Civil Engineering Reference
In-Depth Information
Figure 13.11
Relationships between stress-strain curves and strength.
In Eq. (13.14) the term on the right hand side is the area below the stiffness-strain
curve from the origin to the point X and
q
x
is the stress at the point X. It follows
that the peak strength is equal to the area below the stiffness-strain curve from the
origin to
p
. This places strong restrictions on the permissible shapes of non-linear
stress-strain and stiffness-strain curves.
Figure 13.12(a) shows a typical stress-strain curve up to the peak state and
Fig. 13.12(b) is the corresponding stiffness-strain curve: the stiffness decreases from
an initial value
E
0
to zero at the peak. In Fig. 13.12(a) there is a reference strain
ε
ε
r
defined as
q
p
E
0
ε
=
(13.15)
r
Figure 13.12
Degree of non-linearity of soil.
