Geoscience Reference
In-Depth Information
4.11.3 Conditions for a stationary aggregate to
shear and/or flow
The minimum possible solid concentration,
C
0.52, is
for cubic packing (
/6) and the maximum, 0.74, is for
rhombohedral packing ( ). In practice, as
Reynolds pointed out, natural solid concentration varies
widely, but always between our upper and lower limits.
Both
C
and
P
are obviously important properties of
natural granular aggregates like sediment and sedimentary
rock. They control the ability of such aggregates to hold
fluid in their pore space, be it water in aquifers, hydro-
carbons in reservoirs, or magma melt in the crust or man-
tle. Also, the size of the pores has an important control
over rate of fluid throughflow, termed
permeability
(Sections 4.13 and 6.7).
1
2 ·
3
There is only one force, gravity, that can cause the self pro-
pelled flow of grain aggregates. This may at first seem
strange because it is gravity after all that is keeping the
grain aggregate stable, by pulling each grain downward
toward its neighbors (Fig. 4.59). But, in an experiment
where we suddenly free an aggregate from a container or
containing medium, the grains flow outward, shearing,
colliding, and bouncing as they do so. So, it seems that
the aggregate as a whole has no apparent resistance to
shear! But is this not the characteristic of a fluid? How can
(a)
(b)
(c)
m
= mass of grains
b
<
b
crit
b
>
b
crit
b
= 0
−
t
−
t
t
t
normal
stress,
normal
stress,
b
b
s
=
mg
cos
b
s
=
mg
cos
b
b
b
normal
stress,
s
=
shear stress,
t
=
mg
sin
b
shear stress,
t
=
mg
sin
b
mg
mg
mg
At equilibrium,
t
/
s
=
tan
b
Fig. 4.59
Conditions for grain shear. (a) Grains on a horizontal surface, (b) grains on a slope just prior to granular flow, and (c) grains shearing
on a slope during granular flow.
Granular fluids
Fig. 4.60
A random initial mixture of larger sugar crystals (dark) and glass beads from a reservoir has avalanched down a 45
slope,
spontaneously segregating and stratifying during transport.
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