Geoscience Reference
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250
Multiscale Geomechanics
Figure 9.1.
Reference behavior based on results obtained by
of Bouvard [BOU 82] from [SAI 97]
Roscoe, Schofield and Wroth, the initiators of the critical state concept (Cambridge
School [ROS 58]), first demonstrated it from the results obtained on clays (Cam Clay) in
the 1960s. Previously, researchers who studied the stability of slopes composed of fine
sands noticed the importance of the
in situ
void ratio on the liquefaction potential. They
assumed that liquefaction could only occur in materials with a void ratio higher than a
certain value (Casagrande [CAS 38], Geuze [GEU 48] and Koppejan
et al.
[KOP 48]).
Casagrande and collaborators formulated the concept of critical void ratio in design
methods. This method, known as the
steady state
or
collapse surface
, is described
in detail by Castro
et al.
[CAS 82]. It consists of the limit analysis of potentially
liquefiable soil and is based on the concept of “steady state of deformation”, defined
by Poulos [POU 81], as a state in which a mass of particles deforms continuously
with constant volume, effective normal stress, distortion, and speed. As can be seen,
these two concepts are very similar and the only point of difference seems to be the
requirement that constant speed be included in the concept of
steady state
[SLA 85]. In
Cam Clay theory, it is assumed that the location of all final states of a material having
reached perfect plasticity may be defined by a curve. For sands, it is very difficult or
impossible to obtain this line of isotropic consolidation. Nevertheless, for a given sand,
we can evaluate its capacity for contraction or dilation from its initial state (
e
0
−p
0
−q
0
)
and its position compared to the critical surface.
8) The range of reversible deviatoric behavior of soils is very small. During cyclic
loading, we find that for larger amplitudes of shear strain, the hysteresis loops of stress-
strain are changed at each cycle, either due to the densification of the material in drained
conditions or because of changes in pore pressure in undrained conditions. Classical
(G-
γ
) and (
D
-
γ
) curves are essentially explained by the creation of irreversible strain,
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