Civil Engineering Reference
In-Depth Information
′
Fig. 4.39
v-ln
which can be written as:
v
Γ
−
′
=
ln
p
λ
Γ
−
v
⇒
′
=
p
exp
λ
Hence, the critical state line is that line which satisfies the two equations:
exp
Γ
−
v
q Mp
=
′
and p
′ =
λ
Looking ahead to Section
11.7
where the subject of isotropic consolidation is described, it is seen that
λ
is the slope of the normal consolidation line and N is the specific volume at ln p
′
=
0. The values of M,
N,
Γ
and
λ
vary with the type of soil. From Figs
4.37
and
4.39
we see that the values for remoulded Weald
clay are approximately M
=
0.85; N
=
2.13;
Γ
=
2.09 and
λ
=
0.10.
4.14.3 Residual and critical strength states
The stress conditions that apply at the critical state line represent the ultimate strength of the soil (i.e. its
critical state strength) and this is the lowest strength that the soil will reach provided that the strains within
it are reasonably uniform and not excessive in magnitude. The residual strength of a soil operates, in the
case of clays, only after the soil has been subjected to considerable strains with layers of soil sliding over
other layers.
It is important that the difference between these two strengths is appreciated. Skempton (
1964)
showed
that the residual angle of friction of London clay,
φ
r
, can be less than 10° whereas Schofield and Wroth
(
1968)
reported that the same soil at critical state conditions has an angle of friction
φ
cv
of
22 .
°
.
4.15 Sensitivity of clays
If the strength of an undisturbed sample of clay is measured and it is then re-tested at an identical water
content, but after it has been remoulded to the same dry density, a reduction in strength is often observed.
