Civil Engineering Reference
In-Depth Information
Figure 18.4
Cases where the critical state strength should be used for design.
reduce the strength towards the residual. Consequently, for most purposes the critical
state strength is the worst that needs to be considered in design. The residual strength
should be considered for design in clay soils only if there are pre-existing slip surfaces
or if very large displacements are expected.
After strains of the order of 10% or so the shear stress which can be mobilized is
the critical state strength
τ
f
. For drained loading this is given by
τ
f
φ
c
=
(
σ
−
u
) tan
(18.4)
φ
c
is a material parameter. For undrained loading it is
where the critical friction angle
given by
τ
f
=
s
u
(18.5)
where the critical undrained strength
s
u
depends on the water content and so it is a
state dependent parameter.
Figure 18.4 illustrates two cases in which the critical state strength should be used
in design. In Fig. 18.4(a) the shear stress on the potential slip surface in the slope
is governed by the critical state strength because, even in a stable slope, there will
probably be strains in the ground larger than 1%. In Fig. 18.4(b) the ultimate limit
state of a stiff propped retaining wall should be investigated using the critical state
strength.
Factor of safety
For a safe design it is necessary to ensure that there is an adequate margin against
collapse and this is done by applying a factor of safety
F
s
to the strength. The safe
shear stresses
τ
s
or
τ
s
in the soil are given by:
τ
s
=
τ
φ
F
s
u
)
tan
F
s
=
(
σ
−
(18.6)
=
F
s
=
s
u
F
s
τ
(18.7)
s
