Civil Engineering Reference
In-Depth Information
Comparing Eqs. (9.4) and (9.6) we have
c
u
=
s
u
and
φ
u
=
0. In saturated soil
φ
u
must always equal zero. If you find triaxial test results which give
u
not equal to zero
then either the sample or the drainage leads were not saturated or there was something
wrong with the test.
φ
9.5 Total and effective stress analyses
There are now two different criteria of the strength of soils which determine the shear
stress at the critical state. The first, given by Eq. (9.2), relates the strength to the effective
normal stress through a friction angle. In order to use this equation it is necessary to
be able to calculate the effective stress which requires knowledge of the pore pressure.
In general the pore pressure will be known only if the soil is drained. Analyses using
Eq. (9.2) to determine strength are known as effective stress analyses and they are used
when the soil is fully drained.
The second, given by Eq. (9.4), gives the strength directly as the undrained strength
s
u
and, for a given water content, this is independent of the total normal stress. This
equation can be used when the soil is undrained and the voids ratio does not change
during construction. Analyses using Eq. (9.4) to determine strength are known as total
stress analyses and they are used when saturated soil is undrained.
It is important to get this right. You can do an effective stress analysis if the soil is
fully drained and you know the pore pressure. You can do a total stress analysis if the
soil is saturated and undrained. You must not mix these. If you are uncertain whether
the soil is drained or not you should do both analyses and consider the worst case.
We will meet examples of total and effective stress analyses for foundations, slopes
and retaining walls in later chapters of this topic.
9.6 Normalizing
Representation of the critical state line, as in Figs. 9.4 and 9.5, is relatively straightfor-
ward because, at the critical state
σ
f
and
e
f
are uniquely related and there is only
one critical state line. When we come to deal with peak states and other states before
the critical, the situation is a little more complex and it will be convenient to have a
method of normalizing stresses and voids ratios or specific volumes.
In Fig. 9.6 there is a point A where the state is
τ
f
,
σ
a
and
e
a
and there may also be some
shear stresses (not necessarily at the critical state)
τ
a
. In Sec. 8.3 we found that the
overconsolidation ratio or the current state was an important factor in determining
soil behaviour and so all the states with the same overconsolidation ratio should ideally
have the same equivalent state after normalization. This can be achieved in a variety
of ways and the two most common are illustrated in Fig. 9.6.
We have already seen that the positions of the normal compression and critical
state lines are defined by the parameters
e
0
and
e
and so the line of constant over-
consolidation ratio containing A and A
is given by
σ
a
e
λ
=
e
a
+
C
c
log
(9.7)
σ
a
and
e
λ
decreases with increasing overconsoli-
Notice that
e
λ
contains both
e
a
and
dation ratio.
