Geology Reference
In-Depth Information
rolling at the contacts plays no significant role. The orientations of the contacts at
which active sliding occurs are chosen so as to minimize the energy dissipation by
friction. With the aid of this assumed principle, a ''stress-dilatancy'' relationship is
derived which, in the case of a triaxial compression test, is of the form
tan
2
4
þ
/
l
r
1
r
3
¼
1
þ
1
v
dv
de
1
p
ð
7
:
3a
Þ
2
tan
2
p
4
þ
/
l
or
r
1
r
3
¼
1
þ
d/
de
1
ð
7
:
3b
Þ
2
where r
1
and r
3
are the axial and radial principal stresses, respectively (com-
pression positive; in case of pore pressure, r
1
and r
3
are taken to be the con-
ventional effective stresses), v is the specimen volume, e
1
the axial strain
(shortening positive), / the porosity, and /
l
the friction angle at the sliding
contacts. Horne (
1965
) proceeds further and relates the dilatancy factor, 1
þ
d/
=
de
1
for the triaxial compression test, to a fabric anisotropy measure which is
viewed as changing in the course of the test and so accounting for the various
stages in a test (initial hardening or softening and subsequent constant volume
stages). However, direct microscopial observations have not been used in testing
the theory. Oda (
1972b
,
1974
) has attempted to combine microscopical fabric
observations with mechanical and he has developed a theory along similar lines to
Rowe and Horne, resulting in an expression analogous to (
7.3a
) but with a fabric
factor in place of the dilatancy factor.
It is interesting to compare the form (
7.3b
) with the purely empirical Coulomb
relationship for a cohesionless material
r
1
r
3
¼
tan
2
p
4
þ
/
i
ð
7
:
4
Þ
2
where /
i
is the angle of internal friction (Paterson and Wong,
2005
, p. 25). It is seen
that /
i
[ /
l
during dilation and /
i
\/
l
during compaction. In soil mechanics
studies situations have often arisen where the observations do not appear to fit the
form (7.3) when the real interparticle coefficient of friction tan /
l
is used and so
another angle /
i
is introduced in place of /
l
(for example Rowe
1972
). However,
although an attempt is made to rationalize such a step in terms of a supposed physical
model, the theory takes on a more or less purely empirical character at this point.
Indeed, at no stage can the Rowe-Horne theory be regarded as one fully based on the
microscopical observation of the flow mechanisms. Although there is reference to
groups of grains sliding relative to each other, there is no recognition of the separation
between the ''chains'' of main load-bearing contacts and the actual sites of sliding
contacts, as revealed in the photoelastic and computer modelling experiments
mentioned earlier, nor is any account taken of the possibly important role of the
rotations of granules or groups of granules. Thus such an approach does not seem to
be very promising from the point of view of further physical insight into mechanisms.
