Geology Reference
In-Depth Information
Since a regular array is too artificial a model to represent fully a real granular
aggregate, it is important also to consider irregular packings and, eventually,
mixed sizes and shapes of granules and the possibility of rolling as well as sliding
at contacts. There are several approaches that may be taken. They include purely
statistical, computer modelling and semi-empirical approaches.
In contrast to the analysis of a regular array, for which a specific description of
the geometrical arrangement of the granules is assumed, in the statistical approach
it is assumed that the granules are randomly arranged, although still being spheres
of equal size in the simplest case. The geometry may be expressed in terms of the
number of contacts on individual granules or of the variation in local porosity
(Feda
1982
,
Sect. 4.3.2
)
. In either case, it can be expected that at least two
parameters will be needed for an adequate description of the array, for example,
the mean porosity and the standard deviation of the local porosity, and so the way
is opened for introducing two geometrical parameters into constitutive relations for
granular aggregates. For further consideration, including the use of the thermo-
dynamics of irreversible processes and observations on arrays of steel balls, see
Feda (
1982
,
Sect. 4.3.2
), Mogami (
1965
,
1969
) and Mogami and Imai (
1967
,
1969
).
There is a total lack of specific information about the behaviour of individual
granules in relation to their neighbours in a statistical model. In contrast, the
situation at each granule in a finite array is available in computer modelling
experiments (Cundall
1986
,
1988a
,
1988b
,
1989
; Cundall, et al.
1982
; Cundall and
Strack
1979a
,
1979b
,
1983
; Hart et al.
1988
; Thornton and Barnes
1986a
). Since
there appears to be a paucity of relevant physical observations on real granular
materials at the microscopic scale, apart from a few studies on photoelastic models
(Allersma
1982
; Drescher
1976
; Drescher and de Josselin de Jong
1972
; Konishi,
et al.
1982
, and earlier references given by them; Oda and Konishi
1974a
,
1974b
),
the computer modelling experiments provide a valuable source of ideas about the
micromechanisms of granular flow, confirming and extending those from the
photoelastic models. The granular material has most commonly been simulated by
arrays of discs (for two dimensions) or spheres (for three dimensions), often of
several sizes and arranged initially in more or less random ways. In the compu-
tation, specific assumptions are made about the nature of the interactions at the
contacts (elastic and/or frictional).
The main conclusions about the mechanisms of pure particulate flow in a
granular material from the model studies are the following:
(1) The forces are mainly transmitted through chains of aligned granules, inclined
at relatively small angles to the maximum compressive principal stress, the
other granules being more lightly loaded (Fig.
7.3
).
(2) The shearing processes are concentrated amongst the lightly loaded granules,
roughly defining domains within which there is less relative movement and
more concentration of forces through chains.
(3) The granules rotate relatively to each other in a fairly coordinated fashion,
thereby minimizing the total amount of frictional sliding and contributing in a
