Geoscience Reference
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280
Multiscale Geomechanics
Figure 9.7. Comparison of some empirical relations given for
G max at a mean pressure of 200 kPa
line (compressibility index C c or λ ). When a normally consolidated soil passes from a
state ( e 0 ,p 0 ,p c0 )to( e,p ,p c ), the following relations are valid:
1+e 0 ln p c
= ε v + ε v = − e−e 0
λ
ε v
1+e 0 =
p c0
1+e 0 ln p c
λ
1+e 0 ln p c
κ
p c0 + β ln p c
if n e =1 then
=
p c0
p c0
= p 0 1−n e −p 1−n e
(1−n e )K 1−n e
ref
1+e 0 ln p c
+ β ln p c
λ
if n e =1 then
p c0
p c0
K ln p c
p c0 + β ln p c
1
=
p c0
1+e 0 ln p c
k∗
p c0 + β ln p c
=
p c0
where K and k are equivalent moduli giving the same elastic strain with a logarithmic
law in the range of the considered pressure.
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