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Evolution of conductivity of a granular material during compression
T. Chelidze, E. Barbakadze
To cite this version:
T. Chelidze, E. Barbakadze. Evolution of conductivity of a granular material during compression.
Journal de Physique III, EDP Sciences, 1994, 4 (8), pp.1341-1345. �10.1051/jp3:1994206�. �jpa- 00249188�
Classification Phj,.w(..I Ab,iliac.ts
81.40P 81.40R
Evolution of conductivity of a granular material during compression
T. Chelidze and E. Barbakadze
Institute of Geophysics Ac. Sci. Georgia, Rukhadze st. Tbilisi 380093, Georgia
(Receii,ed 9 Jiilj, /992, ret,ised10 May /994, ac.c.opted /8Maj, /994)
Abstract. Evolution of the conductivity increment AG of a granular material during constant rate
loading has been studied experimentally. Nonlinear behaviour of AG has been observed during compression of samples with low humidity. The effect disappears at high humidity.
Properties of a granular material are of considerable interest now both from theoretical [I]
and practical points of view. A recent paper of Nagel [2] (1992) shows that behaviour of such media can differ significantly from predictions of a model based on self-organized criticality.
In this work increments of conductivity AG and displacement At of a granular material (limestone powders) were recorded on a two-coordinate recorder during loading at a constant rate of the sample in piston-cylinder type apparatus for various grain sizes d, loading velocities
u and water content w. The initial value of G has been compensated, so AG and
At plots begin from the origin. The applied voltage for measuring the conductivity was stable
at -30V. Initial specific conductivity of sample at room humidity was of order of
10~~ mho cm~ '.
The results of experiments are shown in figures 1-3. Figure I corresponds to relatively fast
loading (30 kg/min) at room humidity (, 0.I % volume water content in the sample) and various grain sizes. The behaviour of the AG (At )-curve is peculiar : humps of conductivity
with increasing magnitudes develop as the compression mounts up. As the rate of loading was
constant At axis represents a time axis also. The increments of G are practically instantaneous
but decrements are relatively slow. The humps are actually additions to a background growth of AG with compression and after relaxation the curve returns to its main trace (dashed line).
The increments are to be related to abrupt local accumulations of stress at an almost resting piston position. The decrements are due to local stress relaxations which occurs inspite of the advance of the piston. Thus we have transitions similar to those analysed in modern stick-slip theory [4, 5]. We ascribe the G decrements to local strain relaxation because a similar decrease is registered during external unloading of the apparatus ((he unloading moment is marked by
the letter ii on AG/At curves). Figures la and 16 show that the smaller the grain size the less is the magnitude of humps.
1342 JOURNAL DE PHYSIQUE III N° 8
At 1el.m.
~
,
3 /
2 a
AG
At
3
2 b
i
AG
At
u 3
2
c
~ AG
Ail
3 ~
~~
l~ d
0
0 2 3 4 5 6 AG ret.un.
Fig. I. Evolution of conductivity of a granular material (limestone powder) under compression.
AG and At
are accordingly conductivity and piston displacement increments in relative units.
u, =
0. % vol. Scales :.i-axis 25 mV/division, y-axis 5V/division. Loading rate 30 kg/min. Mean
grain size a) 2.5 mm b) 1.6 mm cl 1.0 mm ; d) 0.3 mm.
Similar results are obtained for relatively slow (12 kg/min) loading at room humidity. The
only difference that now the smallest particles also demonstrate humps (Fig. 2).
At
j a
~
AG
At
2
AG At
2
~
o ~~
At U
3
d i
2 3 4 5 6 AG reLun.
Fig. 2.- Evolution of conductivity of granular material (limestone powder) under compression.
w, =
0.I % vol. The notations are the same as in figure I. Loading rate 12 kg/min.
Saturation of the sample with up to lo % (by volume) of tap water practically kills the effect for all grain sizes and both loading velocities (Fig. 3). We presume therefore that sufficiently high saturation with liquid prevents any significant local stress accumulation.
Thus the effect can be observed only for special friction conditions on grain surfaces.
1344 JOURNAL DE PHYSIQUE III N° 8
At
3
2
~0 2 3 4 5 AGmI.un.
Fig. 3. Evolution of conductivity of granular material at (partial) water saturation. w.
=
10 % vol.
Scales : >-axis 25 V/division, y-axis 5V/division. Loading rate 30kg/min. Mean grain size II 0.3 mm ; 2) 0.63 mm ; 3) 2.5 mm 4) DA mm.
The statistics of humps is not very representative but it seems that a log-log dependence of
total number jjN of humps with magnitude A ~Ao versus magnitude A (Fig. 4) follows a
power law :
jjN~A~~
with D
m 0.84.
logiN
i-s
1.0
o-s
0
1-O
enhancement (conductivity increment). Their destruction causes local stress relaxation
(conductivity decrement). Destruction of domes can be considered as an analog of triggering of
avalanchis in the sand-pile model. The critical parameter in
our case is pressure.
An analytical interpretation of the effect is ambigous. Depending on experimental conditions, the friction process can be stable (Fig. 3), periodically oscillating (stable stick-slip)
or chaotic [4]. In addition there are self-organized criticality and first order phase transition models which also describe collective displacement effects in granular media (sandpile model) [5]. To choose the right model a detailed study of the described effect is needed. The
suggested technique can be more informative for theoretical analysis of the evolution of a
granular media because unlike sand-pile experiments it allows one to monitor variations of a wide range of physical properties in various experimental conditions.
References
[1] Bak P., Tang C. and Wisenfeld K., Self-organized criticality, Phys. Ret>. A 38 (1988) 364-374.
(2] Nagel S. R., Instabilities in a sand, Re». Mod. Ph_v.I. 64 (1992) 321-325.
[3] Edwards E., Oakeshott R. S. B., The transmission of stress in aggregates, Fractals in Physics, J. Feder, A. Aharony Eds. (1990) pp. 88-92.
[4] Gu J. C.. Rice J. R., Ruina A. L. and Tse S. k.. Slip motion and stability of
a single degree freedom elastic system, J. Mech. Phy.I. Sol. 32 (1984) 167-196.
[5] Rabinowicz E., Friction and wear of materials IN. Y., Wiley, 1965).
