Geology Reference
In-Depth Information
spacing of the representative points. Further, even if the mean spacing were to
remain constant (steady flow; no macroscopic dilation), there may be local dila-
tions (positive or negative) associated with the local shearing events mentioned
above,
which
would
have
dynamical
implications,
especially
if
a
relatively
incompressible interstitial phase were present.
For some attempts to give quantitative expression to the micro-geometrical or
kinematic aspects of granular material deformation and to relate them to phe-
nomenological theory, see Cambou (
1982
), Nemat-Nasser (
1982
,
1983
), Oda
(
1982
), Satake (
1982
), Cambou (
1993
).
7.1.3 Granule-Granule Relationships at their Boundaries
We now consider the actual geometry of the granules and their contacts rather than
just the locations of the representative points. This geometry involves both the
extension of the granules in space and their orientations (the latter can be defined,
for a given granule, by the orientation relative to external coordinates of two
material line segments intersecting in the representative point).
If two granules are initially in contact over a certain area of granule boundary,
this contact will, in the absence of granule deformation, be preserved during an
increment of aggregate deformation only if the relative translation vector for the
granules is parallel to the contact area, and, in the case of non-spherical granules, if
there is no relative rotation of the granules. Otherwise, the two granules will tend
either to separate at the initially common boundary or to interfere there. In a real
deformation in which three-dimensional connectivity is maintained, these two
tendencies have to be limited in one or more of the following ways:
(1) the establishment of a self-consistent set of relative granule translations that
are as far as possible both instantaneously parallel to the contact surfaces and
yet such as will give rise to the required neighbour exchange.
(2) insofar as the relative granule translations are not parallel to the contact sur-
faces, the maintenance of sufficient granule contact for connectivity and
control of dilatancy through the transfer of material by processes such as
diffusion or fracturing and rearrangement of the fragments; in general cases,
material may be introduced into or removed from the body itself in an
exchange with the environment.
(3) alternatively to (2), the maintenance of connectivity and control of dilatancy
through intragranular deformations; such deformations may become reversed
in subsequent stages of the flow and, in any case, should sum algebraically to
substantially less than the macroscopic strain (otherwise the deformation
The first of these three aspects of the deformation is of a primary nature, being
an essential part of the granular flow process, while the second and third have a
secondary
or
accommodation
role,
meeting
the
connectivity
and
dilatancy
