Geology Reference
In-Depth Information
behaviour therefore needs to be an important part of theoretical studies, as well as
the role of pore fluid pressure.
7.2.4 Cohesive Granular Flow
We now return to the consideration of granular flows in which the granules are
envisaged as remaining intact during flow, but consider the situation in which the
resistance to relative movement of granules includes a component other than the
simple Amonton-type friction at contacts considered in
Sect. 7.2.2
. Two cases
might be distinguished in respect of the source of the additional resistance.
In the first case there may be a cohesive interaction between the granules at their
contacts. Such a type of interaction could arise from the presence of an intergranular
film having finite shearing strength or viscosity, from electrical interactions
between charged particles (especially important in clays), from long-range surface
forces such as those studied by Israelischvili and coworkers (Israelachvili
1992
),
or from surface energy effects associated with variation in areas of interfacial
contacts.
In the second case, there may be a finite shearing strength in the intergranular
phase, which has to be overcome in accommodating the intergranular movements.
A sandy sediment with a clay interstitial filling would be an example of such a
case.
In the absence of a well-developed physical theory of the mechanism of pure
particulate flow (
Sect. 7.2.2
), little can be added theoretically concerning the
cohesive case. The simplest theoretical step would presumably be to replace the
intergranular friction law F
t
¼
lF
n
by one of a form such as
F
t
¼
F
0
þ
lF
n
ð
7
:
5
Þ
(Jaeger
1959
), where F
t
;
F
n
are the tangential and normal intergranular forces,
respectively, and F
0
and l (
¼
tan /
l
) are material constants. It will be noted that
the friction law (
7.5
) is formally equivalent to the Coulomb failure law
s
¼
s
0
þ
r tan /
i
ð
7
:
6
Þ
commonly used to describe the macroscopic behaviour, s
0
and tan /
i
being
macroscopic material constants and s
;
r the shear stress and normal stress,
respectively, acting on a notional plane inclined at p
=
4
/
i
=
2 to the maximum
compressive principal stress; however, in the absence of an adequate theory, the
empirical constants s
0
and tan /
i
cannot be immediately related to the more
physically meaningful constants F
0
and tan /
l
.
Pore fluid pressure would be expected to have an effect through its modification
of the normal forces at intergranular contacts, in which case it should be possible
to use conventional effective stresses again to express the effect, insofar as the pore
fluid is chemically neutral. However, the presence of a pore fluid may also
