Geology Reference
In-Depth Information
being large compared with atomic dimensions; their scale may still be such as
would require microscopical observation.
For the sake of simplicity, discussion will, in general, be restricted to materials
containing only one kind of solid granule. However, the granules will often not
fully occupy the total volume of the material. In this case the granular material can
generally be considered as consisting of two ''phases'' of extremely or even
infinitely contrasting strength. The granules themselves will constitute the strong
phase and the interstitial medium between them will constitute the weak phase,
which may be just void space or a fluid or even a relatively weak solid. In order to
define the granular material as a solid in the macroscopic sense, it is then necessary
that there be three-dimensional connectivity through the contacts between the
grains of the strong phase. Indeed, the distinction between a suspension and a
granular solid may be expressed in terms of the existence of such a continuous
''skeleton'' of granular contacts through which shear stress is supported. However,
the volume fraction of the granular phase may vary widely, from as low as 0.2 in
unconsolidated sediments (Hamilton
1976
) to unity in fully dense polycrystalline
materials; that is, the porosity, defined as the volume fraction of interstices, may
vary from around 0.8 to zero.
In the following subsections we shall attempt to set out a suitable kinematical
framework in terms of which to discuss the mechanisms of granular flow and the
factors that determine the dynamics of the flow. It will be useful to distinguish two
aspects of the kinematics, as follows:
(1) the pattern of relative grain translations that eventually determine the mac-
roscopic strains
(2) the questions concerned with the extension and boundaries of the grains,
involving the overlaps or gaps that tend to develop and the rotations of the
grains.
The main emphasis here is on the physics rather than the quantitative theory
which is, in any case, still not well developed.
7.1.2 The Pattern of Relative Translations of Granules
In this first aspect of the kinematics we consider the relative movement of a
granule viewed as a featureless entity of undefined volumetric extent. That is, in
place of the real granule we consider only a representative point within it, and so,
of the total geometry of the granular assemblage, only the arrangement of the
representative points is at first taken into account. The only constraint that need
be placed on the choice of the representative point is that it fall within a part of the
original granule that persists as such during the deformation increment under
consideration (it may be helpful at times to think of it as the centroid of the
granule). The relative motions of the granules can then be described in terms of the
displacements of the representative points relative to a set of external coordinates,
