Granular Materials in Civil Engineering: Recent Advances in the Physics of Their Mechanical Behavior and Applications to Engineering Works - Multiscale Geomechanics: From Soil to Engineering Projects - page 36

3.1. Behavior resulting from energy dissipation by friction
3.1.1. Introduction
Since Coulomb's historical publication of 1773, many studies have been devoted
to the role of physical friction in the mechanical behavior of granular materials.
However, a direct link between the initial cause - friction at the grain contacts - and
the elements of practical interest concerning behavior at macroscopic scale, such as
the failure criterion or the 3D stress−strain relationship, has not been clearly
established. Significant advances in this direction have been made, such as Rowe's
stress-dilatancy theory (1962), enriched by Horne (1965-1969), and more recent
statistical mechanics approaches. Their conditions of validity, however, which are
limited to the axisymetric loading condition or 2D granular assemblies made of
disks, etc., are too restrictive to be applied to the general case.
The approach presented has a larger scope and brings a solution to more general
3D static problems for granular media made from grains of irregular shape. It gives
access to an explicit expression of numerous macroscopic properties, such as
dilatancy law, failure criterion, strain localization with the internal structure of the
shear bands, orientation and development of failure lines, etc. Only the main results
will be presented here, a more detailed presentation being available in [FRO 01] and
[FRO 04]. The approach is based on statistical physics ruling energy dissipation by
friction, from elementary contact to macroscopic behavior, using an original
mechanical concept of “internal action”, materialized by a tensor formed by the
product of internal forces and internal movements (see Figure 3.2). The first
invariant of this tensor represents the mechanical work rate. This new concept
allows us to:
− reformulate the friction laws in a form that is more functional in order to solve
the mechanical problem;
− link the microscopic scale at grain contact to the macroscopic scale
corresponding to the equivalent continuous medium, using an intermediate scale
corresponding to the discontinuous granular mass.
This multiscale approach has been developed by using the concept of internal
action combined with a rule of minimum dissipation based on the thermodynamics
of dissipative processes. It leads to a wide set of results.