ANISOTROPY F.

Z.

IN THE ELECTRICAL

CONDUCTIVITY

OF COAL UDC 622.33 + 622.23. 02

Krasnovskii

Coal, like some other sedimentary rocks, has a l a m e l l a r structure and its physical properties are anisotropic. Its strength is a m i n i m u m along the stratification and a m a x i m u m perpendicular to it. The strengths in other d i r e c tions can be c a l c u l a t e d from the formulas in [1-8]. The l a m e U a r structures of coals are a consequence of their v e g e t a b l e origin and of the tectonic processes which caused carbonification of the organic mass of plants with increase of the content of carbon and a rise in the C : H ratio [4]. Figure 1 shows the positions of free carbon atoms in c o a l in the form of plane a t o m i c networks, according to D. P. Ivanov. Thus coal, as well as anisotropic m e c h a n i c a l properties, should also possess anisotropic e l e c t r i c a l conductivity because the v a l e n c e bonds between the carbon atoms in a monolayer are stronger than those between monolayers. With this system of bonds, movement of electrons parallel to the monolayers will m e e t less resistance than perpendicular to them. This structural feature of e l e m e n t a r y carbon m a y evidently also be responsible for the strength anisotropy. On this basis we can assume that the e l e c t r i c a l conductivity in coals in various directions m a y be given by a formula analogous to that for the compressive strengths in various directions, as r e c o m m e n d e d in [1]:

P" =

'[

14

Ap Px

Ap Ap + m4 ......

Py

A, ]Kp ' + n 4 .... p~

(1)

where Pu is the resistivity of the c o a l in the direction given by direction cosines l, m, and n; Px, Py, and Pz are the resistivities in the directions of the coordinate axes, of which Px and Pz are p a r a l l e l to the stratification, and py is perpendicular to it, Ap = p~ Py m" Pz n' ; and Kp is an exponent equal to a quarter the v a l u e of p when l = m = n. As in the definitions of the elastic constants, we can assume that Px = Pz and that py is independent of n, and that n = 0, Then (1) becomes somewhat simpler:

Ap PU

14 Ap Px

+ m~ Ap ]Kp

(2)

P.v

and can be c h e c k e d experimentally. The exponent Kp is d e t e r m i n e d at ~ = 45 ~ where cx is the angle between the working face of the specimen and the plane of the stratification. The existence of e l e c t r i c a l and strength anisotropy in coals has been c h e c k e d e x p e r i m e n t a l l y in the TPI Mining Machines Laboratory in a large number of experiments in which the strength and e l e c t r i c a l properties of coal specimens were studied simultaneously in various directions.

TsNIGRL Tula. Translated from F i z i k o - T e k h n i c h e s k i e Problemy Razrabotki Poleznykh Iskopaemykh, No. 1, pp. 118-121, January-February, 1970. Original a r t i c l e submitted August 19, 1968.

@1970 Consultants Bureau, a d i v i s i o n o f Plenum P u b l i s h i n g Corporation, 227 West 17th Street, N e w York, N. Y. 10011. A l l rights reserved. This article cannot be reproduced for any purpose w h a t s o e v e r without p e r m i s s i o n o f the publisher. A copy o f this article is available from the p u b l i s h e r for $15.00.

i00

/ / / / / / 4 /

Monolayer 3

Monolayer 1 /

Sr)~l:im~la. ..I // ,, .f

.4

-//

,'x\~\\,,,

IP=/~176l~oh~ Monolayer 2

l_m~

Fig. 1

Hg. 2

2,~'cr

62, k g / c m 2

s.,o4~..~

/ ~,exp

s.,0%

~. r ~

62. 4404] %~/I meor

'~x~.

-,5 " I --'-~'-'=" "-so

th~or

2"~~

:~oo

x

.

"

~.~o~1

o4os,

J ~176

2~t~

[225~ o o o~ 180~ 1

o

-25 oe

o,,r

0

0~

75"

30

45

60

75

Fig. 3

~2

5000 fl

UM -2 Hg. 4

5r

e700,a -. .g_ _g.i_&

90 o~~

a

After some experiments to develop the method, we carried out e x periments to study the e l e c t r i c a l conductivity in various cRrections r e l a tive to the plane of the stratification on specimens 50 x 80 x 120 m m in size, in which the working faces were at angles a of 0, 15, 30, 45, 60, 75, and 90 ~ to the stratification. We also m a d e c o m b i n e d investigations of the e l e c t r i c a l conductivity and strength on the same specimens, c u b i c a l in shape and 50 m m on a side, with the same w o r k i n g - f a c e orientations r e l a t i v e to the stratification, and used various methods to measure the e l e c t r i c a l conductivity on one large specimen in various directions r e l a t i v e to the stratification.

Fig. 5

The specimens were prepared from coals of the Moscow c o a l field. The e x p e r i m e n t a l e q m p m e n t consisted of hydraulic presses of various types fitted with standard manometers c a l i b r a t e d against a DS-5 d y n a m o m e t e r and electrodes formed by m e t a l frames with pads soaked in KC1 solution so as to m a k e good liquid contact with the ends of the specimens. The resistances were measured by means of a Tt-2 o h m m e t e r at a pressure of 100 kg. The e x p e r i m e n t a l arrangement is shown in Fig. 2. One experiment was performed with dry brass disk contacts to which the ends of the specimens were carefully ground. The resistance was measured by means of a UM-2 universal bridge at a %rce of 100 kg, and the breaking strength was measured by means of a DS-5 dynamometer. The e x p e r i m e n t a l results were processed by the method r e c o m m e n d e d in [5]. The resistivities found e x p e r i m e n t a l l y for a = 0, 45, and 90 ~ were substituted in (2), and thus we c a l c u l a t e d the t h e o r e t i c a l values of the resistivity for i n t e r m e d i a t e angles; the data obtained were c o m p a r e d with the e x p e r i m e n t a l results for the same i n t e r m e d i a t e angles. From the e x p e r i m e n t a l and t h e o r e t i c a l results (Pig. 3) we can draw the following conclusions. Coals have anisotropic e l e c t r i c a l conductivity with symmetry analogous to the plane elastic symmetry. The e l e c t r i c a l c o n d u c t i v i t y is a m a x i m u m perpendicular to the stratification and a m i n i m u m parallel to it. There is a correlation b e -

101

tween the e l e c t r i c a I and strength properties which is e v i d e n t l y due to their general nature. This relation can be e x pressed by correlation coefficients which r e m a i n stable over most of the curves: thus we can find the elastic c o n stants in any direction from the known strength in one direction and the known e l e c t r i c a l resistivities in this and two other directions. The relation between the e l a s t i c constants and the angle of measurement r e l a t i v e to the plane of the stratification is represented by a formula o f type (2) to an accuracy adequate for engineering purposes. When an analogy had been demonstrated between the e l e c t r i c a l resistivity and the m e c h a n i c a l properties, it was necessary to determine the e l e c t r i c a l resistivity directly in the solid coal, because it is difficult to find the m e c h a n i c a l properties under these conditions. For this purpose we measured the resistance with the aid of surface electrodes, which were applied to marked points on the surface of the specimen, and the resistance between t h e m was measured. The results were c h e c k e d by means of the formula Ap

[14 AR + m ' A" ' e I,,R / Ry ]

(3)

We found that t h e theoretical and e x p e r i m e n t a l results were in almost c o m p l e t e agreement. The resistivity curves R = / ( ~ ) and p = f ( ~ ) in these experiments had falling parts from 0 to 60 ~ and were very fiat from 60 to 90 ~, i . e . , where the compressive strengths were m i n i m a l . This enables us to find the direction of least resistance to m e c h a n i c a l fracture with fair accuracy from only one measurement of ohmic resistance. We measured the resistance with the aid of electrodes which were driven into the c o a l like a punch. The r e sistance between t h e m was measured with a UM-2 bridge. The e x p e r i m e n t a l arrangement is shown in Fig. 4 and the remits in Hg. 5 in the form of a polar diagram. The arrows i n d i c a t e the direction of the stratification. Fromthese d a t a w e can find the law of variation of the e l e c t r i c a l resistivity in a c o a l seam with the aid of electrodes driven in at four points - one at the center of an arc of some radius r, and three others on the arc a r ranged so that the radii at the points of installation of the electrodes are at 0, 45, and 90 ~ to the planes of the stratification. The measured resistivities need be c o m p a r e d only with a single compressive strength value, e.g., that perpendicular to the stratification, and having found t h e conversion coefficient we can construct curves of the elastic constants of the coal. Note that we can find the e x t r e m a of (2) and (3) and thus deduce a formula giving the directions of m i n i m u m resistance and m i n i m u m strength of the c o a l from resistance measurements between electrodes driven in at four points. The final formula for the direction of m i n i m u m resistance (notation same as in (3)) is as follows: 12 -

Rx

~-

Ke

R~ + Ry

L (1 - KR)

R2x +

Rx

(Rx+Ry) 2 +

Rx+Ry

(4) +

LU (1 - - K ) '

where L = In ,% -

LITERATURE I. 2.

3. 4. 5.

102

in Ry.

CITED

h i I. Slobodldn, Principles of the A n a l y t i c a l Theory of Coal Cutting gn Russian], Izd. UGTI, Moscow (1947). M, I. Slobodkin, "On determinning the stresses due to a cutting instrument in a c o a l seam," Sb. Trudov MGI, No. 10, Izd. MGI, Moscow (1952) [Symposium of Work from Moscow University]. M. L Slobodkin, "Some t h e o r e t i c a l topics in rock m e c h a n i c s , " Sb. Trudov TMI, No. 12, Ugletekhizdat, Moscow (1958) [Symposium of Work from Tula M e c h a n i c a l Institute]. D. P. Ivanov, "Questions of crystallization of graphite in iron-carbon alloys," in: Wrought Iron [in Russian], Mashgiz, Moscow (1954). Encyclopedic Handbook: Mechanical Engineering [in Russian], Vol. 1, Pt. I, Mashgiz, Moscow (1947).