Page 130 - Numerical Analysis and Modelling in Geomechanics

STABILITY OF UNSATURATED SOIL SLOPES 111

(4.9)

By comparing equations (4.4) and (4.9), it can be deduced that S =γ m . For
w
s
w
water flow in saturated soils, u =u , then equation (4.6) becomes:
a
w
(4.10)
where m is equivalent to the coefficient of volumetric change m which is common
v
a
to saturated soil mechanics.
Theory of shear strength for unsaturated soils

The mechanical behaviour of soils is governed by stress state variables which
control the equilibrium of the soil structure. Physically meaningful stress state
variables must be expressed in terms of measurable quantities such as the
total stress σ, the pore water pressure u , and the pore air pressure, u . Matyas
a
w
and Radhakrishna [16] introduced the two stress state parameters, (σ–u ) and
a
(u – u ), to describe the volumetric behaviour of unsaturated soil. These two
w
a
stress state parameters were subsequently adopted by Fredlund and Morgenstern [17
] to conduct stress analysis of unsaturated soils on the basis of multi-phase
continuum mechanics.
For soil located above the main water-table, the pore water pressure is
negative with respect to the atmospheric pressure. This negative pore water
pressure is commonly referred to as the matrix suction of soil. To account for the
influence of this negative pore water pressure on soil shear strength and hence
the factor of safety, Fredlund et al. [18] developed a modified form of the Mohr-
Coulomb failure criterion for unsaturated soils, as follows:
(4.11)

where σ n is normal stress and ф b is an angle defining the increase in shear
strength for an increase in matrix suction. Based on some recent triaxial test
results on completely decomposed granite (CDG) with suction measurements
(Gan and Fredlund [19]), effective cohesion c'=10kPa, angle of friction ф'=38°
b
and ф =15° were adopted in the limit equilibrium analyses. It should be noted
that shear strength varies with matrix suction in a non-linear fashion (Gan et al. [
b
20]). The value of ф decreases with increasing suction. However, for simplicity
and the small suction range considered in the stability analyses, a constant ф b
value was assumed.