Civil Engineering Reference
In-Depth Information
Figure 9.9
Parameters for normalizing triaxial test results.
From the geometry of Fig. 9.9,
ln
p
a
v
λ
=
v
a
+
λ
(9.12)
ln
p
c
=
−
v
a
(9.13)
λ
Figure 9.10 shows critical state and normal compression lines normalized with
respect to
p
c
and
v
λ
: these correspond to Fig. 9.7 for shear tests. Again a broken
line has been drawn representing important states between the normal compression
and critical state lines; we will consider these states in later chapters. Note that, for
triaxial tests, there will be two critical state lines, one for compression and one, with
negative values of
q
, for extension.
The undrained strength
s
u
is uniquely related to the voids ratio, and hence to the
specific volume. From Eqs. (9.10) and (9.11), noting that
s
u
1
2
(
1
σ
a
−
σ
r
)
f
2
q
f
=
=
we have
ln
2
s
u
M
=
−
v
(9.14)
λ
which is comparable to Eq. (9.5). Undrained strength may be measured in unconfined
compression tests (i.e. tests with
0) or in triaxial tests with any confining pressure
provided that the voids ratio does not change. Figure 9.11 shows Mohr circles of total
and effective stress for confined and unconfined compression tests on samples with the
same voids ratio. The Mohr circles of effective stress are identical; they both touch
the lines given by
σ
r
=
φ
c
. The Mohr circles of total stress have the
same diameter (because the voids ratios of the samples are the same) but they are in
different positions, so the pore pressure in the unconfined compression test sample is
negative. It is this negative pore pressure that produces positive effective stresses and
gives rise to the unconfined compressive strength; this accounts for the strength of a
sandcastle and the stability of a trench with steep sides.
τ
f
=
σ
f
tan
τ
f
=
s
u
and
