Geology Reference
In-Depth Information
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Fig. 7.1 Depicting how an array of spheres can undergo macroscopic shape change by exchange
of neighbours
the origin of which may conveniently be chosen to coincide with the representative
point of one of the granules. However, this description will differ from that for a
continuous medium, familiar in the classical theories of elasticity and plasticity,
because the constraints of continuity, whereby neighbouring points remain
neighbouring, no longer apply. Indeed, it is an essential part of the mechanics of a
granular material that granules can change neighbours in the course of the
deformation.
The practical description of the relative translations of granules thus firstly
involves the question of the scale of the local heterogeneity of movement leading
to neighbour exchange. At the macroscopic scale the pattern of relative grain
translations will be statistically homogeneous, more or less by definition, but this
statistical aspect of the pattern contains little information about the local hetero-
geneities that essentially characterize the granular flow mechanism. The latter
involves the individual relative translations of the granules. Thus a question that
arises in relation to the description of the mechanism is how large a sample or
elementary representative group of granules is required to define the essentials of
the mechanism, the macroscopic strain being obtainable from the averaging of the
deformations of these groups
In choosing an elementary representative group of granules it is necessary to
take into account that the movement pattern may be continually changing. At any
instant, relative movement of granules may be concentrated in certain locations,
and these locations may change from one instant to another. Such a situation does
not readily lend itself to very neat analysis. However, two aspects of the behaviour
can be brought out by considering specific model situations, as follows:
(1) Neighbour-exchange aspect. The essential character of a neighbour-exchange
process is illustrated in the notional, two-dimensional model of Fig.
7.1
; here,
grains 1 and 3 are initially separated by grain 2 but become immediate
neighbours through the deformation, while grains 1 and 4 become separated.
Since the relative translations to the new configuration are shown in the figure
as occurring as directly as possible, it is evident that the amount of strain
required for completion of a neighbour exchange is quite large, of the order of
at least 0.3-0.4 natural strain (cf. Ashby and Verrall
1973
). Thus deformation
to fairly large strains is required in the observation and study of the neighbour-
exchange process.
