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possible to speak of
reference behavior
(Figure 9.1), which J. Biarez divided into two
states:
- the pre-peak behavior;
- the post-peak behavior.
The post-peak behavior, which determines the strength of a material, depends on test
conditions. When experimental precautions are taken to obtain a homogeneous state of
stresses and/or strains to avoid strain localization, critical state or perfect plasticity can
presumably be reached, as represented by two lines in the (
q−p
) and (
e−log p
) planes
with
M
and
λ
slopes, respectively. When the test is no longer homogeneous, kinematic
discontinuities will appear. The pre-peak behavior is governed by an additional
parameter which shows the distance compared to the critical state. For granular
materials, this additional parameter represents, simultaneously, the role of density and
the confinement on behavior. For clays, it describes the degree of over-consolidation
and confinement. The space is thus decomposed into a zone of dilative behavior and an
area of contractive behavior. Friction mobilization is thus connected to the contractive
or dilative behavior of soil.
9.3.2.
Constitutive models used for computation
Throughout its history, soil behavior has been modeled under different approaches.
The earliest models were based on theories of elasticity and plasticity. From a practical
point of view, seeing that it is easy to use and to apply, despite its shortcomings, the
non-linear model developed by Duncan and Chang [DUN 70] was one of the most
widely used models for certain applications, such as earth dams. However, unable to
take into account such aspects as volumetric or cyclic behavior, its use very quickly
became limited to the estimation of settlement.
The theory of plasticity provided a solid and practical framework for developing
constitutive models. From Drucker's work in 1949 [DRU 49], which established the
concepts of modern plasticity, many models have appeared. The first important
contribution in the field of soil mechanics was inclining the yield surface from the
origin downward and across the mean stress axis and, then, the introduction of the
concepts of critical state and density-hardening. Gradually, it was found to be necessary
to introduce deviatoric strain hardening and non-associated flow laws.
The need to generate plastic deformation at the beginning of loading resulted
in generalized plasticity models, such as the concept of
bounding surface
[DAF 82,
PAS 85]. Moreover, the introduction of multiple yield surfaces and kinematic hardening
[MRO 67] increased the ability of models to describe cyclical phenomena. Thus,
multisurface models have emerged [AUB 82, HUJ 79, MRO 81] and the theoretical
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