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CSL
CSL
e ss(A)
ψ
e 0(B)
e 0(B)
e 0(A)
e 0(A)
ψ
e ss(B)
p 0(A)
p 0(B)
p 0(A)
p c0
p 0(B)
lnp
lnp
(a)
(b)
Figure 9.15. Initial state: a) [BEE 85], definition of state parameter ( ψ );
b) definition of the initial state in the ECP family models. CSL - critical state line
normally consolidated clay, as the void ratio varies with depth, the ratio σ c0 0 may
be considered constant. On the other hand, in the case of sand, the change in void ratio
with depth is low and, for a given D r , σ c0 remains constant.
In summary, under isotropic loading conditions, the initial state of a clay is known
when we know the initial stress (or void ratio) and its OCR . For sands, knowing the
void ratio (or relative density) and the initial stress is sufficient. Under anisotropic
conditions, the degree of shear mobilization should be added.
We can obtain the following relation for clays:
σ c0
σ =
C u
σ 0 tan φ pp
[9.91]
where C u is the undrained shear strength. In practice, the ratio C u
σ 0 can be obtained
from laboratory tests or by using correlations such as the one given below:
C u
σ 0
=(0.23 ± 0.04)OCR 0.8
[ JAM 85 ]
[9.92]
According to Been and Jefferies [BEE 85], the ratio σ c0
σ for sands may be obtained
from coefficients such as the state index ψ (which should not be confused with the
dilatancy angle) or I s used by Ishihara [ISH 93]. The state index given by Been and
Jefferies is defined as the difference of void ratios at the initial state e 0 and that at
critical state e ss under the same level of stress (see Figure 9.15).
In the previous sections, a methodology of identifying the ECP elastoplastic model
parameters was presented. This methodology consists of two objectives. The first is to
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