Civil Engineering Reference
In-Depth Information
specific volumes and together these will form a peak state surface. The surface can
be reduced to a line by normalization as described in Sec. 9.6. The normalized peak
state boundary surface can be represented by either the Mohr-Coulomb equation or a
power law equation and these are shown in Figs. 10.7 and 10.10 respectively. The peak
state boundary surface on the dry side of critical shown in Fig. 11.4(a) is close to, but
not the same as, the power law peak state envelope in Fig. 10.10(a).
The peak state surface is a boundary on the dry side of critical and it is now necessary
to examine whether there is a well-defined state boundary on the wet side. If there is
it will join the isotropic normal compression and critical state lines and it might look
like the broken line in Fig. 11.4.
Figure 11.5 shows paths for three different initial states all on the wet side of critical.
P and V are on the isotropic normal compression line; P is sheared drained with
p
constant and V is sheared undrained and the paths cross at S. R is initially anisotrop-
ically compressed and it is compressed further at a constant stress ratio
q
/
p
=
η
so
that the state passes through the point S. (Notice that the normal compression line is
like this path but with
η
=
η
=
M
.) We can
easily arrange for all the stress paths in Fig. 11.5(a) to pass through the same point S,
but the question is whether they all have the same specific volume at S in Fig. 11.5(b).
The best way to examine this is to normalize the states with respect to the critical
pressure
p
c
or with respect to the equivalent volume
v
λ
. The resulting normalized
state boundary surface is shown in Fig. 11.6. As before, the critical state and isotropic
normal compression lines reduce to single points and the anisotropic compression line
RS reduces to a single point S. Also shown in Fig. 11.6 are the parts of the state
0 and so is the critical state line but with
Figure 11.5
State paths for normally consolidated soil.
