Page 65 - Numerical Analysis and Modelling in Geomechanics

46 A.A.JAVADI
Effects of air flow on shear strength of the soil

Theory of shear strength for unsaturated soils
16
Fredlund et al. proposed a shear strength equation for unsaturated soils, as an
extension to that of saturated soils:

(2.11)

where τ is shear strength of the soil, c' is effective cohesion, σ is total stress, u a
b
and u are pore-air pressure and pore-water pressure respectively, ф' and ф are
w
effective friction angles with respect to changes in net normal stress and matric
suction respectively, (σ–u ) is net normal stress and (u –u ) is matric suction.
a
a
w
This equation incorporates two independent stress state variables. The
b
effective cohesion, c', and the internal friction angles, ф', and ф , are the strength
parameters and relate the shear strength of an unsaturated soil to the stress state
variables. The shear strength parameters represent many factors simulated in the
test such as density, void ratio, degree of saturation, mineral composition, stress
history, and strain rate. In other words, these factors are combined and expressed
17
mathematically as the strength parameters. Equation (2.11) describes a planar
surface called the “extended Mohr-Coulomb failure envelope”. This surface is
tangent to the Mohr circles at failure.
The state of stress at failure can also be represented by the stress point failure
envelope. A Mohr-Coulomb failure envelope and a stress point envelope can
both be used to represent the stress state of a soil at failure; the former is
obtained by drawing a surface tangent to the Mohr circles while the latter is a
surface connecting the stress points of the failure Mohr circles. The stress point
envelope is usually assumed to be planar and can be defined by the following
equation 17 although evidence of nonlinearity of the failure surface has been
reported in the literature: 16
(2.12)

where
q is half of the deviator stress at failure (i.e., (σ —σ ) /2),
1
3 f
f
σ and σ are major and minor principal stresses at failure respectively,
1f
3f
d' is the intercept of the stress point envelope on the q-axis,
P =((σ +σ ) /2−u ) is the mean net normal stress at failure,
a
f
1
3 f
r =(u −u ) is the matric suction at failure, and
f
a
w f
b
Ψ' and Ψ are slopes of the stress point envelope with respect to the mean net
stress and matric suction respectively.
In this study, the stress point failure envelope has been used to predict the
shear strength behaviour of the soil due to the air flow in compressed air
tunnelling.