1046
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
stress to decide the soil deformation and strength and the soil
skeleton stress equation of the unsaturated soil can be
considered as the effective stress equation of the unsaturated
soil.
In terms of shearing strength of the unsaturated soil,
Vanapalli and Fredlund gave the following shearing strength
formula after the experiment and analysis:
'
tan
f
t
a
e a
w
c
u S u u
'
(26)
We can find the stress expression in the square bracket of
such formula is the above mentioned unsaturated soil skeleton
stress, which indicates that the unsaturated soil shearing
strength is controlled by the skeleton stress, as the same with
that of saturated soil. The shearing strength formula of saturated
soil and unsaturated soil is uniform with the concept of the soil
skeleton stress.
No adequate experiment data is found on unsaturated soil
volume changing.
7 DISCUSSION ON THE PRINCIPLE OF EFFECTIVE
STRESS
The soil skeleton stress is the real internal force acting on the
soil by the external load, or the effective stress by Terzaghi. The
effective stress is not the virtual stress in such meaning. It is the
real stress of the soil skeleton with definite physical meaning.
The essence of the effective stress principle is that the soil
skeleton stress decides the soil strength and deformation in case
of ignoring the effect of the pore fluid pressure.
The effective stress principle is the most important one in the
soil mechanic and the foundation of the modern soil mechanics.
Such principle, put forward by Terzaghi in 1936, states that
the stress of any point at the soil section will be calculated with
the total major stress
1
2
3
of such point. In case of the
soil pores are filled with water under the stress of
u
, the total
major stress consist of two parts: the first is ,the stress acting
on the water and solid with the equivalent strength in various
directions, which is called the neutral stress or pore water
pressure; the second is the difference of the total stress
， ，
u
and
the neutral stress, namely,
1
1
,
2
2
,
, which can act in the solid phase of the soil.
u
u
3
3
Such part of the total major stress is considered as the main
effective stress. The changing neutral stress does not cause the
volume changing actually. The neutral stress is not linked with
the damaging soil in the stress conditions.
u
Porous materials (as sand, clay and concrete) is
incompressible in the action to , just like the internal friction
equal to zero. The measured results of the changing stress such
as compression deformation and changing shearing resistance
are only caused by the changing effective stress
,
and
.”
u
1
2
3
To sum up, the principle of effective stress consists of two
parts: the first is that the changing soil volume and shearing
strength depends on the changing effective stress completely
and the second is that the soil effective stress is equal to the
difference of the total stress and pore water pressure.
The study in this thesis provides the theoretical foundation
for the effective stress principle and also expresses that the
effective stress principle by Terzaghi requires no further
amendments and that the effective stress principle may be
expanded to the unsaturated soil. Vanapalli and Fredlund made
experiments and analysis, showing the soil skeleton stress
(effective stress) controls the shearing strength of the
unsaturated soil. No adequate experiment data is found on
unsaturated soil volume changing.
8 CONCLUSIONS
(1) The effect of the pore water pressure and pore air
pressure on the soil skeleton constitutes the balance force
system respectively, keeping the soil skeleton in balance. If the
soil skeleton stress is defined as the soil skeleton internal force
from the external forces excluding the pore fluid pressure, the
soil skeleton stress is the effective stress by Terzaghi.
Therefore, the effective stress is not the virtual internal force but
the real internal force strength of the soil skeleton.
(2) The effective stress equation by Terzaghi is tenable,
unnecessary to make any amendment for the saturated soil, in
case of ignoring the effect of the pore water pressure on the soil
strength and volume changing.
(3) On the basis of the differential equation of equilibrium
of the unsaturated soil, we can obtain the relationship
expression of the skeleton stress (effective stress) from the
external forces excluding pore water and pore air pressure and
the total stress, pore water and pore air pressure, which is
considered as the soil skeleton stress (effective stress) equation:
=
t
a
e a
w
u S u u
The above formula will be the effective stress equation by
Terzaghi for the saturated soil. The experiments and
engineering experience show that the effective stress decide the
strength and deformation of the saturated soil. The experiment
results by Vanapalli et al prove that the effective stress decides
the shearing strength of the unsaturated soil.
(4) If consideration is taken on the effect of the pore water
and pore air pressure, the equivalent expression of the shearing
strength and soil volume changing equivalent shall be
respectively:
'
tan
(1
)
tan
c
t
a
e
a
u S u u
a
w
'
1
s
t
a
e a
C u S u u
C
w
It will be the equivalent effective equation by Skempton in
the saturated condition.
Therefore, the effective stress equation and equivalent stress
equation of the unsaturated soil are the uniform effective stress
equation and equivalent stress equation in the soil mechanics.
9 REFERENCES
TERZAGHI K. 1948. Theoretical soil Mechanics. London: Chapman
and Hall Limited.
BISHOP A W. 1959.The principle of effective stress. Teknisk Ukeblad,
106(39),113–143.
BLIGHT G E. 1965. A study of effective stress for volume change.
Moisture Equilibria and Moisture Changes in Soils Beneath
Covered Areas. Sydney: Butterworths, 259–269.
SKEMPTON A W. 1961. Effective stress in soils, concrete and rocks,
pore pressure and suction in soils. Conf organized by the British
National Society of Int Society of soil Mech. and Foundation Eng.
London: Butterworths, 4–16.
SHAO L T. 1996. Pore medium mechanics analysis method and its
application in soil mechanics. Dalian: Dalian University of
Technology
FRELUND D G, Rahardjo H. 1993. Soil Mechanics for Unsaturated
Soils. New York: John Wiley & Sons, Inc.
Vanapalli S K. Fredlund D G. Pufahl D E. Clifton A W. 1996. Model
for the prediction of shear strength with respect to soil suction.
Canadian Geotechnical Journal, 33(3): 379-392
TERZAGHI K. 1936. The shearing resistance of saturated soils and the
angle between the planes of shear. Proc 1st Conf Soil Mech, 54–56.
JENNINGS J E B, BURLAND J B. 1962. Limitations to the use of
effective stresses in unsaturated soils. Géotechnique, 12: 125–144.
