Civil Engineering Reference
In-Depth Information
(c) Compressibility
From Fig. 9.4 the compressibility of a soil is given by the gradient
C
c
of the
normal compression and critical state lines and this is a material parameter.
From Fig. 9.5
s
u
is proportional to
σ
so the critical state line can be drawn as
Fig. 18.8 and
−
=
=
e
LL
e
PL
C
c
log 100
2
C
c
(18.12)
Since
e
=
wG
s
and noting that
e
is a number while
w
is a percentage, Eq. (18.12)
becomes
I
p
G
s
100
C
c
=
(18.13)
Hence
C
c
is related to the Atterberg limits and this is a consequence of the
100-fold difference between the undrained strengths at
the liquid and plastic
limits.
(d) Critical state line
It turns out that the critical state lines with axes
e
and log
σ
for many fine grained soils
pass through the same point called the
(omega) point. The approximate coordinates
σ
=
of the
point given by Schofield and Wroth (1968) are
e
=
0.25 and
15 MPa
and these are fundamental constants. From Eq. (9.3)
e
=
0.25
+
C
c
log 15,000
(18.14)
From Eqs. (18.13) and (18.14) the parameters
C
c
and
e
, which define the critical state
line for fine grained soils, can be obtained from the Atterberg limits. There are simple
relationships between
C
c
and
λ
and between
e
and
.
Figure 18.8
Determination of compressibility from the Atterberg limits.
