Civil Engineering Reference
In-Depth Information
Fig. 11.15
Isotropic and one-dimensional consolidation.
11.7.1 Equivalent isotropic consolidation pressure,
p
e
Consider a particular specific volume, v. Then the value of consolidation pressure which corresponds to v
on the normal isotropic consolidation curve is known as the equivalent consolidation pressure and is given
the symbol
′
tive consolidation pressure
′
′
′
p
x
. The procedure for determining
p
e
is illustrated in the diagram. Note that
as P is below AB, it represents a state of overconsolidation.
For a normally consolidated clay, subjected to an undrained triaxial test,
′
=
′
p
e
σ
but with drained tests
p
e
will vary.
′
11.7.2 Comparison between isotropic and one-dimensional consolidation
If a sample of clay is subjected to one-dimensional consolidation in an oedometer and another sample of
the clay is subjected to isotropic consolidation in a triaxial cell then the idealised forms of the v-ln p
′
plots
for the tests will be more or less as illustrated in Fig.
11.15.
The values of the slopes of the two normal consolidation lines are very close and, for all practical pur-
poses, can both be assumed to be equal to
−
λ
. Similarly the slopes of the swelling lines can both be
taken as equal to
−
κ
.
Note that the values of ln p
′
for the one-dimensional test are taken as equal to ln
σ
′
, where
σ
′
=
the
normal stress acting on the oedometer sample.
As the compression index C
c
is expressed in terms of common logarithms we see that:
λ
≈
C
c
2 3
.
11.8 Two-dimensional stress paths
As discussed in Chapter
4,
the state of stress in a soil sample can be shown graphically by a Mohr circle
diagram. In a triaxial compressive test the axial strain of the test specimen increases up to failure and the
various states of stress that the sample experiences from the start of the test until failure can obviously
be represented by a series of Mohr circles. The same stress states can be represented in a much simpler
form by expressing each successive stress state as a point. The line joining these successive points is
known as a
stress path
.
