used in for the dam in Songsat reservoir (Ninhthuan
province) representing for the fill soils in the Central and Northwest area (Yenbai province)
in Vietnam.
IV. CONTENT OF THE THESIS
- 2 -

The main content of this study aims to solve the following problems: (1) Study an overview
about earthen dams in general and instability problems of earthen slopes, the saturated and
unsaturated soil environment, the present situation and application of the physical and
mechanical parameters of unsaturated soil in Vietnam and foreign countries. (2) Concentrate
deeply on the theories and methods for defining the unsaturated soil parameters such as: the
soil water characteristic curve; the coefficient of permeability and shear strength. (3) Based
on the achieved results, propose the procedure for the triaxial test for unsaturated soil,
especially with the modified triaxial equipment, suitably used under Vietnamese conditions.
(4) Experimental study to find out the soil – water characteristic curve for different soils
used in practical structures and the shear strength of soil corresponding to different matric
suctions, defining a curve that show the relationship between the shear strength  and the
matric suction (u
a
-u
w
). (5) Study the relationship between the soil water characteristic curve

from that point out the amount of influence of the unsaturated soil shear strength to the slope
stability factor of safety.
This thesis also has large contribution on applying the experimental equations in modeling
unsaturated soil parameters in Vietnam, examine the influence of unsaturated soil
parameters in calculating and designing earthen dams to define the suitable dam cross
section that satisfy both the scientific and economic conditions, so contributing to the
application of an advance in the development of the hydraulic construction field in Vietnam.
- 3 -

VII. SUMmARY OF NEW CONTRIBUTIONs OF THIS THESIS
The thesis has had some contribution in scientific and realistic meaning as follow:
(1) The triaxial compression apparatus for unsaturated soil that have been modified from the
triaxial compression apparatus for saturated soil at the Geotechnical Laboratory - Water
Resources University based on the principles given by Fredlund and Rahardjo (1993).
(2) The soil – water characteristic curves was obtained for some typical soil in Vietnam and
also for defining the permeability coefficient and shear strength function for these soils.
Develop a graph for obtaining the correction coefficient  versus I
p
for different soil (from
slight clay, loam, heavy loam to clay) in Vietnam. The results from this study of the shear
strengths show that shear strength parameters (’, c’ and 
b
) from the same soil but with
different apparatus (direct shear test, triaxial consolidation drain test and constant moisture
content triaxial test) gave relatively close to each other. Therefore it would be suggest that
when lacking of the triaxial compression apparatus for unsaturated soil, the direct shear test
can be used for preliminary determining the shear strength parameters of unsaturated soils.
(3) When the matric suction in the soil changes, the effective cohesion c’ would change,
however the internal friction angle, ’, is almost unchanged for some type of soil in
Vietnam.

the slip surface is a circular sliding surface due to the fact that the using of this type with the
- 4 -

cross section is a segment of a circle would give a reasonable result with high degree of
accuracy without complicated calculation. In general, effective shear strength parameters (c’
and ’) are used when the saturated earthen slopes are analyzed.
It is possible to assume that the negative pore water pressure can be neglected for cases that
larger part of the slip surface is located under the water level. However, in the situation that
the ground water level is deep or when the shallow failure is predicted to happen, it would be
not reasonable to ignore the negative pore water pressure.
1.2. OVERVIEW ABOUT THE SATURATED AND UNSATURATED SOIL CONDITIONS
Saturated soil is the biphase one (solid and liquid phases) and existing positive pore water
pressure. Unsaturated soil is the multiphase one and existing negative pore water pressure.
Lambe and Whitman (1979) defined that unsaturated soil is a three - phase soil system
including: solid, liquid and air. According to Fredlund and Morgensten (1977), when
analyzing the stresses in a multiphase continuous environment, it is important to note that
the intermediate air - water phase behaves as an independent phase, so that the unsaturated
soil would be a system of four phases: solid, air, water and the surface tension phase.
The matric suction, soil water characteristic curve, permeability coefficient and shear
strength are basic parameters of unsaturated soil. The shear strength of unsaturated soil is
different from saturated soil by the cohesion due to matric suction. This additional cohesion
depends on (u
a
- u
w
), and the value of 
b
.
1.3. THE SITUATION OF STUDYING THE UNSATURATED SOIL PARAMETERS IN
THE WORLD AND IN VIETNAM

for Vietnamese scientists. Together with the world’s scientists we also have a great
contribution on the development and fulfillment the theory in unsaturated soil mechanics. In
this thesis, the author suggests a study to define unsaturated soil parameters for some soil
types in Vietnam and apply these parameters in earth dam stability calculation.
Chapter 2
THEORETICAL BASIS OF UNSATURATED SOIL
2.1. STRESS STATE VARIABLES IN SOIL ENVIRONMENT
Bishop (1959) suggested an experimental equation to define the effective stress and it has
been applied popularly (for example the lecture in Oslo, Norway, 1955):
s’ = (s - u
a
) + (u
a
- u
w
) (2.2)
where: u
a
– pore air pressure;  - the parameter related to the degree of situation
In 1977, Fredlund and Morgenstern has studied and concluded that any two of three normal
stress variables (total stress s, pore water pressure u
w
and pore air pressure u
a
) can be used to
describe the stress state of unsaturated soil. In other words, three combinations can be used
to describe stress state variables, compatible with soil structure and the surface tension in
unsaturated soil: (s-u
a
) and (u

moisture content is the equation of Fredlund & Xing (1994).
Fredlund and Xing:  =
 
m
n
a
e
C























pore water pressure equal to zero and putting into the sample a positive air pore pressure.
Therefore the matric suction in the soil sample can be changed [(u
a
- u
w
) where u
w
is kept
equal to zero by acting different air pressure into the sample. This method is in the group of
“axial transitivity” technique.
2.3 THE SHEAR STRENGTH OF UNSATURATED SOIL
2.3.1. The saturated soil shear strength equation
- 6 -

Terzaghi (1936) used the Mohr – Coulomb criteria and the effective stress definition to
describe saturated soil shear strength:

ff
= c’ + (s
f
- u
w
)
f
tan’ (2.11)
where: 
ff
– shear stress on the failure plane at failure; c’ – the effective cohesion; (s
f
- u

 
b
f
wa
f
afff
uuuc
s
tan'tan' 
(2.13)
where: 
ff
– the shear stress on the failure surface at failure state, c’ - effective cohesion, (s
f
-
u
a
)
f
– net normal stress on the failure surface at failure state, ’ – effective internal friction
angle corresponding to the net normal stress (s
f
-u
a
)
f
, (u
a
-u
w

where:  - a adjusted argument used to find the calculated values that fit the measured
values;  - the volumetric water content that has been normalized ( = q
w
/q
s
); q
w
–
volumetric water content; q
s
– volumetric water content at saturation
2.4. THE METHOD TO ANALYZE THE PERMEABILITY IN THE SATURATED AND
UNSATURATED ENVIRONMENT
The soil permeability coefficient can be determined by indirect method from SWCC or
direct method (the permeability test). Leong and Rahardjo (1977) suggested an equation to
predict the permeability coefficient based on the saturated permeability coefficient and the
soil water characteristic curve, as follow:

p
s
w
s
p
sw
kkk






CHAPTER 3
EXPRERIMENTAL Research FOR OBTAINING UNSATERATED SOIL
PROPERTIES
3.1. BASIS SOIL PROPERTIES
Thesis is concentrated to study on unsaturated soil at three areas in Vietnam: on the North –
West, North - East and in the Central part. The compacted soils used for testing are at the
Ninhthuan dam of Phuocthang village, Bacai Distric and Ninhthuan province. The second
compacted soils for testing is at the Khecat earth fill dam of Hailang village, Tienyen district
and Quangninh province. The third soils are undisturbed samples at the natural slope of
Yenbai city, Yenbai province. The procedure of the soil testing was following TCVN 1995
standards and soil properties are presented in Tables 3.1a and 3.1b.
Table 3.1a. Soil properties of the compacted specimens
Soil properties Notation

Unit

Songsat 1

Songsat 2

Songsat 3

Khecat

Particle size
>10.000 mm

% 0,00 0,21 2,59 0,00
5,000 - 10,000 mm


Liquid limit W
l

%
24,83 23,83 24,08 52,60
Plastic limit W
p

%
14,99 13,20 15,16 34,47
Plastic index I
p

%
9,84 10,62 8,91 18,13
Maximum dry density

dmax

g/cm
3

1,867 2,024 1,997 1,550
Optimum water content W
opt

%
12,73 11,06 10,97 24,50
Table 3.1b. Soil properties of the Yenbai undisturbed samples
Soil properties Notation

Grain size
>10.000 mm

% 6,08 0,00 0,00 0,00 0,00
5,000 - 10,000 mm

% 8,08 8,23 0,85 0,17 2,49
Gravel 2,000 - 5,000 mm

% 24,62 21,64 1,60 3,29 5,46
Sand 0,500 - 2,000 mm

% 6,22 7,52 3,62 9,74 6,10
0,250 - 0,500 mm

% 3,81 4,71 4,70 3,68 4,23
0,100 - 0,250 mm

% 4,97 5,11 6,20 5,52 5,33
0,050 - 0,100 mm

% 8,67 13,02 20,34 17,48 17,21
Silt 0,010 - 0,050 mm

% 8,17 9,34 29,43 28,42 25,57
0,005 - 0,010 mm

% 2,12 2,99 6,47 5,46 6,94
Clay <0,005 mm


volume of 60cm3. The dry density
was compacted at 95% of the
maximum dry density and optimum
water content. The soil sample at
Yenbai was trimmed with 20 mm in
thickness and volume of 60cm
3
.
The specimens used for obtaining
SWCC were prepared in the same
manner as the soil specimens for triaxial tests. The space between the disk and the rubber
membrane serves as a water compartment. The water compartment is connected to a
burette line that is opened to atmospheric pressure. The number of specimens that can be
tested in a pressure plate depends on the available disk space. The ceramic disk was
saturated prior to test.
3.2.3. Saturation soil specimen and pressure plate
The saturation was done by pouring the de-aired distilled water on top of the disk and
applying a high air pressure of 500 kPa while opening the valve of the burette line for
about 1 hour. Due to the high pressure in the chamber, the distilled de-aired water
infiltrated through the ceramic plate. The soil properties are presented in Tables 3.2a and
3.2b.
Table 3.2. Soil properties of the compacted specimen
Properties Notation

Unit

Songsat 1

Songsat 2


Volumetric water content
q
s0,348 0,345 0,390 0,456
Coefficient
of permeability at
saturated condition
k
s

m/s

5,0.10
-8
1,6.10
-7
2,0.10
-7
1,9.10
-8

Table 3.2b. Properties of undisturbed soil specimen of Yenbai
Properties Notation

Unit

Yenbai 1


s0,447 0,410 0,496 0,510 0,515
Coeficient of
permeability
at saturated condition
k
s

m/s

6,5.10
-7

2,4.10
-7

9,1.10
-8

9,6.10
-8

6,2.10
-7

3.2.4. Tests for obtaining SWCC
In this test, the air pressure was applied at different level. The pore-air pressure, ua was
applied by air pressure, while water pressure opened to atmospheric pressure (i.e., u

- u
w
) (kPa)
Volumetric water content,
w
Khecat specimen
Songsat specimen 1
Songsat specimen 2
Songsat specimen 3

0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
0,50
0,55
1 10 100 1000
Matric suction, (u
a
- u
w
) (kPa)
Volumetric water content,
w
Yenbai specimen 1
Yenbai specimen 2







i
is
C
q
q
(3.2) n =
 
*2
31,1
1
s
mC
i
m


(3.3)
 Comparison the results with Fredlund vµ Xing (1994) method
The detailed of the calculation SWCC based on this study are presented in tables III.2 and
III.6 Appendix III of the full thesis. The comparison calculation of SWCC by using fredlund
and Xing (1994) and the results from this study are presented in Figures from 3.4 to 3.7.
0,0
0,1
0,2

(kPa)
Volumetric water content,
q
w
Measured
Predicted (Fredlund and Xing, 1994)
Predicted (Proposed Equation)

Figure 3.4. SWCC of the Khecat
compacted soil
Figure 3.5. SWCC of the Songsat
compacted soil specimen 1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,1 1 10 100 1000 10000 100000 1000000
Matric suction, u
a
- u
w
(kPa)
Volumetric water content,
w
Measured
Predicted (Fredlund and Xing, 1994)
Predicted (Proposed Equation)

using equation 2.10 with m and n from equation 3.2 and 3.3. The prediction of coefficient
of permeability from SWCC by this study and Fredlund and Xing 1994 for compacted soil
specimens are presented in Figures 3.8, 3.9, 3.10 and 3.11.
1,0E-21
5,0E-09
1,0E-08
1,5E-08
2,0E-08
2,5E-08
0,1 1 10 100 1000 10000 100000 1000000
u
a
- u
w
(kPa)
k
w
(m/s)
Predicted from SWCC by Fredlund and Xing (1994)
Predicted from SWCC by this study

1,0E-21
1,2E-08
2,4E-08
3,6E-08
4,8E-08
6,0E-08
7,2E-08
0,1 1 10 100 1000 10000 100000 1000000
u

m = 0,75

n = 0,66
a = 80,0
m = 0,69

n = 0,38

q
s
=0,345
a = 70,0
m = 0,37

n = 0,86

a = 70,0
m = 0,35

n = 0,50

q
s
= 0,390
a = 40,0
m = 0,79
n = 0,65
a = 40,0
m = 0,73


u
a
- u
w
(kPa)
k
w
(m/s)
Predicted from SWCC by Fredlund and Xing (1994)
Predicted from SWCC by this study

Figure 3.10. Coefficient of permeability
versus matric suction of Songsat specimen 2
Figure 3.11. Coefficient of permeability
versus matric suction of Songsat specimen 3
The results from figures show that the coefficient of permeability with respect to matric
suction based on this study is good agreement to the experimental data.
3.3. Obtaining SHEAR STRENGTH OF UNSATURATED SOILS USING DIRECT
SHEAR APPARATUS
3.3.1. Direct shear apparatus
Layout of the direct shear apparatus is
presented in Figure 3.12.
3.3.2. Direct shear test procedure
Right after suction equilibrium at each
matric suction value, three soil samples have
been tested using direct shear apparatus at
normal stress of 100kPa, 200kPa and
300kPa. The soil specimens have been tested
immediately after taken out of pressure plate
in order to keep suction unchanged. The

figure 3.15 show that the shear strength the
increase

Figure 3.12. Lay out of the direct shear
apparatus

Figure 3.14. Extended Mohr-Coulomb
failure envelope of Khecat specimen
- 12 -

with increasing in net
normal stress. At
specific value of net
normal stress, the shear
strength is increase
when matric suction
increase. The shear
strength envelope on  ~
(s - u
a
) is nearly
paralleled and proves
that the shear strength is
increased when matric
suction increased.
Figure 3.16 show the intersection line between extended Morh-Coulomb failure envelope
and  ~ (s - u
a
) plane at net normal stress of zero kPa. The result from this figure shows that
the relationship between shear stress and matric suction is nonlinear.

a
) plane at
net normal stress is
shown in figure 3.19.
The results from
figure 3.19 clearly
show that the shear strength envelops with respect to matric suction is nonlinear. The 
b
is as
13
0
at matric suction less than air-entry value and decrease as 7
0
at matric suction of 200kPa.
3.3.4.3. Testing result of the Songsat 3 compacted specimens
0
100
200
300
400
0 100 200 300 400
Net normal stress, (
s
- u
a
) (kPa)
Shear strength,
f
(kPa)
ua - uw = 0 kPa

a
-u
w
) at net
normal stress of zero 0 kPa

Figure 3.17. Extended Morh-Coulomb
failure envelope of Songsat specimen 2
0
100
200
300
0 100 200 300 400
Net normal stress, (
s
- u
a
) (kPa)
Shear strength,
f
(kPa)
ua - uw = 0 kPa
ua - uw = 20 kPa
ua - uw = 50 kPa
ua - uw = 100 kPa
ua - uw = 200 kPa

0
100
200



’ = 13
o

- 13 -

Figure 3.20 show the experimental results on
extended Morh-Coulomb failure plane
envelope. The results from figure 3.20 show
that the effective friction angle, ’ = 13
0
and
effective cohesion, c’ = 14 kPa. The shear
strength is increased with the increasing in
matric suction, but 
b
decrease from 
b
= ’ at
matric sution smaller than air-entry value. The
effective friction angle remains nearly
unchanged (’  13
0
).
The intersection lines between extended Morh-
Coulomb failure envelope and  ~ (s - u
a
)
plane are show in

pressure (C). The high pressure disk in this
research is the 5 bar (500kPa) one;
3.4.2. Process and procedure of test
The triaxial compression test procedure for
saturated soil sample (Head, 1986) and for
unsaturated one (Fredlund vµ Rahardjo, 1993) have been used here. The initial matric
suctions of the specimens were established using the axis-translation technique (Hilf, 1956).

Figure 3.20. Extended Morh-Coulomb
failure envelope of Songsat specimen 3
0
100
200
300
0 100 200 300 400
Net normal stress, (
s
- u
a
) (kPa)
Shear strength,
f
(kPa)
ua - uw = 0 kPa
ua - uw = 20 kPa
ua - uw = 50 kPa
ua - uw = 100 kPa
ua - uw = 200 kPa

0

Figure 3.23. Modified triaxial cell for
unsaturated soils testing (after Fredlund
and Rahardjo, 1993)

’ = 13
o

- 14 -


Soil sample preparation
The soil samples are compacted at dry unit mass equal 95% of maximum unit one with
corresponding moisture content after compacting (table 3.2). The height and diameter of the
soil sample are respectively equal 100mm and 50mm.

Saturation phase of soil sample
All of the samples used in this experiment programme are saturated first aiming at creating
the identically initial moisture content. After that the samples are saturated by means of
gradually increasing the confining pressure steps (σ
3
) and backpressures, u
w
, under effective
stress equal 10kP until the coefficient of water pore pressure B attains proximity of 1.

Consolidation phase
After finishing saturation phase, the soil sample are consolidated under confined pressure,
σ
3
, and pore water pressure, u

a
vµ u
w
), the soil sample is sheared by axial pressure in conditions of air escape and
no for pore water (schema CW) or both air and pore water escape (schema CD), with
constant velocity of shearing. In this study, the displacement velocity of 0,02 mm/minute is
selected. The procedure of shearing is finished at maximun deviatoric stress. If the above
failure condition is not accessible, stop the experiment at 25% of axial deformation. The
shearing phase elongates in 24 hours.
3.4.3 Test programmed
Triaxial compression test was using the compacted soil samples of Khecat and Songsat 3, in
which 9 samples of Khecat (according to schema CD) and 18 samples of Songsat 3
(according to schema CD and CW).
3.4.4. The results of triaxial compression test using consolidated - Drained (CD)
schema
3.4.4.1 Experimental results of Khecat compacted samples
3.4.4.1.1 Shear strength properties of experimental soil samples
The figures 3.33 and 3.35 show the relationship between deviator stresses and axial strains
under different real confined pressure with the same matric suction equal 0 kPa and 200kPa.
0
200
400
600
800
1000
0 8 16 24 32 40
Axial strain,

(%)
Deviatoric stress, (

1
-s
3
) versus with the
same initial matric suction of 0 kPa.
Figure 3.35. (s
1
-s
3
) versus with the
same initial matric suction of 200 kPa.
- 15 -

At the same matric suction equal 0 kPa, the more the samples sustained higher net confining
pressure, the more the peak deviator stress increases. At the same matric suction, when the
real confined pressure gradually increases on the soil sample, its shear strength also
increases correspondingly.
3.4.4.1.2. The extended Mohr-Coulomb failure
envelope surface
The extended Mohr-Coulomb failure envelope
surface is given in the figure 3.39. On the
figure 3.39, it is shown that the envelope
surface is curve along the matric suction axe.
Projection of the failure envelope surface on
the  ~ (s – u
a
) plane gives the matric suction
contours as shown in the figure 3.40. These
lines have different cohesive intercepts belong
to their correspondent matric suctions. The

Figure 3.39. Extended Mohr-Coulomb
failure envelope of Khecat specimen for
CD tests
0
100
200
300
400
0 100 200 300 400 500 600
Net normal stress, (
s
- u
a
) (kPa)
Shear strength,
f
(kPa)
ua - uw = 0 kPa
ua - uw = 100 kPa
ua - uw = 200 kPa

0
100
200
300
400
500
0 100 200 300
Matric suction, (u
a

f
versussu
a
) plane
Figure 3.41. Horizontal
projections of the failure
envelope onto the 
f
versusu
a

– u
w
) plane
0
80
160
240
320
0 5 10 15 20 25 30
Axial strain,

(%)
Deviatoric stress, (
1
-
3
)

(kPa)

Figure 3.46. (s
1
-s
3
) versus with the
same initial matric suction of 200 kPa.
- 16 -

With the matric suction equal 200 kPa, the
shear strength is more increased in comparison
with which equal 0 and 100 kPa. This is shown
that the matric suction increases the shear
strength of the sample.
3.4.4.2.2 The extended Mohr- Coulomb failure
envelope surface
The extended Mohr-Coulomb failure envelope
surface is shown in the figure 3.50. Figure 3.50
shows the trend of decreasing 
b
when
increasing the matric suction however ’ nearly
unchanged and 
b
= ’ when the matric suction
is less than the critical air entry value.
Projections of the failure envelope surfaces on
the  ~ (s – u
a
) plane give the matric suction
contours. All identical

failure envelope of Songsat specimen 3
for CD tests
0
100
200
300
0 100 200 300 400
Net normal stress, (
s
- u
a
) (kPa)
Shear strength,
f
(kPa)
ua - uw = 0 kPa
ua - uw = 100 kPa
ua - uw = 200 kPa

0
100
200
300
0 100 200 300
Matric suction, (u
a
- u
w
) (kPa)
Shear strength,

Figure 3.52. Horizontal projections
of the failure envelope onto the 
f

versusu
a
– u
w
) plane
0
80
160
240
320
0 5 10 15 20 25 30
Axial strain,

(%)
Deviatoric stress, (
1
-
3
)

(kPa)
CW50-0
CW100-0
CW200-0

0

same initial matric suction of 200 kPa.

c’=14 kPa

- 17 -

3.4.5.3. The extended Mohr-Coulomb failure
envelope surface
The extended Mohr-Coulomb failure envelope
surface is shown in the figure 3.62. From this
figure, it is seen that: when increasing the matric
suction, 
b
is reduced from 
b
= ’ at the 0 kPa
until 
b
= 4
0
in accordance with 200 kPa matric
suction. The angle of internal friction ’of the
soil sample seemed still to keep true to 13
0

despite the matric suction increases.
Projection of the failure envelope surface on the
 ~ (s – u
a
) plane is shown in figure 3.66. All of

direct shear test curves, from
which it seems no much
0
40
80
120
0 5 10 15 20 25 30
Axial strain,

(%)
Variation of pore water pressure,

u
w
(kPa)
CW50-0
CW100-0
CW200-0

0
40
80
120
0 5 10 15 20 25 30
Axial strain,

(%)
Variation of pore water pressure,

u

(kPa)
ua - uw = 0 kPa
ua - uw = 100 kPa
ua - uw = 200 kPa

0
100
200
300
0 100 200 300
Net normal stress, (u
a
- u
w
) (kPa)
Shear strength,
f
(kPa)
= 50 kPa
= 100 kPa
= 200 kPa
s
3
- u
a
s
3
- u
a
s

) (kPa)
Shear strength,
f
(kPa)
Direct shear tests
CD tests

0
50
100
150
200
0 50 100 150 200 250
Matric suction, u
a
- u
w
(kPa)
Shear strength,
f
(kPa)
Direct shear tests
CD tests

Figure 3.69. 
f
versus (u
a
-
u

 φ' and when the matric suction increases until some value, the angle φ
b
gradually
decreases.
Table 3.6. Comparison of the effective parameters of shear strength
Khecat material quarry Songsat 3 material quarry
Effective parameters of shear
strength
Direct
shear test

CD test
Direct
shear test

CD test CW test
'(degree)
23°29' 23°11' 13°03' 13°02' 13°00'
c' (kPa) 34,00 37,00 13,53 14,20 14,00

b
(degree)

0 23,47 23,18 13,15 13,11 13,08
20 23,35 12,99
50 23,03 12,37
100 10,11 7,97 5,24 4,86 4,12
Matric suction (kPa)

200 8,35 6,28 4,40 4,01 3,60

- u
w
(kPa)
Shear strength,
f
(kPa)
Direct shear tests
CW tests

0
50
100
150
200
0 50 100 150 200 250
Matric suction, u
a
- u
w
(kPa)
Shear strength,
f
(kPa)
CW tests
CD tests

Figure 3.71. 
f
versus (u
a

p
.
clay
slight loam
loam

heavy loam

’ = 13
o

- 19 -Experimental and calculated results for Yenbai soil samples are given in appendix III of the
thesis. From calculating results shown in figures from 3.74 to 3.79, it is seen that the
calculation of shear strength versus matric suction using our corrected coefficient  will give
the relationship 
f
~ (u
a
- u
w
) more adequate with test result.
3.6. CONCLUSION FOR CHAPTER 3.
(1) Test results to define the SWCC curve show that the more the high plasticity index I
p
of
soil, the more its great matric suction. The author proposes two formulas for the coefficients
m and n in the equation, so that to express more adequate some of experimented soils of

) (kPa)
Shear strength,
f
(kPa)
Measured
Predicted (Fredlund and Vanapalli, 1996)
Predicted (Proposed Equation)

0
100
200
300
0 100 200 300
Matric suction, (u
a
- u
w
) (kPa)
Shear strength,
f
(kPa)
Measured
Predicted (Fredlund and Vanapalli, 1996)
Predicted (Proposed Equation)

0
100
200
300
0 100 200 300

Figure 3.76. 
f
versus (u
a

– u
w
) of Songsat specimen 3
from direct shear tests.
0
100
200
300
0 100 200 300
Matric suction, (u
a
- u
w
) (kPa)
Shear strength,
f
(kPa)
Measured
Predicted (Fredlund and Vanapalli, 1996)
Predicted (Proposed Equation)

0
100
200
300

Figure 3.77. 
f
versus (u
a

– u
w
) of Khecat specimen
from CD tests.
Figure 3.78. 
f
versus (u
a

– u
w
) of Songsat specimen 3
from CD tests.
Figure 3.79. 
f
versus (u
a

– u
w
) of Songsat specimen 3
from CW tests.
- 20 -

4.1.2. Khecat

* Total cohesion: in case to have enough test material parameters of unsaturated soil,
the total cohesion method will be applied in order to exactly analysis the actual working of
the earth dam.
4.3.2.1. Stability analysis according to no consideration of

b
method
The result of stability analysis for the downstream slope without consideration of

b
gives
the minimum factor of stability, F
s
, equal 1,195.
4.3.2.2.Stability analysis according to the assumption

b
= 1/2

’
The result of stability analysis for the downstream slope gives F
s
= 1,307.
4.3.2.3. Stability analysis
according to the total cohesion
method
In order to calculating in the
unsaturated area, the upstream,
the impermeable core, and the
downstream incremental loading

-
1
2
0

-
1
0
0

-
8
0

-
6
0 -40


20
0

2
8
0Distance (m)
0 20 40 60 80 100 120 140 160 180 200
Elevation (m)
125
130
135
140
145
150
155
160
165
170
175
180
Figure 4.2. Pore pressure distribution lines in the
dam body and foundation (MC5A)
Impervious core
Downstream

The analysis result of
the pore water pressure
using SEEP/W
(GEOSTUDIO 2004)
is shown in the figure
4.5. From this, it is
seen that the value of
negative pore pressure
in the area above the saturation line is under -200 kPa.
4.4.2. Slope stability analysis
The slope stability analysis of Khecat earth dam is done by three methods: no consideration
of 
b
; assumption 
b
= 1/2 ’; total cohesion.
4.4.2.1. Slope stability analysis using no consideration of

b
method
The result of stability analysis of the downstream slope for the earth dam according to this
method gives the minimum stability factor, F
s
, equal 2,573.
4.4.2.2. Slope stability analysis using assumption 
b
= 1/2 ’
The result of stability analysis of the downstream slope for the earth dam according to this
method gives the minimum stability factor, F
s

gives the slope minimum stability coefficient F
s
equal
1,018.
4.5.2.2. Stability analysis using assumption

b
= 1/2

’ method
The calculated result for slope stability gives the minimum stability coefficient F
s
equal
1,250. Figure 4.5. The water pore pressure distribution line in the dam
body and its foundation (MC 0+200)

Figure 4.6. Cross section for analyzing
stability according to total cohesion method
Completely weathered
Residual soil
Bedrock
-160
-140
-120

-
9


0Distance (m)
0 3 6 9 12 15 18 21 24 27 30
Elevation (m)
50
52
54
56
58
60
62
64
66
68
70
72

Figure 4.8. The pore water
pressure distribution lines in the
slope body and its foundation
- 22 -

4.5.2.3. Stability analysis using total cohesion
method
The calculated cross section is shown in the figure
4.9. The result of slope stability analysis using total
cohesion slope method gives the minimum stability

=1,478).
4.6.2. The slope stability analysis results of Khecat
dam
Figure 4.11 show the factor of safety obtained from
Khecat dam slope stability analysis by three methods.
The factor of safety obtained when assuming 
b
=1/2’
increase to 5,13% compared with ignoring unsaturated
soil properties method while the one given by using
total cohesion method increase to 8,08% (i.e.,
Fs=2,781).
The factor of safety obtained by using total cohesion
method with the
unsaturated soil properties
suggested
by author increase about 0,47% compared with the one
calculated following Fredlund and Vanapalli (i.e.,
F
s
=2,794).
4.6.3. The stability analysis results of natural slope
in Yenbai
The slope stability analysis results by three methods are shown in Figure 4.12. The factor of
safety obtained by assuming 
b
=1/2’ method increase to 22,79% compared with ignoring
unsaturated soil properties method while the one given by using total cohesion method
increase to 23,58% (i.e., Fs=1,258).
2

72

Figure 4.9. Slope cross section for
stability analysis using total matric
suction method
1,15
1,21
1,27
1,33
1,39
1,45
1,51
1 2 3 3
Method
Fs

Figure 4.10
2,54
2,59
2,63
2,68
2,72
2,77
2,81
1 2 3 3
Method
Fs

Figure 4.11
Ignoring

Total
cohesion
by
F - V
Total
cohesion
by this
study
- 23 -

The factor of safety obtained by using total cohesion
method with the
unsaturated soil properties

determined following author research increase to
2,07% compared with the one based on research of
Fredlund and Vanapalli (i.e., F
s
=1,284).
4.7. CONCLUSION OF CHAPTER 4
The slope stability analyses results illustrate the effect
of application of unsaturated soil properties in
calculation of slope stability. The shear strength of
unsaturated soil increase as increasing matric suction
making the factor of safety of the earth dam
increasing. The factor of safety obtained by using total
cohesion method with the unsaturated soil properties
calculated by using author experimental study results
increase to 4,67% for Songsat dam, 0,47% for Khecat
dam and 2,07% for natural slope in Yenbai compared

b
) of the same soil
obtained by different cutting method (direct shear test, consolidation drain triaxial test,
and shear with unchanged moisture content) gave approximately the same values, so
the author suggests that in case lacking of laboratory triaxial aparatus for unsaturated
soil, it is possible to use the direct shear one to find out the shear strength parameters
of unsaturated soil followed the procedure as announced in the thesis.
4.
Establish the curves that can be used to calculate SWCC parameters, permeability
coefficient and shear strength for some soil type in Vietnam to avoid using unsuitable
SWCC curves from other country. Establish a graph showing the relationship between
0,98
1,03
1,09
1,14
1,19
1,25
1,30
1 2 3 3
Method
Fs
8

Figure 4.12
Ignoring

b