Civil Engineering Reference
In-Depth Information
where
G
is the shear modulus,
K
is the bulk modulus and
J
are moduli that couple
shear and volumetric effects. For undrained loading for which
δε
=
0, we have
v
d
q
d
3
G
s
=
(13.2)
ε
d
p
d
J
ε
s
=
(13.3)
and, for isotropic compression for which
δε
s
=
0, we have
d
p
d
K
v
=
(13.4)
ε
d
q
d
J
v
=
(13.5)
ε
Notice that for undrained loading Eq. (13.2) also defines the undrained shear modulus
G
u
and hence
G
G
u
=
(13.6)
Figure 13.2 shows the general characteristics of shearing and compression stress-strain
curves for undrained shearing and isotropic compression tests with stages of loading,
unloading and reloading. In Fig. 13.2(a) the gradient of the curve is the shear modulus
3
G
and in Fig. 13.2(b) the gradient is the bulk modulus
K
; we could obtain similar
curves and evaluate
J
1
and
J
2
by plotting
q
against
p
against
δε
s
. In Fig. 13.2
the soil had been unloaded from B and Q and so the initial states C and R are inside
the state boundary surface and the soil yields at D and S.
In Fig. 13.2 the stress-strain lines CDE and RST look non-linear, but it is difficult
to see exactly how the soil is behaving, especially for small increments at the start of
the reloading. The principal features of stress-strain curves can be seen more clearly
by examining how stiffness changes as loading progresses. Tangent moduli are more
important than secant moduli but it is not easy to calculate tangent moduli from test
δ
δε
v
and
δ
Figure 13.2
Shearing and compression of soils.
