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where the suffix
s
refers to a particular slip plane. In principle, shear strength
depends on cohesion, internal friction and the effective stress. In Fig 7.3 the local
critical stress state for a landslide along a slip plane (
s
) is worked out for its
orientation, and its equilibrium.
The Mohr-Coulomb model is commonly applied for slope stability (straight slip
plane or circular slip planes). A landslide occurs when along a failure plane
everywhere the stress state is critical. In reality, a slide may involve zones with
plasticity and local slip in different directions. It may appear that the Mohr-
Coulomb model does not always describe the most critical situation and then other
constitutive models should be used.
displacem
e
nt
passive
active
slipline direction
c cotg
passive
active
h
'
p
h
'
a
v
'
m
p
m
p
sin
Figure 7.4 Rankine stress states, with cohesion effect (after Bell)
C
COEFFICIENT OF EARTH PRESSURE
34
The horizontal effective stress usually differs from the vertical stress. See for
example equation (5.3), which refers to an elastic state without horizontal strain.
The ratio of horizontal and vertical stress, expressed by so-called coefficient of
earth pressure at rest
K
0
, is then
is the Poisson ratio. Instead, one
may adopt the correlations for
K
0
, mentioned in Table 7.1.
Depending on (historic) deformation or actual displacement of the soil, the stress
ratio
/(1
), where
v
'
can vary significantly. Using the Mohr-Coulomb failure criterion, two
limit states can be identified in soil, one with maximum (passive) and one with
minimum (active) horizontal stress. In the plastic wedges, as shown in Fig 7.4,
shearing resistance is supposed to be fully mobilised. This observation has led to
h
'
/
34
The earth pressure coefficient is applied for effective stresses. Sometimes, it refers to
total stresses, but in case of saturated soil, special care is required for the involvement of
pore pressures.
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