1045
Technical Committee 105 /
Comité technique 105
(a) (b) (c)
(a) Unsaturated soil infinitesimal body
(b) Surface force of skeleton free body in direction of x axis
(c) Effect of matrix suction on soil skeleton
Fig. 3 Stress of unsaturated soil element and skeleton
Soil-water characteristic test shows that some content of
water is always in the soil, however much the pressure (matrix
suction) acting on the soil, which is considered as the residual
water content, of which the corresponding saturation shall be
S
r
.
The electro-mechanical interacting force of the pore water and
the soil skeleton corresponding to the residual water content is
so strong that the soil no longer shows the property of the fluid,
but that of the solid or semi-solid. Therefore, in the force
analysis on the unsaturated soil, the pore water corresponding to
the residual water content may be considered as part of the soil
skeleton. Now, the soil porosity is considered as , porosity of
pore water phase and pore air phase
ew
n
and
ea
respectively.
The saturation without calculating the residual water content is
the effective saturation, namely
S
e
, indicated with the formula:
e
n
n
1
r
e
r
S S
S
S
(6)
Similar to saturated soil, according to the internal force
analysis figure, we can obtain the equation of equilibrium of
each phase, and the equation of equilibrium of the soil element
without any term of inter-phase acting force.
( )
(
)
,
,
,
(
)
1
ij j
e w i
e a
sfi
i
S u
S u X
+
+ -
+
0=
(13)
Or
(14)
(
)
(
)
,
,
,
0
ij j
a i
a
w
sfi
i
u S u u
X
+ -
-
+ =
To compare the equation (13) or (14) with the total stress
equation of equilibrium, then obtain:
(1 )
ij
tij
ij e w ij
e a
S u
S u
= -
-
-
(15)
Or
)
(
u uS
u
w a e ij
a ij
tij
ij
This is the soil skeleton stress equation of unsaturated soil,
or the relationship expression of the total soil stress, soil
skeleton stress and pore water pressure and pore air pressure,
(16)
For saturated soil,
e
, then the soil skeleton stress
equation for unsaturated soil will be that of the saturated soil, or
the effective stress equation by Terzaghi.
1
S
5 SOIL VOLUME CHANGING OR STRENGTH
EQUIVALENT STRESS
Besides the soil skeleton stress, the forces on the soil
skeleton also include the action of pore fluid pressure and
arising internal force, which have different effect on the soil
shearing strength and deformation. The latter only causes the
volume deformation of the grains and pressure stress on contact
points of soil grains, affecting the shearing strength of the soil.
In case of fully considering the effect of the soil skeleton stress
and pore fluid pressure, the shearing strength and volume
changing expression for the unsaturated soil will be:
(
)
tan
tan
tan
f
t
a
e a
w
c a
c e a
w
c
u S u u
a u
a S u u
(17)
t
a
e a
w
s
s
e a
w
V C
u
S u u
C
V
C S u u
a
u
(18)
which can be written into in the further:
tan
tan
(1
)
(1
)
tan
tan
tan
c
c
f
t
a
e a
w
a
a
c
u
S u u
(19)
1
1
s
s
t
a
e a
V
C
C
C
u
S u
V
C
C
w
u
(20)
Where,
and
s
is internal friction angle and coefficient of
compressibility of the soil grains respectively;
C
and
the
shearing strength and coefficient of compressibility of the soil.
From it, obtain the equivalent stress expression for unsaturated
soil:
C
(1) Shearing strength equivalent:
'
tan
(1
)
tan
c
t
a
e
a
u S u u
a
w
(21)
(2) Soil volume changing equivalent:
'
1
s
t
a
e a
C u S u u
C
w
(22)
Generally, the pore air pressure in the soil is not high, the
contacting area of soil grains is small and the value of is
close to zero. Then, the effect of the pore fluid pressure on the
shearing strength and volume changing can be ignored,
t
a
e
, indicating only the effect of the
soil skeleton stress.
'
a
w
u S u u
When the pore air pressure
u
, then
0
a
'
'
tan
(1
)
tan
1
c
t
e
s
t
e w
a
S u
C S u
C
w
(23)
When the soil is fully saturated,
e
, the above mentioned
formula (21) and (22) changes into the equivalent stress
expression by Skempton.
1
S
According to the principle of causing equivalent volume
changing on the soil infinitesimal or the shearing strength
equivalent, A. W. Skempton educed the equivalent stress
expression of the saturated soil and made experimental
verification.
Shearing strength equivalent:
t
tan
(1
)
tan
a
u
w
(24)
Soil volume changing equivalent:
s
t
(1 )
C u
C
w
(25)
The equivalent stress expressions of the saturated soil and
unsaturated soil are uniform.
6 EFFECT OF SOIL SKELETON STRESS EQUATION OF
UNSATURATED SOIL
The above educed soil skeleton stress equation of
unsaturated soil will be that of the saturated soil in the saturated
condition, thus considered as the uniform soil skeleton stress
equation of the saturated soil and unsaturated soil, which has
two effects at least:
Firstly, to obtain the soil skeleton stress with the soil
skeleton stress equation directly in the condition of learning the
total stress and pore water and pore air pressure of any point in
the soil;
Secondly, the skeleton stress is the soil effective stress.
The soil skeleton is the supporting phase of the soil or the
structural phase of the soil, whose deformation and strength is
the deformation and strength of the soil skeleton. The forces of
the soil skeleton decide the strength and deformation of the soil
skeleton. As above mentioned, the contribution of the pore
water and pore air pressure on the soil strength and deformation
can be ignored. Thus, the soil skeleton stress is the effective
