E. Frossard. Expert,
Bureau d’ingénieursconseils Coyne et Bellier, frossardetienne@aol.com
Abstract: This communication establishes first, that
basis of discontinuous granular materials mechanics, are the explicit result of
a new approach of the physics of energy dissipation by friction, and second,
that these mechanics of discontinua, transposed to the equivalent continuous media,
as used in geomechanics, is directly responsible for a large set of practical
properties of these materials, part of the fundamentals of Soil Mechanics.
These physics of energy dissipation are developped
on the original concept of energy rate tensor of internal actions.
The
communication displays first:

an original tensorial pattern
underlying the well known laws of friction, at the elementary scale of moving
contact;

the macrostructural solution for the
discontinuous granular mass, under general threedimensional movements, as a
result of a tensorial structure associated with the distribution of moving
contacts.
It is shown that the jump from the individual
behaviour (elementary contact) to the collective behaviour (granular mass)
makes appear into the general dissipation equation, a population effect, related
to the intensity of a kind of interaction between moving contacts, the
“internal feedback”(réalimentation interne), and related to the grade of disorder
in the distribution of moving contacts, interaction and disorder
determining the intensity of energy dissipation.
Among
the solutions, appear those of minimal dissipation, associated with ordered
patterns in the distribution of moving contacts orientations: in plane
strain these ordered patterns result precisely into the RANKINE sliplines,
well known in geomechanics.
Concerning
the equivalent continuous media, the communication draws a parallel with a
dissipation equation for the continuum, established an published long ago by
the author, on the basis of physical interpretation of a wide set of
experimental results on these materials. This equation leads analytically to:
 the ROWE “stressdilatancy” relations;
 the COULOMB failure criterion, at critical state;

the densification by cyclical strains,
in certain conditions, and other features of the “characteristic domain”.
The structure of this dissipation equation for the
equivalent continuum, is shown to be formally identical to the general
dissipation equation for the discontinuous granular mass, including the
presence of a particular energy rate tensor of internal actions, build on
stress and strain rate tensors.This identification leads to express the
macroscopic quantities, stress and strain rates,in function of microscopic
variables, contact forces, sliding velocities, and geometry of packing.
It is shown also that experimental results suggest
strongly the presence of a minimum energy principle: according to limit
conditions allowance, the movements into the material tend towards one of the
minimal dissipation solutions.The physical meaning of this principle, is
then related to a key result of the thermodynamicians of irreversible
processes (Prigogine): the theorem of minimum entropy production.
poudres & grains NS 2, 156 (décembre 2001)