Geoscience Reference
In-Depth Information
l
=
h/h
0
and
d
=
dh/h
(5.6)
Elaboration yields the following relation between the natural and linear strain
concept
21
d
= dh/h = d
(
h/h
0
)/(
h/h
0
)
= d
(ln(
h/h
0
))
= d
(ln((
h
0
h
)/
h
0
))
= d
(ln(1
l
))
=
ln(1
l
)
(5.7)
-
h
-dh
h
0
h
1.6
1.6
1.2
1.2
l
l
0.8
0.8
0.4
0.4
0.0
0.0
0.2
0.2
0.4
0.4
0.6
0.6
0.8
0.8
Figure 5.2 Uniaxial compression and strain concept.
For small strains (less than 20%) linear and natural strain are practically similar.
For large strains, which may occur in soft soils, natural strain should be applied.
The original German(-Austrian) approach is based on measuring the voids ratio
e = n
/(1-
n
), the ratio between pore volume and solid volume, based on the idea
that deformation should be related only to the change of pore volume (solid grains
are relatively stiff), i.e. the fabric (arrangement of grains) changes and this causes
deformation. Using the fact that the total soil volume
V
can be expressed in terms
of voids ratio and volume of solids
V
s
, according to
V
s
= (1-
n
)
V = V
/(1+
e)
, the
relation between voids ratio and natural strain becomes for uniaxial compression,
using a similar development as for (5.7) and incompressible soil grains (
V
s
=
constant),
d
= dh/h = dV/V = d
((1
e)V
s
)/((1
e
)
V
s
)
=
21
Alternative method:
=
h
o
h
h
1
dh =
h
o
h
d
ln(
h
)
=
ln(
h/h
0
)
=
ln(1
l
).
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