Civil Engineering Reference
In-Depth Information
σ
y
is the yield point which lies at the intersection of
the swelling line through B with the normal compression line. Compare the definition
of
Y
0
for one-dimensional overconsolidation with the definition of
Y
p
in Eq. (8.8) for
isotropic over-consolidation.
σ
0
is the current stress and
where
8.6 Horizontal stress in one-dimensional loading
During the increase and decrease of
σ
z
in one-dimensional loading and unloading the
σ
h
changes since
σ
z
and
σ
h
are
horizontal stresses
ε
h
is held constant. The variations of
illustrated in Fig. 8.11(a). The ratio
=
σ
h
σ
z
K
0
(8.13)
is known as the coefficient of earth pressure at rest (i.e. corresponding to zero horizon-
tal strain) and the variation of
K
0
with yield stress ratio
Y
0
is illustrated in Fig. 8.11(b).
For states OACD on the normal compression line
Y
0
=
1 and the value of
K
0
is
K
0nc
for normally consolidated soil: for many soils this can be approximated by
φ
c
K
0nc
=
−
1
sin
(8.14)
φ
c
is the critical friction angle (see Chapter 9). For overconsolidated states
ABC the value of
K
0
increases with overconsolidation and
K
0
may well exceed 1.0 as
the horizontal stress exceeds the vertical stress at large values of
Y
0
. Figures 8.11(a)
and (b) illustrate substantial hysteresis in
K
0
during unloading and reloading, but
if this is neglected then
K
0
is found to vary with
Y
0
and an approximate empirical
relationship is
where
K
0nc
Y
0
K
0
=
(8.15)
σ
h
are generally unequal and
so there are shear stresses in the soil and any comparison between isotropic and
σ
z
and
During one-dimensional loading and unloading
Figure 8.11
Horizontal stresses during one-dimensional loading and unloading.
