Eléments
de mécanique quasi-statique des milieux granulaires mouillés ou secs

P.
Evesque: Lab MSSM, UMR 8579 CNRS, Ecole Centrale Paris, 92295 Châtenay-Malabry,
France , **evesque@mssmat.ecp.fr**

** **

**Abstract: **This lecture describes the rheology of
granular materials and soils in the quasi static regime and at a macroscopic
scale. It recalls the behaviour at large deformation, starting from the Coulomb
approach, and its link with the “critical” state or of “plasticité parfaite”,
with its friction angle j.
It then focus on the behaviour at small and intermediate strain and proposes a
simple model that takes into account the plastic nature of the deformation,
even at small strain and the experimental main characteristics. This allows to
predict for the first time the limit natural strain ratio in oedometer from the
friction angle j . It
describes correctly deformation at constant volume too It seems that the model
works till the maximum of stress in the stress-strain curve. It is a unifying
approach since it makes evident links between Rowe’s law of dilatancy,
“characteristic” state and “critical state”; it can be also used to understand
cyclic behaviours, as it is shown.

So, the book starts with few recalls on stress (s) and strain (e) tensors, on Mohr circle,
on solid friction, cohesion, porosity and permeability. Role of water is
emphasized at this stage. Then the book takes the part to consider only the
effective granular stress tensor s’,
which is the total stress tensor minus the pore pressure u_{w} minus
the cohesion and minus the viscous drag; and it describes the granular
mechanics within these reduced parameters s’ and e,
and the specific volume v. Then it
keeps on this point of view all along the text book. This is the simpler way to
describe the mechanics linked to the deformation of an ensemble of grains
packed together.

Chapters 3 and 4 describe the typical (s,e) experimental behaviours obtained during uniform
loading and chapter 6 for cyclic behaviours. Roles of friction and dilatancy
are exemplified and their link with the deviatoric stress q=(s_{1}-s_{3}),
the deviatoric stress ratio q/p’ and
the variation of volume v is emphasized. The (q,v,p) space is introduced and
used systematically to describe the evolution of the sample. Principles of cyclic compaction, cyclic
loosening and of soil liquefaction are described (ch. 6) and linked to the
deviatoric stress ratio q/p’. Particular attention is paid to relate these
behaviours to the so-called “critical state” (plasticité parfaite) , to the
Rowe’s law of dilatancy and to the initial density. Notion of normally
consolidated state is defined.

Once the experimental behaviours are known, the
book tends to describe these behaviours within the simpler way. First it presents
an original assumption on the plastic dissipation law f(q,p, dv/de_{1}), which
is assumed to depend only on the stress applied (q,p’) and on the way the
sample deforms K= -de_{v}/de_{1}
; this allows to get the main characteristics of stress-strain curves. Then one
analyses the data using the theory of dynamical systems which allows to analyse
the trajectories in the (q,v,p’) state.

Chapter 7 proposes a modelling which describes
granular deformation in the quasi static regime in the small deformation range;
it is based on plastic behaviour modelled through an isotropic incremental law
at small deformation, then the plasticity theory with a single mechanism shall
be applied at larger deformation. The small-strain modelling uses the Rowe’s
law; this fixes the pseudo Poisson coefficient. Using this modelling one
describe the stress ratio in oedometric test and the main trend for an
undrained test. It allows also to understand cyclic behaviour: liquefaction,
compaction and loosening.

The last chapter (ch 8) proposes a view on
statistical mechanics of granular materials from their microscopic properties,
and their link with macrocopic quantities. Applying a principle of maximum
disorder, the contact force distribution is found, and the distribution of pore
size too; the compaction model of Boutreux and de Gennes for the tap-tap is
recalled; and is used to propose a theory that explains the e-log(p) law ; it is also used to predict densification and
expansion due to cyclic loading in quasi-statics.

*poudres
& grains* **NS 1**, 1-56 (décembre
2000)