Civil Engineering Reference
In-Depth Information
Figure 10.15
Dilation and peak strength related to state.
τ
/
σ
>
φ
c
; at P both
τ
/
σ
have their maximum
ψ>
ψ
path A-D C
0 and
tan
and
values.
The maximum angle of dilation and the peak strength are related to the voids ratio
at the peak states. Figures 10.15(a) and 10.15(b) show the behaviour of two samples
of the same soil in shear tests and they are the same as that shown in Fig. 10.13.
The peak states at P are a consequence of the rate of dilation
through Eq. (10.19).
In Fig. 10.15(b) the volumetric strains start from zero and end at different strains but
the voids ratios start from different initial values and end at the same critical voids ratio
as shown in Fig. 10.15(d). The specific volumes at the peak state are
e
1
and
e
2
and these
have different values of
e
λ
, as shown in Fig. 10.15(c). Sample 2, which has the larger
peak strength, has the smaller voids ratio: it is more dense and its overconsolidation
ratio is larger.
Figure 10.16(a) shows the peak states
P
1
and
P
2
with axes
ψ
τ
/
σ
and
e
λ
. The critical
τ
/
σ
φ
c
and
e
λ
=
state line is at
=
tan
e
and the normal compression line is at
τ
/
σ
e
0
. The peak strength points and the critical state line are on a
smooth curve and this can be extended to the normal compression line. Figure 10.16(a)
is similar to Fig. 9.7(b).
=
0 and
e
λ
=
