On the Study of the Physicomechanical Properties of Certain Bituminous Coal Seams in Kuzbass Mines

V. P. Shubin

Introduction

As a sedimentary organogenic rock, bituminous coal has an amorphous structure and is an anisotropic solid. At the same time, bituminous coal is a solid body possessing great resistance to compressive deformation. Individual seams of bituminous coal possess great cohesion, caused by forces of mutual adhesion; this is the principal distinction of bituminous coal, as a solid body, from metal. As is known, in metals there exists an intercrystalline layer consisting both of atoms of the metal itself and of foreign impurities. Bituminous coal and other rocks belong to brittle bodies, which fully corresponds to their internal structure. However, under certain conditions, bituminous coals and the rocks surrounding them are capable of deformation without obvious destruction, i.e., of plastic deformation.

As far as we know, no systematic study of the plastic deformations of rocks in general, and of bituminous coal in particular, has been carried out to any significant extent, because of the difficulties of experimentation. Bituminous coals and the rocks surrounding them must be assigned to bodies of imperfect density, i.e., to bodies possessing, to a certain degree, both density and porosity. By the density of bituminous coal and other rocks we shall understand the degree to which a given volume of rock is filled with substance. Analytically this is determined by the ratio of volumetric weight to specific weight. Introducing the relative density \(\Delta\), we have:

\[ \Delta = \frac{\gamma}{q}\cdot 100. \]

In addition to the porosity of a bituminous-coal seam and of the rocks surrounding it, we introduce, as an indispensable condition, the presence of fracturing. In this fracturing, stresses are concentrated during the deformation of bituminous coal. It is obvious that the formation of sedimentary bituminous-coal rock took place under very great pressure. Adams and Gibson [1], studying the question of deformation of rocks under high pressure, came, by experiment, to the conclusion that in the earth’s crust, even at a depth of 17 km, small cracks and voids may exist. Cracks and pores, according to their dimensions, are subdivided into visible and hidden, inaccessible to the armed eye. The presence of these cracks lowers the mechanical properties of bituminous coal.

A considerable part of rocks, in particular bituminous coal, does not obey Hooke’s linear law. This deviation from the law of propor-

…tionality is especially noticeable in many igneous rocks, in which the forces of cohesion between crystals or the strength of the cement are less than the strength of the grains themselves. Quartzites, in which the cement has a strength equal to that of the grains, obey Hooke’s law. According to the investigations of Phillips [2], under dynamic application of load, Hooke’s law is valid also for granite and other crystalline granular rocks. According to the investigations of M. V. Klassen-Neklyudova [3], nonobservance of the linear Hooke’s law is generally characteristic of polycrystals.

Bituminous coal, while possessing a sufficiently high compressive strength, has very low tensile strength; moreover, according to our investigations (Table 1), the ratio \(\sigma_{v,\mathrm{tens}}\) to \(\sigma_{v,\mathrm{comp}}\) varies within the following limits (load parallel to the bedding).

Table 1

Name of coal	\(\sigma_{v,\mathrm{tens}}\)	\(\sigma_{v,\mathrm{comp}}\)	\(\dfrac{\sigma_{v,\mathrm{tens}}}{\sigma_{v,\mathrm{comp}}}\), in %
Anzhero-Sudzhensk	6.75	49.4	13.65
Lenin	10.15	47.6	21.3
Prokopyevsk-Kiselevsk	12.5	21.1	5.89
Khakass	10.0	47.0	20.85
Cheremkhovo (Irkutskugol)	11.0	36.6	29.9

Alongside the sufficiently well-studied properties of various rocks, despite the broad development of scientific research work with respect to the fossil coals of the USSR, the latter still remain very little studied from the standpoint of their mechanical properties. As for the mechanical properties of Siberian coals and, in particular, the coals of the Kuznetsk Basin, they have been almost completely unstudied. We have only one work by Engineer P. K. Murzin [4], carried out by him on assignment from the Department of Solid-Fuel Technology of the Siberian Chemical-Technological Institute. Samples of coal from the “Moshchnyi” seam of the Prokopyevsk deposit were subjected to static investigation. In their physical properties, the coals of this seam are characterized by great hardness and relatively high resistance to destruction; they are typical of the coals of the entire Prokopyevsk-Kiselevsk district. For testing, 68 specimens were prepared, of which 64 were tested in compression with determination of the normal modulus of elasticity \(E\) and the proportional limit. The geometrical form of the specimens was a regular prism with dimensions \(25 \times 25 \times 60\) mm. The remaining 4 specimens were cubes measuring \(25 \times 25 \times 25\) mm and were tested to determine the temporary resistance to compression.

Engineer P. K. Murzin carried out the tests on an Amsler machine with a capacity of 2 t, using a Martens mirror device as the extensometer.

All specimens had a height oriented with respect to the bedding, namely: height parallel to the bedding; height perpendicular to the bedding; and height at an angle of \(45^\circ\) to the bedding. The magnitude of the load on the specimen was applied at intervals of 50 kg. According to the graphs obtained by Engineer P. K. Murzin, the relationship between stresses and deformations at stresses of \(100\ \mathrm{kg/cm^2}\) and higher approaches a straight line. Up to a stress of \(100\ \mathrm{kg/cm^2}\), a straight-line relationship is not observed. The experimental data obtained by Engineer P. K. Murzin are presented in Table 2.

Table 2

Orientation of the height of specimens relative to the beds	Temporary resistance, $\sigma_v$, kg/cm²: from–to	Temporary resistance, $\sigma_v$, kg/cm²: average	Modulus $E$, kg/cm²: from–to	Modulus $E$, kg/cm²: average
Perpendicular	258–278	272	30800–35600	32600
Parallel	205–250	226	29900–40800	34600
At 45°	145–206	190	25300–28900	28600

With respect to the mechanical properties of coals from other deposits, we also have very limited information. In the works of Professor L. B. Levenson [5], reference is made to studies carried out in Dnepropetrovsk under the direction of Academician A. I. Dinnik with certain Donbass coals (the “Smolyaninovsky” and “Butovsky” seams) and by engineer Beronovsky—in Leningrad—with Donetsk anthracites. As a result of these studies, values were obtained for coals of the destructive compressive stress and of the modulus of elasticity of the first kind. A. A. Peskovatsky [6] describes these experiments and gives a table of the results obtained (see Table 3). The author points out that these experiments were carried out for the first time in the USSR.

In engineer Beronovsky’s experiments the following was obtained:

\[ \begin{array}{ll} \text{for coal} & \sigma_v = 20\text{–}40\ \text{kg/cm}^2,\\ \text{for anthracite} & \sigma_v = 90\ \text{kg/cm}^2. \end{array} \]

Table 3

Sampling location	Upper bench: $\perp$ to beds $\sigma_v$	Upper bench: $\perp$ to beds $E$	Upper bench: along beds $\sigma_v$	Upper bench: along beds $E$	Upper bench: from the sides $\sigma_v$	Upper bench: from the sides $E$	Lower bench: $\perp$ to beds $\sigma_v$	Lower bench: $\perp$ to beds $E$	Lower bench: along beds $\sigma_v$	Lower bench: along beds $E$	Lower bench: from the sides $\sigma_v$	Lower bench: from the sides $E$, kg/cm²
1. Smolyaninovsky seam, mine 12–18 of the Budenovsky deposit, 7th eastern longwall	17	6700	36	5500	26	6000	48	8500	46	8500	31	12000
2. Butovsky seam, Butovka mine of the Stalin deposit, 16th eastern longwall	—	—	—	—	—	—	—	—	43	18600	47	23000

The author’s notation has been retained in the table. Here $\sigma_v$ is the temporary resistance; $E$ is the modulus of elasticity.

Detailed experiments on testing the strength and elasticity of coal and other rocks were carried out by engineer O. Möller. He indicates that, when coal cubes were tested in compression in a special steel form open only on one side, at a pressure of 100 kg/cm² delamination of the coal was observed parallel to the exposed plane, and at a pressure of 170 kg/cm² complete destruction of the specimen occurred.

When tested by Kármán’s method with all-round compression of the specimens, the following relationship was obtained between the magnitude of the temporary resistance of coal to compression and the magnitude of the lateral pressure (Table 4).

Table 4

Lateral pressure, kg/cm²	0	250	500	750
Compressive strength, kg/cm²	200	1250	1700	1930

From these figures it follows that under all-around compression coal can withstand pressures many times greater than under uniaxial compression. The author further indicates that the following relationship was obtained between pressure and deformation of coal, in percent, under all-around compression (Table 5).

Table 5

Pressure, kg/cm²	200	300	400	500	1000
Deformation, %	0,63	0,83	1,08	1,25	2,22

The value of the modulus of elasticity \(E\), obtained from the same experiments, proved to be:

\[ E = (0{,}24 \div 0{,}557)\,10^{11}. \]

O. Fleischer gives the following data on the temporary resistance of coal to compression (Table 6).

Table 6

Coal	Temporary compressive strength, kg/cm²: from and to	Temporary compressive strength, kg/cm²: average	Modulus of elasticity \(E\), kg/cm²: from and to	Modulus of elasticity \(E\), kg/cm²: average
Bright	156÷386	247	20000÷37200	26520
Banded	174÷385	254	16400÷38100	25648
Dull	216÷390	300	30000÷47500	36449

The relationship between the temporary resistance of coal to compression and the temporary resistance to shear in various directions relative to the bedding was established by Prof. M. M. Protodyakonov [7] in the briquetting laboratory of the Moscow Mining Institute. The following results were obtained by him (Table 7).

Table 7

Deformation	Force parallel to bedding	Force perpendicular to bedding	Force at 45° to bedding
Compression, kg/cm²	88, 130, 188, 220, 224, 262, 288, 318, 396 Average 234	40, 62, 63, 75, 90, 100, 114, 115, 121, 126, 135, 142, 144, 148, 156, 173, 178, 178, 264, 335, 356 Average 151	26, 26, 29, 32, 40, 42, 48, 56, 72, 78 Average 45
Shear, kg/cm²	17,4; 30,8; 40,6; 43,2; 44,4; 62,4. Average 40,2.	15,4; 16,2; 17,8; 20,2; 21,4; 31,4. Average 20,4	20,6

Taking the breaking force in the direction perpendicular to the bedding under compression and shear as 100%, Prof. Protodyakonov gives a comparative table of strength (Table 8).

Table 8

Deformation	Force parallel to bedding, %	Force perpendicular to bedding, %	Force at 45° to bedding, %
Compression	100	65	19
Shear	100	60	33

All of Prof. Protodyakonov’s experiments were carried out with coal taken from the MMI boiler room, from a seam and deposit unknown. This, to some extent, reduces the value of the conclusions obtained.

Of very substantial importance in the theory of percussive perforator drilling is the question of the coefficient of friction of coal on steel and coal on coal. Prof. M. M. Protodyakonov [7] gives a number of values for the coefficients of friction of coal on steel. Thus, according to Prof. P. S. Kuzmin [8], the values of the coefficients of friction of coal on steel are:

\[ \begin{aligned} \text{anthracite} \qquad & f_{\partial v}=0.29 \\ \text{resinous coal} \qquad & f_{\partial v}=0.32 . \end{aligned} \]

According to Prof. A. S. Ilyichev [9], the coefficient of friction of coal on steel in motion and at rest has the following value (Table 9).

Table 9

Source	\(f\) at rest	\(f\) in motion
According to Sklénar	0.4–0.5	0.35
According to Marcus	0.5	0.2
According to Kuprer	0.4	0.3
According to L. B. Levenson for Moscow Region coal	0.42–0.63	—

Eng. V. A. Mirov [10] gives the following data on the coefficient of friction at rest and in motion of coal on iron (Table 10).

Table 10

Source	Coal grade	\(f\) at rest	\(f\) in motion
According to A. N. Dinnik and G. A. Skuratov	anthracite	0.84	0.29
According to A. N. Dinnik and G. A. Skuratov	brown coal	1.00	0.58
According to A. N. Dinnik and G. A. Skuratov	fine coal	0.84	0.32
According to A. N. Dinnik and G. A. Skuratov	resinous coal	0.84	0.32
According to E. F. Meller	anthracite	0.24–0.3	—
According to E. F. Meller	coal	0.35–0.6	—

The value of \(f_{\text{motion}}\), according to E. F. Meller, may be taken as

\[ f_{\text{motion}} = 0.75 f_{\text{rest}} . \]

Prof. V. I. Belov [11] takes \(f_{\text{motion}}=0.4\) for coal.

Finally, Prof. M. M. Protodyakonov [7] conducted a series of experiments on coal using an apparatus he had designed. In doing so, he determined the value of the coefficient of sliding friction under various loads from 5 to 30 kg. He obtained highly varied values without any regularities. Table 11 gives the average values from 5 measurements at each load.

Table 11

Seam	Coefficient of friction at load (kg): 5	10	15	20	25	30	Average
Fominsky	0,07	0,07	0,10	0,11	0,11	0,10	0,10
Removsky	0,04	0,12	0,17	0,17	0,14	0,13	0,13
Maidanovsky	0,13	0,19	0,19	0,17	0,17	0,11	0,16
Khrustalny	0,26	0,13	0,16	0,19	0,18	0,17	0,18

Doctor of Technical Sciences, Prof. V. M. Ogievsky [12] gives the thermal parameters of a number of rocks, including bituminous coal. The determination of the thermal conductivity and thermal diffusivity of rocks was carried out under laboratory conditions by the method of cooling the tested specimens in an aerodynamic tube with a forced air flow. The accuracy of determination varied within the following limits:

for thermal conductivity	5–8%
for thermal diffusivity	3–5%
for specific heat capacity	4–6%

In Table 12 we give the data relating only to coal.

Table 12

No.	Rock types	Bulk weight	Thermal parameters: heat capacity \(a\)	Thermal parameters: thermal diffusivity	Thermal parameters: thermal conductivity
1	Brown coal of the Chelyabinsk deposit	1210	0,270	6,65	0,218
2	Brown coal of the Korkino deposit	1202	0,273	6,59	0,216
3	Bituminous coal of the Karaganda deposit	1275	0,252	7,15	0,230
4	Bituminous coal of the Kizel deposit	1346	0,244	7,18	0,238
5	Anthracite of the Egorshino deposit	1410	0,226	8,64	0,282

Here

\[ a=\frac{\lambda}{c\gamma}; \]

where \(a\) is the coefficient of thermal diffusivity;

\[ \lambda \]

is the coefficient of thermal conductivity;

\(c\) is the specific heat capacity;

\(\gamma\) is the bulk weight (density).

Prof. V. M. Ogievsky established that the temperature parameters are affected by the porosity of rocks: the greater it is, the lower the thermal conductivity.

and thermal diffusivity, and vice versa. Moisture content is also of great importance; with an increase in moisture content, the thermal conductivity of rocks increases.

The question of the hardness of bituminous coals has been developed extremely poorly. We have at our disposal only one work devoted to this problem [13]. In this work the hardness of the principal types of coal near Moscow was determined using Shor’s scleroscope. The results are given in Table 13.

Table 13

Name of coals	Shor hardness, minimum	Shor hardness, maximum	Shor hardness, average
Sapropelites
Bogheads	45	60	53
Semi-bogheads	35.5	49.1	40.5
Humites
Semilustrous	31.1	37.3	35.2
Semidull humic
Homogeneous	32.1	40.0	35.97
Striated	32.3	37.4	34.24
Banded	32.5	36.1	34.6
Layered	31.1	34.9	33.65
Dull
Homogeneous	23.2	32.9	27.7
Striated	24.7	35.2	29.06
Banded	26.5	33.0	30.1
Layered	26.9	31.8	29.2

In concluding the review, it is necessary to point out the method proposed by A. V. Yatsenko [14] for determining the strength of coal by prying it out of the face with a special lever apparatus (author’s certificate No. 127242, 5/VI—34). The prying is carried out with the short arm of a lever, which is inserted into a borehole drilled at 45° to the coal surface. The author proposes taking, as an index of coal strength, the force in kilograms per 1 cm of the line of least resistance when the face plane is perpendicular to the direction of cleavage and the apparatus is installed perpendicular to the plane of bedding of the seam. Unfortunately, there are no experimental data in the article. Nor are such data available, in general, in any of the works.

Summing up all that has been set forth above, one may conclude that the question of investigating the physicomechanical properties of bituminous coal is in an embryonic state. The most varied values available for one or another index do not make it possible to make any generalization for the purpose of using them in the practice of calculating and designing percussion drilling machines. Moreover, for a number of characteristics of the properties of bituminous coal—such as hardness, plasticity, elasticity, Poisson’s ratio, relaxation properties, and shear modulus—there are no data at all.

The bituminous-coal seams of the mines of the Kuznetsk Basin, in this respect, appear to be completely uninvestigated. All this gives us grounds to undertake a series of experimental studies on bituminous coals

Kuzbass. We set ourselves the task of determining the following physicomechanical properties of bituminous coal:

1. The temporary tensile strength of coal.
2. The temporary compressive strength of coal.
3. The temporary shear strength of coal.
4. The modulus of normal elasticity \(E\) in compression.
5. The value of Poisson’s ratio \(\mu\).
6. The relationship between the strength limits for different deformations.
7. The temporary torsional strength of coal.
8. The shear modulus \(G\) in torsion.
9. The plastic properties of bituminous coal and its relaxation qualities.
10. The coefficient of friction of coal on steel and of coal on coal.
11. The hardness of coal—static and dynamic.

For this purpose we investigated coals from the Kuznetsk Basin:

Anzhero-Sudzhensk district,
Leninsk district,
Prokopyevsk-Kiselevsk district,
Khakass.

In addition, we had at our disposal Cheremkhovo bituminous coal.

All experimental work was carried out in the laboratory of the Department of Strength of Materials of the Tomsk Polytechnic Institute named after S. M. Kirov. Below we present the data of our investigations with a detailed description of the method by which the work was carried out. All the experimental numerical material is given in the protocol section of the work.

Temporary Tensile Strength of Kuzbass Coals

To determine the ultimate tensile strength of coals, we prepared specimens having the dimensions: \(a = 60\) mm; \(b = 20\) mm; \(l = 200\) mm. The scheme of the specimens is shown in Fig. 1. The tests were carried out on an Amsler system machine with a capacity of 2000 kg. In view of the fact that bituminous coal, under tensile deformation, fractures in a brittle manner, it is not possible to determine the values of the modulus of normal elasticity and the proportionality limit. For this reason we confined ourselves to determining only the ultimate strength and, solely for the purpose of comparing the strength of coals, the compressive resistance and tensile resistance. The results of the tests are summarized in Table 14.

Fig. 1

Comparing the values of \(\sigma_{b}\) in tension with the value of \(\sigma_{b}\) in compression, one may conclude that bituminous coals from all deposits of Kuzbass have a very insignificant tensile resistance.

(force perpendicular to bedding)

Table 14

Coal	Specimen No.	Specimen dimensions, cm: \(a\)	Specimen dimensions, cm: \(b\)	Specimen dimensions, cm: \(l\)	Cross-sectional area \(F\), cm²	Breaking force \(P\), kg	\(\sigma_v\), kg/cm²	Average \(\sigma_v\)
Anzhero-Sudzhensk	1	6.0	2.0	2.0	12	74.0	6.2	6.75
Anzhero-Sudzhensk	2	—	—	—	12	87.0	7.3	6.75
Leninsky	1	—	—	—	12	126.0	10.5	10.15
Leninsky	2	—	—	—	12	118.0	9.8	10.15
Prokopyevsky	1	—	—	—	12	146.0	12.2	12.5
Prokopyevsky	2	—	—	—	12	153.0	12.8	12.5
Khakassky	1	—	—	—	12	120.0	9.9	10.0
Khakassky	2	—	—	—	12	121.0	10.1	10.0
Cheremkhovsky	1	—	—	—	12	136.0	11.4	11.0
Cheremkhovsky	2	—	—	—	12	127.0	10.6	11.0

(force perpendicular to bedding)

Table 15

Coal	\(\sigma_v\) in tension	\(\sigma_v\) in compression	\(\dfrac{\sigma_v \text{ in tension}}{\sigma_v \text{ in compression}}\)
Anzhero-Sudzhensk	6.75	49.4	13.65
Leninsky	10.15	47.6	21.3
Prokopyevsky	12.5	212.1	5.89
Khakassky	10.0	47.9	20.85
Cheremkhovsky	11.0	36.6	29.9

Testing Kuzbass Coals for Compressive Deformation

In the mechanical laboratory of the Department of Strength of Materials of the Tomsk Polytechnic Institute, specimens were prepared from the coals obtained by us for testing them in compression. All specimens accepted for testing had the dimensions of cubes \(25 \times 25 \times 25\) mm. It should be noted that it was very difficult to achieve exact dimensions, owing to which, in some specimens, deviations in one direction or the other within the limits of \(1 \div 2\) mm were observed. The calculation of the strength limit of such specimens was processed by recalculation for the case of a cube with dimensions \(25 \times 25 \times 25\) mm.

Table 16

Determination of the ultimate compressive strength of coal

Mine	Sample No.	Specimen dimension \(b\), mm	Specimen dimension \(a\), mm	Specimen dimension \(h\), mm	Cross-sectional area	Breaking load \(P\), kg	Parallel to bedding \(\sigma_b\)	Parallel to bedding, mean	Perpendicular to bedding \(\sigma_b\)	Perpendicular to bedding, mean	At an angle of 45° \(\sigma_b\)	At an angle of 45°, mean
Anzhero-Sudzhensk	1	25	25	25	6.25	400	64		—		—
Anzhero-Sudzhensk	2	25	25	25	6.25	340	54.4		—		—
Anzhero-Sudzhensk	3	25	25	25	6.25	200	32.0		—		—
Anzhero-Sudzhensk	4	25	25	25	6.25	181	28.9		—		—
Anzhero-Sudzhensk	5	25	25	25	6.25	457	73.1		—		—
Anzhero-Sudzhensk	6	25	25	25	6.25	260	41.6	49.4	—		—
Anzhero-Sudzhensk	7	25	25	25	6.25	395	63.2		—		—
Anzhero-Sudzhensk	8	25	25	25	6.25	255	41.3		—		—
Anzhero-Sudzhensk	9	25	25	25	6.25	400	64.0		—		—
Anzhero-Sudzhensk	10	25	25	25	6.25	336	53.8		—		—
Anzhero-Sudzhensk	11	25	25	25	6.25	195	31.2		—		—
Anzhero-Sudzhensk	12	25	25	25	6.25	283	46.9		—		—
Anzhero-Sudzhensk	1	25	25	25	6.25	600	—		96
Anzhero-Sudzhensk	2	25	25	25	6.25	317	—		50.7
Anzhero-Sudzhensk	3	25	25	25	6.25	475	—		77.0
Anzhero-Sudzhensk	4	25	25	25	6.25	630	—		101.0
Anzhero-Sudzhensk	5	25	25	25	6.25	570	—		91.3
Anzhero-Sudzhensk	6	25	25	25	6.25	342	—		55.0	75.6
Anzhero-Sudzhensk	7	25	25	25	6.25	325	—		52.1
Anzhero-Sudzhensk	8	25	25	25	6.25	454	—		72.7
Anzhero-Sudzhensk	9	25	25	25	6.25	508	—		81.4
Anzhero-Sudzhensk	10	25	25	25	6.25	600	—		96.1
Anzhero-Sudzhensk	11	25	25	25	6.25	348	—		55.7
Anzhero-Sudzhensk	12	25	25	25	6.25	492	—		78.6
Anzhero-Sudzhensk	1	25	25	25	6.25	289	—		—		46.2
Anzhero-Sudzhensk	2	25	25	25	6.25	226	—		—		36.2
Anzhero-Sudzhensk	3	25	25	25	6.25	195	—		—		31.3	38.1
Anzhero-Sudzhensk	4	25	25	25	6.25	280	—		—		44.8
Anzhero-Sudzhensk	5	25	25	25	6.25	203	—		—		32.5
Leninsk	1	25	25	25	6.25	391	62.5
Leninsk	2	25	25	25	6.25	318	50.9
Leninsk	3	25	25	25	6.25	222	35.6
Leninsk	4	25	25	25	6.25	437	70.0
Leninsk	5	25	25	25	6.25	320	51.2
Leninsk	6	25	25	25	6.25	210	33.6	47.6
Leninsk	7	25	25	25	6.25	250	40.0
Leninsk	8	25	25	25	6.25	243	38.9
Leninsk	9	25	25	25	6.25	315	50.4
Leninsk	10	25	25	25	6.25	276	44.2
Leninsk	11	25	25	25	6.25	292	46.7
Leninsk	12	25	25	25	6.25	300	48.1

1	2	3	4	5	6	7	8	9	10	11	12	13
Leninsky	1	25	25	25	6,25	565	—	—	90,6	103.8
Leninsky	2	25	25	25	6,25	785	—	—	125,5	103.8
Leninsky	3	25	25	25	6,25	957	—	—	153,1	103.8
Leninsky	4	25	25	25	6,25	771	—	—	123,5	103.8
Leninsky	5	25	25	25	6,25	760	—	—	121,8	103.8
Leninsky	6	25	25	25	6,25	500	—	—	80,0	103.8
Leninsky	7	25	25	25	6,25	496	—	—	77,5	103.8
Leninsky	8	25	25	25	6,25	580	—	—	92,8	103.8
Leninsky	9	25	25	25	6,25	632	—	—	101,0	103.8
Leninsky	10	25	25	25	6,25	715	—	—	114,2	103.8
Leninsky	11	25	25	25	6,25	560	—	—	89,6	103.8
Leninsky	12	25	25	25	6,25	500	—	—	80,1	103.8
Leninsky	1	25	25	25	6,25	250	—	—	—	—	40,1	53,0
Leninsky	2	25	25	25	6,25	280	—	—	—	—	44,7	53,0
Leninsky	3	25	25	25	6,25	356	—	—	—	—	53,0	53,0
Leninsky	4	25	25	25	6,25	392	—	—	—	—	62,8	53,0
Leninsky	5	25	25	25	6,25	400	—	—	—	—	64,0	53,0
Prokopyevsky	1	25	25	25	6,25	1250	200
Prokopyevsky	2	25	25	25	6,25	1280	205
Prokopyevsky	3	25	25	25	6,25	1238	198
Prokopyevsky	4	25	25	25	6,25	1180	189
Prokopyevsky	5	25	25	25	6,25	1450	232
Prokopyevsky	6	25	25	25	6,25	1500	240
Prokopyevsky	7	25	25	25	6,25	1350	216	212,1
Prokopyevsky	8	25	25	25	6,25	1245	193
Prokopyevsky	9	25	25	25	6,25	1260	202
Prokopyevsky	10	25	25	25	6,25	1560	250
Prokopyevsky	11	25	25	25	6,25	1360	217
Prokopyevsky	12	25	25	25	6,25	1240	198
Prokopyevsky	1	25	25	25	6,25	1550	—	—	248	250,2
Prokopyevsky	2	25	25	25	6,25	1600	—	—	256	250,2
Prokopyevsky	3	25	25	25	6,25	1780	—	—	278	250,2
Prokopyevsky	4	25	25	25	6,25	1530	—	—	242	250,2
Prokopyevsky	5	25	25	25	6,25	1440	—	—	230	250,2
Prokopyevsky	6	25	25	25	6,25	1370	—	—	219	250,2
Prokopyevsky	7	25	25	25	6,25	1530	—	—	245	250,2
Prokopyevsky	8	25	25	25	6,25	1360	—	—	218	250,2
Prokopyevsky	9	25	25	25	6,25	1620	—	—	259	250,2
Prokopyevsky	10	25	25	25	6,25	1720	—	—	282	250,2
Prokopyevsky	11	25	25	25	6,25	1670	—	—	267	250,2
Prokopyevsky	12	25	25	25	6,25	1580	—	—	254	250,2
Prokopyevsky	1	25	25	25	6,25	890	—	—	—	—	142	167,1
Prokopyevsky	2	25	25	25	6,25	870	—	—	—	—	139	167,1
Prokopyevsky	3	25	25	25	6,25	960	—	—	—	—	154	167,1
Prokopyevsky	4	25	25	25	6,25	1260	—	—	—	—	202	167,1
Prokopyevsky	5	25	25	25	6,25	1240	—	—	—	—	198	167,1

Basin	No.	2	3	4	5	6	7	8	9	10	11	12	13
Khakass	1	25	25	25	25	6.25	390	62.5	47.9	—	—	—	—
Khakass	2	25	25	25	25	6.25	330	52.8	47.9	—	—	—	—
Khakass	3	25	25	25	25	6.25	210	33.6	47.9	—	—	—	—
Khakass	4	25	25	25	25	6.25	191	30.6	47.9	—	—	—	—
Khakass	5	25	25	25	25	6.25	417	65.1	47.9	—	—	—	—
Khakass	6	25	25	25	25	6.25	277	43.2	47.9	—	—	—	—
Khakass	7	25	25	25	25	6.25	306	49.0	47.9	—	—	—	—
Khakass	8	25	25	25	25	6.25	268	41.3	47.9	—	—	—	—
Khakass	9	25	25	25	25	6.25	400	64.1	47.9	—	—	—	—
Khakass	10	25	25	25	25	6.25	326	52.2	47.9	—	—	—	—
Khakass	11	25	25	25	25	6.25	215	34.4	47.9	—	—	—	—
Khakass	12	25	25	25	25	6.25	290	46.4	47.9	—	—	—	—
Khakass	1	25	25	25	25	6.25	560	—	—	89.6	69.7	—	—
Khakass	2	25	25	25	25	6.25	337	—	—	53.9	69.7	—	—
Khakass	3	25	25	25	25	6.25	400	—	—	64.1	69.7	—	—
Khakass	4	25	25	25	25	6.25	600	—	—	96.1	69.7	—	—
Khakass	5	25	25	25	25	6.25	520	—	—	83.2	69.7	—	—
Khakass	6	25	25	25	25	6.25	330	—	—	52.8	69.7	—	—
Khakass	7	25	25	25	25	6.25	315	—	—	50.5	69.7	—	—
Khakass	8	25	25	25	25	6.25	420	—	—	67.2	69.7	—	—
Khakass	9	25	25	25	25	6.25	480	—	—	76.7	69.7	—	—
Khakass	10	25	25	25	25	6.25	520	—	—	83.2	69.7	—	—
Khakass	11	25	25	25	25	6.25	340	—	—	54.4	69.7	—	—
Khakass	12	25	25	25	25	6.25	400	—	—	63.9	69.7	—	—
Khakass	1	25	25	25	25	6.25	270	—	—	—	—	43.2	38.1
Khakass	2	25	25	25	25	6.25	236	—	—	—	—	37.8	38.1
Khakass	3	25	25	25	25	6.25	215	—	—	—	—	34.4	38.1
Khakass	4	25	25	25	25	6.25	260	—	—	—	—	41.6	38.1
Khakass	5	25	25	25	25	6.25	210	—	—	—	—	33.6	38.1
Cheremkhovsky	1	25	25	25	25	6.25	210	33.6	36.6	—	—	—	—
Cheremkhovsky	2	25	25	25	25	6.25	250	40.1	36.6	—	—	—	—
Cheremkhovsky	3	25	25	25	25	6.25	150	24.0	36.6	—	—	—	—
Cheremkhovsky	4	25	25	25	25	6.25	270	43.2	36.6	—	—	—	—
Cheremkhovsky	5	25	25	25	25	6.25	300	48.0	36.6	—	—	—	—
Cheremkhovsky	6	25	25	25	25	6.25	265	42.4	36.6	—	—	—	—
Cheremkhovsky	7	25	25	25	25	6.25	190	30.4	36.6	—	—	—	—
Cheremkhovsky	8	25	25	25	25	6.25	180	28.8	36.6	—	—	—	—
Cheremkhovsky	9	25	25	25	25	6.25	195	31.3	36.6	—	—	—	—
Cheremkhovsky	10	25	25	25	25	6.25	200	32.0	36.6	—	—	—	—
Cheremkhovsky	11	25	25	25	25	6.25	250	40.1	36.6	—	—	—	—
Cheremkhovsky	12	25	25	25	25	6.25	280	44.8	36.6	—	—	—	—
Cheremkhovsky	1	25	25	25	25	6.25	820	—	—	131.0	148.3	—	—
Cheremkhovsky	2	25	25	25	25	6.25	1530	—	—	245.0	148.3	—	—
Cheremkhovsky	3	25	25	25	25	6.25	930	—	—	148.5	148.3	—	—
Cheremkhovsky	4	25	25	25	25	6.25	900	—	—	143.8	148.3	—	—
Cheremkhovsky	5	25	25	25	25	6.25	795	—	—	127.1	148.3	—	—
Cheremkhovsky	6	25	25	25	25	6.25	1100	—	—	160.0	148.3	—	—
Cheremkhovsky	7	25	25	25	25	6.25	940	—	—	150.1	148.3	—	—
Cheremkhovsky	8	25	25	25	25	6.25	860	—	—	137.5	148.3	—	—
Cheremkhovsky	9	25	25	25	25	6.25	790	—	—	126.2	148.3	—	—
Cheremkhovsky	10	25	25	25	25	6.25	940	—	—	150.1	148.3	—	—
Cheremkhovsky	11	25	25	25	25	6.25	940	—	—	150.1	148.3	—	—
Cheremkhovsky	12	25	25	25	25	6.25	830	—	—	132.8	148.3	—	—
Cheremkhovsky	1	25	25	25	25	6.25	420	—	—	—	—	67.2	70.0
Cheremkhovsky	2	25	25	25	25	6.25	390	—	—	—	—	62.4	70.0
Cheremkhovsky	3	25	25	25	25	6.25	430	—	—	—	—	68.8	70.0
Cheremkhovsky	4	25	25	25	25	6.25	500	—	—	—	—	79.9	70.0
Cheremkhovsky	5	25	25	25	25	6.25	450	—	—	—	—	72.0	70.0

In making the specimens, great attention was paid to trimming the end faces, since the degree of uniformity in the distribution of the compressive force over the areas of the end faces depends on this. The specimens were made in such a way that their height, relative to the bedding, was either parallel, or perpendicular, or at an angle of 45°. For each grade of coal, 29 specimens were prepared: 12 of them parallel to the bedding, 12 perpendicular to the bedding, and 5 specimens at an angle of 45° (with respect to the height).

The tests were carried out on a two-ton Amsler machine. The results of the experiments are summarized in Table 16.

Below we give a table of the mean values of the strength limit (Table 17).

Table 17

Coal	Compressive strength limit \(\sigma_{\mathrm{в}}\): Perpendicular to bedding	Compressive strength limit \(\sigma_{\mathrm{в}}\): Parallel to bedding	Compressive strength limit \(\sigma_{\mathrm{в}}\): At an angle of 45°
Anzhero-Sudzhensk	75.6	49.4	38.2
Anzhero-Sudzhensk	100%	65.3%	50.5%
Leninsk	103.8	47.6	53.0
Leninsk	100%	45.8%	51.1%
Prokopyevsk	250.2	212.1	167.1
Prokopyevsk	100%	84.8%	66.8%
Khakass	69.7	47.9	38.1
Khakass	100%	68.6%	54.6%
Cheremkhovo	148.3	36.6	70.0
Cheremkhovo	100%	24.6%	47.1%

Analysis of this table shows that, of the Kuzbass coals we studied, the coal from the Prokopyevsk deposit proved to be the strongest. It was also established that the greatest strength of coal corresponds to the case in which the force is applied perpendicular to the bedding. It should be noted that the coals of the Cheremkhovo deposit resist the acting forces well in the direction perpendicular to the stratification and resist the force parallel to the bedding very poorly. In this case, the Cheremkhovo coal splits at an insignificant strength limit. If the compressive strength limit of the Prokopyevsk coal is taken as 100%, then the remaining coals are arranged in the following order according to their compressive strength limits (Table 18).

Table 18

Coal	Ultimate strength \(\sigma_{в}\): perpendicular to bedding, %	Ultimate strength \(\sigma_{в}\): parallel to bedding, %	Ultimate strength \(\sigma_{в}\): at an angle of \(45^\circ\), %
Prokopyevsk	100	100	100
Anzhero-Sudzhensk	30.2	23.3	22.8
Leninsk	41.6	22.5	31.7
Khakass	27.9	22.6	22.8
Cheremkhovo	59.4	17.3	41.8

Testing Kuzbass Hard Coals for Shear Resistance

The shear resistance of coal was determined on specimens made in the form shown in Fig. 2. The dimensions of the specimens were kept approximately at the following values: \(a = 20\) mm, \(b = 20\) mm, \(h = 20\) mm. From each grade of coal, 4 specimens were prepared, of which two had the height \(h\) parallel to the bedding and two perpendicular to the bedding. To carry out the shear, the device shown in Fig. 3 was made.

Fig. 2

Fig. 3

Labels visible in Fig. 4: “plane of action of the force,” “line of rupture,” “direction of beds,” “bedding of beds,” “line of rupture \(45^\circ\).”

Fig. 4

The specimen was inserted with its lower part into the opening of the apparatus, and a force was transmitted to the upper part of the specimen, which produced shearing of the protruding part of the specimen along the length \(h\). The results of the tests are given in Table 19.

Table 19

Coal	\(N\)	Dimensions \(b\)	Dimensions \(h\)	\(F\), cm²	\(P\), kg	\(\parallel\) seams \(\tau\), kg/cm²	\(\parallel\) seams \(\tau_{\text{avg}}\)	\(\perp\) seams \(\tau\), kg/cm²	\(\perp\) seams \(\tau_{\text{avg}}\)
Anzhero-Sudzhensky	1	2,24	2,03	4,66	72	15,4	16,15	—	—
Anzhero-Sudzhensky	2	2,12	2,10	4,46	80	17,9	16,15	—	—
Anzhero-Sudzhensky	3	2,00	2,10	4,20	112	—	—	26,7	25,0
Anzhero-Sudzhensky	4	2,16	2,12	4,58	106	—	—	23,2	25,0
Leninsky	1	2,00	2,00	4,00	76	19,0	19,5	—	—
Leninsky	2	2,10	2,08	4,18	82	20,0	19,5	—	—
Leninsky	3	2,08	2,16	4,50	100	—	—	22,2	26,65
Leninsky	4	2,20	2,00	4,40	128	—	—	29,1	26,65
Prokopyevsky	1	1,95	2,18	4,28	160	37,4	34,8	—	—
Prokopyevsky	2	1,96	2,00	3,92	126	32,2	34,8	—	—
Prokopyevsky	3	2,10	1,90	4,00	166	—	—	41,5	41,4
Prokopyevsky	4	2,20	2,10	4,62	190	—	—	41,2	41,4
Khakassky	1	2,3	1,9	4,38	90	20,5	20,5	—	—
Khakassky	2	2,2	1,9	4,18	86	20,5	20,5	—	—
Khakassky	3	2,0	2,1	4,20	120	—	—	28,6	28,6
Khakassky	4	2,1	2,2	2,62	132	—	—	28,6	28,6
Cheremkhovsky	1	2,08	2,08	4,34	40	9,2	10,1	—	—
Cheremkhovsky	2	2,10	2,08	4,36	48	11,0	10,1	—	—
Cheremkhovsky	3	2,12	2,10	4,46	116	—	—	26,0	28,6
Cheremkhovsky	4	1,96	2,00	3,92	122	—	—	31,1	28,6

During the test we observed that the specimens in which the direction \(h\) coincided with the direction of bedding gave shear along the seams; for specimens in which the direction \(h\) was perpendicular to the bedding, as a rule, failure occurred along a plane directed at approximately an angle of \(45^\circ\). The failure patterns are shown in Fig. 4.

We consider it necessary to present a comparative table of the ultimate strengths in compression and shear (Table 20).

Table 20

Coal	\(\parallel\) to bedding: \(\sigma_{\text{compr.}}\)	\(\parallel\) to bedding: \(\tau_{\text{shear}}\)	\(\perp\) to bedding: \(\sigma_{\text{compr.}}\)	\(\perp\) to bedding: \(\tau_{\text{shear}}\)	Average value, %
Anzhero-Sudzhensk	49.4	16.15	75.6	25.0	30
Anzhero-Sudzhensk	100%	32.8%	100%	33.1%	30
Leninsk	47.6	19.5	103.8	26.65	25
Leninsk	100%	40.9%	100%	25.7%	25
Prokopyevsk	212.1	34.8	250.2	41.4	16
Prokopyevsk	100%	16.4%	100%	16.6%	16
Khakass	47.9	20.5	69.7	28.6	41
Khakass	100%	41.8%	100%	41.2%	41
Cheremkhovo	36.6	10.1	148.3	28.6	20
Cheremkhovo	100%	27.6%	100%	19.3%	20

Determination of the modulus of normal elasticity \(E\) of Kuzbass coals

To determine the modulus of normal elasticity of bituminous coal, specimens were prepared having the form shown in Fig. 5. All tests were carried out on a two-ton Amsler system machine. The measuring instruments for deformations were Huggenberger tensometers with a scale division value of 1 micron. The experiments were carried out also in order to determine the value of Poisson’s ratio for bituminous coal; therefore, on a number of specimens two tensometers were installed: one parallel to the plane of action of the force, and the other perpendicular to the direction of the acting force. Thus, we measured both the absolute change in dimensions along the axis of the specimen and the change in the transverse dimension.

In Table 21 are given the values of the numerical material obtained as a result of the experiments. The data of these materials may be presented in the form of a series of graphs, similar to that shown in Figs. 6 and 7 (the table is appended to

Fig. 5

Table 21

No.	Coal	Sample size, mm: \(l\)	Sample size, mm: \(b\)	Sample size, mm: \(h\)	Load \(P\), kg	Teksometer reading, longitudinal	Teksometer reading, transverse	Value \(E\), kg/cm²	Value \(\mu\)
1	Anzhero-Sudzhensk	64,6	23	27,6	0	0	0	45000	0,23
1	Anzhero-Sudzhensk \(E=\dfrac{300\cdot64{,}6\cdot1000}{67\cdot23\cdot27{,}6}=45000\) \(\varepsilon=\dfrac{91}{1000\cdot64{,}6}=0{,}0014\) \(\varepsilon'=\dfrac{8{,}9}{1000\cdot27{,}6}=0{,}00032\) \(\mu=0{,}23\)	64,6	23	27,6	50	8	10	45000	0,23
1	Anzhero-Sudzhensk	64,6	23	27,6	100	19	10	45000	0,23
1	Anzhero-Sudzhensk	64,6	23	27,6	150	24	2,5	45000	0,23
1	Anzhero-Sudzhensk	64,6	23	27,6	200	37	3,0	45000	0,23
1	Anzhero-Sudzhensk	64,6	23	27,6	250	48	4,6	45000	0,23
1	Anzhero-Sudzhensk	64,6	23	27,6	300	58	5,4	45000	0,23
1	Anzhero-Sudzhensk	64,6	23	27,6	350	69	6,7	45000	0,23
1	Anzhero-Sudzhensk	64,6	23	27,6	400	80	7,8	45000	0,23
1	Anzhero-Sudzhensk	64,6	23	27,6	450	91	8,9	45000	0,23
1	Anzhero-Sudzhensk	64,6	23	27,6	500	100		45000	0,23
2	Anzhero-Sudzhensk	65,2	22,0	28,0	0	0	—	39900	—
2	Anzhero-Sudzhensk \(E=\dfrac{300\cdot65{,}2\cdot1000}{80\cdot22{,}0\cdot28{,}0}=39900\)	65,2	22,0	28,0	50	7	—	39900	—
2	Anzhero-Sudzhensk	65,2	22,0	28,0	100	11	—	39900	—
2	Anzhero-Sudzhensk	65,2	22,0	28,0	150	16	—	39900	—
2	Anzhero-Sudzhensk	65,2	22,0	28,0	200	27	—	39900	—
2	Anzhero-Sudzhensk	65,2	22,0	28,0	250	46	—	39900	—
2	Anzhero-Sudzhensk	65,2	22,0	28,0	300	55	—	39900	—
2	Anzhero-Sudzhensk	65,2	22,0	28,0	350	70	—	39900	—
2	Anzhero-Sudzhensk	65,2	22,0	28,0	400	82	—	39900	—
2	Anzhero-Sudzhensk	65,2	22,0	28,0	450	96	—	39900	—
2	Anzhero-Sudzhensk	65,2	22,0	28,0	500	102	—	39900	—
3	Anzhero-Sudzhensk	60,0	22,0	30,0	0	0	—	38100	—
3	Anzhero-Sudzhensk \(E=\dfrac{300\cdot60\cdot1000}{72\cdot22\cdot30{,}0}\)	60,0	22,0	30,0	50	8	—	38100	—
3	Anzhero-Sudzhensk	60,0	22,0	30,0	100	16	—	38100	—
3	Anzhero-Sudzhensk	60,0	22,0	30,0	150	20	—	38100	—
3	Anzhero-Sudzhensk	60,0	22,0	30,0	200	35	—	38100	—
3	Anzhero-Sudzhensk	60,0	22,0	30,0	250	46	—	38100	—
3	Anzhero-Sudzhensk	60,0	22,0	30,0	300	54	—	38100	—
3	Anzhero-Sudzhensk	60,0	22,0	30,0	350	67	—	38100	—
3	Anzhero-Sudzhensk	60,0	22,0	30,0	400	80	—	38100	—
3	Anzhero-Sudzhensk	60,0	22,0	30,0	450	92	—	38100	—
3	Anzhero-Sudzhensk	60,0	22,0	30,0	500	103	—	38100	—

1	2	3	4	5	6	7	8	9	10
								\(=41000\ \mathrm{kg/cm^2}\)
1	Leninsky	61.8	22.2	38.2	0	0	0
1	Leninsky			$$E=\frac{350\cdot61.8\cdot1000}{66.6\cdot22.2\cdot38.2}=38300$$ $$\varepsilon=\frac{126}{1000\cdot61.8}=0.00204$$ $$\varepsilon'=\frac{12.9}{1000\cdot38.2}=0.00034$$ $$\mu=0.17$$	50	18	1.0	38300	0.17
1	Leninsky				100	32	2.1	38300	0.17
1	Leninsky				150	48	3.2	38300	0.17
1	Leninsky				200	60	4.3	38300	0.17
1	Leninsky				250	72	5.5	38300	0.17
1	Leninsky				300	82	6.9	38300	0.17
1	Leninsky				350	92	8.0	38300	0.17
1	Leninsky				400	102	9.2	38300	0.17
1	Leninsky				450	112	10.4	38300	0.17
1	Leninsky				500	120	11.5	38300	0.17
1	Leninsky				550	126	12.9	38300	0.17
1	Leninsky				600	136	14.0	38300	0.17
2	Leninsky	61.7	23.0	28.4	0	0	—
2	Leninsky			$$E=\frac{200\cdot61.7\cdot1000}{51.6\cdot23.0\cdot28.4}=36800$$	50	10	—	36800
2	Leninsky				100	26	—	36800
2	Leninsky				150	34	—	36800
2	Leninsky				200	50	—	36800
2	Leninsky				250	62.6	—	36800
2	Leninsky				300	71	—	36800
3	Leninsky	61.7	22.2	30.2	0	0	—
3	Leninsky			$$E=\frac{200\cdot61.7\cdot1000}{57.1\cdot22.2\cdot30.2}=32200$$	50	10.0	—	32200
3	Leninsky				100	22.1	—	32200
3	Leninsky				150	32.2	—	32200
3	Leninsky				200	50.6	—	32200
3	Leninsky				250	67.2	—	32200
3	Leninsky				300	72.0	—	32200
4	Leninsky	62.0	23.0	29.5	0	0	0
4	Leninsky			$$E=\frac{250\cdot62.0\cdot1000}{55.0\cdot23.0\cdot29.5}$$ $$\varepsilon=\frac{67}{1000\cdot62}=0.00108$$ $$\varepsilon'=\frac{5.45}{1000\cdot29.5}=0.00018$$ $$\mu=0.168$$	50	9.0	1.0	39300	0.168
4	Leninsky				100	18.0	2.1	39300	0.168
4	Leninsky				150	27.0	3.2	39300	0.168
4	Leninsky				200	40.0	3.9	39300	0.168
4	Leninsky				250	59.9	4.3	39300	0.168
4	Leninsky				300	67.0	5.45	39300	0.168
4	Leninsky				350	78.0	—	39300	0.168

\[ E=36650\ \mathrm{kg/cm^2} \]

1	2	3	4	5	6	7	8	9	10
1	Khakassky $$E=\frac{500\cdot 53{,}4\cdot 1000}{41\cdot 36{,}6\cdot 46{,}3}=38500\ \mathrm{kg/cm^2}$$ $$\varepsilon=\frac{88}{1000\cdot 53{,}4}=0{,}00165$$ $$\varepsilon'=\frac{3}{1000\cdot 46{,}3}=0{,}000065$$ $$\mu=0{,}0394$$	53,4	36,6	46,3	0 100 200 300 400 500 600 700 800 900 1000	0 30 47 58 67 74 81 88 92 96 101	0 0,3 0,7 1,0 1,0 1,0 2,0 3,0 4,0 5,0 6,0	38500	0,0394 =0,04
2	Khakassky $$E=\frac{700\cdot 520\cdot 1000}{47\cdot 46{,}6\cdot 47{,}0}=35000$$	52,0	46,6	47,0	0 100 200 300 400 500 600 700 800 900 1000	0 20 30 40 47 53 58 63 67 71 74	— — — — — — — — — — —	35000
3	Khakassky $$E=\frac{600\cdot 54{,}0\cdot 1000}{41\cdot 44{,}0\cdot 46{,}0}=39100$$	54,0	44,0	46,0	0 100 200 300 400 500 600 700 800 900 1000	0 25 39 49 57 63 70 76 80 84 89	— — — — — — — — — — —	39100

$$E=37530\ \mathrm{kg/cm^2}$$

1	2	3	4	5	6	7	8	9	10
1	Cheremkhovsky $$E=\frac{600\cdot 80{,}7\cdot 1000}{41\cdot 59{,}3\cdot 30{,}7}=64700$$ $$\varepsilon=\frac{74}{1000\cdot 80{,}7}=0{,}0009$$ $$\varepsilon'=\frac{15{,}5}{1000\cdot 59{,}3}=0{,}00026$$ $$\mu=0{,}29$$	80,7	30,7	59,3	0 100 200 300 400 500 600 700 800 900 1000	0 10 19 28 36 43 49 56 64 69 74	0 2 4 7 9 11,0 12,5 13,5 14,0 14,0 15,5	64700	0,29

1	2	3	4	5	6	7	8	9	10
2	Cheremkhovo	70.5	30.0	60.0	0 100 200 300 400 500 600 700 800 900 1000	0 8 16 24 32 40 44 51 60 62 70	— — — — — — — — — — —	52600

\[ E=\frac{700\cdot 70.5\cdot 1000}{52\cdot 30.0\cdot 60.0}=52600 \]

1	2	3	4	5	6	7	8	9	10
3	Cheremkhovo	75.0	30.0	60.0	0 100 200 300 400 500 600 700 800 900 1000	0 9 17 26 34 42.5 47 53.5 62.0 65.5 72	— — — — — — — — — — —	60400

\[ E=\frac{700\cdot 75.0\cdot 1000}{48.5\cdot 30\cdot 60.0}=60400 \]

load perpendicular to the bedding planes

\[ E=60430\ \mathrm{kg/cm^2} \]

Cheremkhovo coal

coal

Scale: \(P\) — 1 cm = 100 kg; \(\Delta l\) — 1 cm = \(10\cdot 0.001\)

Fig. 6

Cheremkhovo coal

crosswise

Scale: \(P\) — 1 cm = 100 kg; \(\Delta h\) — 1 cm = \(10\cdot 0.001\)

Fig. 7

of the present work). The value of the modulus of normal elasticity was determined by the known formula:

\[ E=\frac{(P_A-P_B)l}{(\Delta l_A-\Delta l_B)F}, \tag{1} \]

where \(P_A\) and \(P_B\) are the values of the force for the interval of the Hooke line between points \(A\) and \(B\),

\(\Delta l_A\) and \(\Delta l_B\) are the corresponding deformations at these points,

\(F\) is the cross-sectional area of the specimen,

\(l\) is the length of the specimen before the experiment.

As average values of the moduli of normal elasticity for various grades of bituminous coal, we recommend the values given in Table 22.

Table 22

No.	Name of coal	Value of \(E\), kg/cm\(^2\)
1	Anzhero-Sudzhensk	41000
2	Leninsk	36650
3	Khakass	37530
4	Cheremkhovo	60430 \(\perp\) to bedding

Note: In studying bituminous coals from the Khakass deposit, we found that these coals exhibit good relative longitudinal deformation and almost no transverse deformation, i.e., they behave like a cork.

The Poisson’s ratio for Khakass coals, determined for 5 cases, showed a value not exceeding 0.05.

Determination of the Poisson’s ratio \(\mu\) for bituminous coal

In the literature up to now there have been absolutely no data on the values of Poisson’s ratio and the modulus of shear elasticity of bituminous coals, whereas all coal-cutting machines operate on the principle of cutting coal and in fact deal with the shear of coal. For an exact determination of the resistance of bituminous coal to shear, knowledge of the magnitude of the shear modulus \(G\) is entirely necessary. We decided to carry out some investigations in this direction. With the aid of Hugenberger strain gauges we succeeded in measuring the transverse compression of bituminous coal during testing for longitudinal compression. Table 23 shows the processing of the results of experiments for determining Poisson’s ratio.

Table 23

Name of bituminous coal	\(a\)	\(b\)	\(l\)	Load \(P\), kg	\(\Delta l\)	\(\varepsilon=\dfrac{\Delta l}{l}\)	\(\Delta a\)	\(\varepsilon'=\dfrac{\Delta a}{a}\)	\(\mu\)
Anzhero-Sudzhensk	23	27.6	64.6	500	0.091	0.00145	0.0089	0.00032	0.23
Leninsk	30.2	32.2	74.5	450	0.0814	0.00109	0.0055	0.000185	0.17
Khakass	36.0	36.3	53.4	700 \(\perp\) to bedding	0.0892	0.00165	0.0030	0.000083	0.05
Cheremkhovo	30.7	59.3	80.7	1000	0.074	0.0009	0.0155	0.00026	0.29

Force \(\perp\) to bedding

Using the values of Poisson’s ratios indicated above and the values of the modulus of normal elasticity \(E\), by the well-known formula of the theory of elasticity relating the values of the moduli of normal and shear elasticity,

\[ G=\frac{E}{2(1+\mu)}. \tag{2} \]

we calculated the values of \(G\) for certain bituminous coals. These values are shown in Table 24.

Table 24

Coal	\(E\), kg/cm²	\(\mu\)	\(G\), kg/cm²
Anzhero-Sudzhensk	41000	0.23	16600
Leninsk	36650	0.17	15680
Khakass	37530	0.05	17850
Cheremkhovo	60430	0.29	23400

The obtained values of Poisson’s ratios \(\mu\) and of the shear modulus \(G\), owing to the absence of literature sources, cannot be compared with any other values of these quantities. As a check, we set ourselves the further task of determining \(G\) by a somewhat different method.

Shear Modulus of Bituminous Coal

Experiments to determine the shear modulus \(G\) were carried out on an apparatus designed by I. R. Konyakhin, senior lecturer in the Department of Strength of Materials of the Tomsk Polytechnic Institute, kindly placed at our disposal. A description and the methods of working with I. R. Konyakhin’s apparatus are set forth in his work [15].

The schematic diagram of the apparatus is shown in Fig. 8.

We tested two grades of coal: Cheremkhovo and Leninsk. The specimens were made in the form of cylinders with diameter \(d = 19\) mm and length, for Cheremkhovo bituminous coal, \(l = 47\) mm, and for Leninsk bituminous coal, \(l = 60\) mm. In both cases the diameter of the roller on which the mirror of the apparatus was mounted had the value \(d_v = 17.5\) mm.

Diagram of the apparatus of Eng. Konyakhin
Fig. 8

The angle of twist is determined by the formula

\[ \varphi = \frac{S d_v}{2 L L_0}, \tag{3} \]

where

\[ \begin{aligned} S &\text{ — reading on the scale,}\\ L_0 &\text{ — reduced length of the lever of the apparatus } = 579\ \text{mm,}\\ L &\text{ — distance from the mirror to the scale } = 1500\ \text{mm,}\\ d_v &\text{ — diameter of the mirror roller } = 17.5\ \text{mm.} \end{aligned} \]

The shear modulus \(G\) is determined from the well-known formula

\[ G = \frac{M_{\mathrm{tw}}\, l}{I_p\, \varphi}. \tag{4} \]

Below is Table 25, which shows the results of experiments with a specimen of Leninskii bituminous coal.

Table 25

Lever up	Lever up	Lever down	Lever down
$P$	reading	$P$	reading
0	80	0	70
23	100	24	75
46	120	46	80
62	140	70	85
84	160	96	90
106	180	114	95
138	200	142	100
154	220
170	240
184	260
196	280
200	300

Since, in the course of the test, elastic displacement of the tested specimen at the point of embedment (below) is evidently possible, we carried out a double test with the lever in the upper position, and also with the lever in the lower position of the specimen. The difference of the readings was adopted for the calculation.

Leninskii bituminous coal

Vertical axis: $P$
Horizontal axis: $S$
Curve labels: lever up; lever down
Scale: $P$—$1\ \mathrm{cm}=20$; $S$—$1\ \mathrm{cm}=30\ \mathrm{m}$

Fig. 9

From the data of Table 25 the graph in Fig. 9 was constructed. The modulus $G$ was determined for point “A” of the diagram:

\[ \varphi=\frac{S\cdot d_b}{2L\cdot L_o} =\frac{140\cdot 17.5}{3000\cdot 579} =0.00138 \]

\[ M_{\mathrm{cr}}=0.18\cdot 15\ \mathrm{kg/cm}, \]

\[ l=6\ \mathrm{cm}, \]

\[ G=\frac{M_{\mathrm{cr}}l}{I_p\varphi} =\frac{0.18\cdot 15\cdot 6}{1.28\cdot 0.00138} =9160\ \mathrm{kg/cm^2}. \]

To avoid placing the lever above and below the specimen in turn, we changed the procedure; namely, two levers were installed simultaneously, as shown in the diagram (Fig. 10). The mirror of the instrument was placed between the levers. This allowed us immediately to take a reading for determining the angle of twisting of the upper section relative to the lower one. Table 26 gives the result of an experiment with Cheremkhovo hard coal.

Fig. 10. Diagram of the setup: upper lever; lower lever; mirror; beam; scale; \(P\).

Table 26

\(P_{gr}\)	0	200	400	600	800	1000	1200	1400
\(S_{mm}\)	0	67	157	250	346	443	516	684

Figure 11 shows the graph of the experiment

\[ \varphi=\frac{S\cdot d_{b}}{2L\cdot L_{o}}=0{,}0052 \]

\[ M_{kr}=P\cdot l_{o}=1{,}2\cdot 15=18\ \mathrm{kg/cm} \]

\[ G=\frac{M_{kr}\cdot l}{I_{p}\varphi} =\frac{18\cdot 6{,}0}{0{,}0052\cdot 1{,}28} =16200\ \mathrm{kg/cm^{2}} \]

Fig. 11. Cheremkhovo hard coal. Scale: \(P\): 1 cm = 200 g; \(S\): 1 cm = 40 mm.

Fig. 12. Sandstone. Sample. [[unclear: vertical label next to the left line]]. Scale: \(P\): 1 cm = 50 g; \(S\): 1 cm = 60 mm.

Since sandstone is the predominant rock among which the coal seams of Kuzbass occur, we decided to determine the value of the shear modulus \(G\) for sandstone. For this purpose a cylindrical specimen was prepared, \(d = 19\ \text{mm}\) and \(l = 40\ \text{mm}\). The specimen was tested on the apparatus described above, and the results are summarized in Table No. 27, from whose data the graph in Fig. 12 was constructed.

Table 27

Lever at top, \(P_{gr}\)	Lever at top, reading, mm	Lever at bottom, \(P_{gr}\)	Lever at bottom, reading, mm
0	−20	0	50
25	0	70	51
45	20	130	52
95	60	190	53
110	80	—	—
145	120	—	—
190	160	—	—
230	200	—	—
300	240	—	—
335	280	—	—
370	320	—	—
410	360	—	—
450	400	—	—
490	440	—	—
520	480	—	—

\[ \varphi = \frac{S d_{bal}}{2 L \cdot L_o} \]

In this experiment \(d_{bal} = 0.7\ \text{cm}\). The reduced length of the lever is \(L_o = 582\ \text{mm}\).

\[ \varphi = \frac{400 \cdot 0.7}{3000 \cdot 582} = 0.00016 \]

\[ M_{kr} = P \cdot l_o = 0.45 \cdot 15\ \text{kg/cm} \]

\[ G = \frac{M_{kr} l}{I_p \cdot \varphi} = \frac{0.45 \cdot 15 \cdot 4}{0.00016 \cdot 1.28} = 134500\ \text{kg/cm}^2 . \]

On the elastic-plastic properties of hard coal

To establish the dependence between load and plastic deformation of hard coal, we refrained from carrying out experiments on the Gagarin press, as was done in our work with metals [16]. The reason for this is the fact that when a ball, even one with \(d = 2.5\ \text{mm}\), is pressed in on the Gagarin press, it is not possible to achieve a smooth increase of small loads. This leads to the load increasing in jumps and makes it impossible to take readings. At the same time, when the ball is pressed in at loads \(P = 40 \div 50\ \text{kg}\), the hard coal cracks and the specimen fails. The load scale on the Gagarin press at \(P = 1000\ \text{kg}\), as is known, is equal to \(2\ \text{kg}\) per division. Such a scale is too coarse for testing hard coal. For this reason we abandoned the use of the Gagarin press and used the apparatus of engineer I. R. Konyakhin, with his consent, making in it a small attachment shown in Fig. 13.

Here: \(A\)—a cylinder with a cut parallel to its diameter,
\(B\)—a lever of hardened steel, lying freely in the cut,
\(C\)—a steel pad serving as a support for lever \(B\),
\(D\)—the tested specimen of bituminous coal,
\(K\)—a cone of chromium-nickel steel, hardened without tempering,
with an angle of \(90^\circ\).

The load \(P\) was transmitted to lever \(B\) through a traverse according to the scheme shown in Fig. 14. A long lever \(N\), made of light wood and ending in an aluminum attachment, rests on the surface of lever \(B\);

Fig. 13

the attachment rests on the roller of the mirror (Fig. 15). When the load \(P\) is applied to the spring \(T\), lever \(B\) turns about support \(n\). Together with lever \(B\), under the action of its own weight, lever \(N\) also turns, thereby setting the mirror roller in rotation. In the optical tube, the displacement of the mirror was measured on a scale. The diameter of the mirror roller is \(d_b = 17.5\) mm. The magnification of the readings of the displacement of the lever about the axis of rotation, with the aid of the mirror, in the optical tube is equal to 10000 (rotation about point \(0\)). Obviously, if the point of rotation is point \(n\), then the magnification will be different, namely:

Fig. 14

\[ \lambda = \frac{10000 \cdot (57.2 + 2.6)}{57.2} = 10430 \]

In our investigation, the system of levers rotated not about the central axis \(OO\), but about point \(n\). Therefore the increase in the displacement of the cone is found from the simple relation:

\[ \lambda_1=\frac{\lambda}{5.2}=\frac{10430}{5.2}=2000. \]

Fig. 15

This means that \(1\) mm of displacement of the beam on the scale corresponds to

\[ \frac{1}{2000} \]

mm of displacement of the cone. The force \(Q\) transmitted to the specimen is determined from the ratio of the arms of lever \(B\) according to the scheme shown in Fig. 16:

\[ \frac{P}{2}\cdot 17.6-Q\cdot 5.2+\frac{P}{2}\cdot 12.4=0. \]

\[ Q=2.89\cdot P \]

In order to eliminate the influence of the apparatus and compression of the specimen, a preliminary test was carried out without the cone in lever \(B\). In this case

Fig. 16

lever \(B\) rested with its plane on one end face of the specimen, while with the other end the specimen rested against cylinder \(A\). The results of the experiment are given in

Table 28

\(P_2\)	0	110	570	1170	1670
\(S_{\text{mm}}\)	0	5	10	15	24

Figure 17 shows the graph for this experiment.

Having thus determined the influence of the apparatus, we assume that when the point of the cone is introduced into a coal specimen all these phenomena are preserved, and these preliminary data must be subtracted from the scale readings.

For the tests, specimens of coal were prepared in the form of a cylinder with dimensions: \(d = 1\ \text{cm}\) and \(l = 12\ \text{mm}\). These specimens were placed under the point of the cone, and by stretching the spring \(C\), previously calibrated, a load \(Q\) was transmitted to the specimens, under the action of which the cone was pressed into the end surface of the specimen. The magnitude of indentation, on the magnification scale \(\lambda^1\), was read from the scale. After the experiment, using an optical microscope with a scale division value of \(0.005\ \text{mm}\), we examined the imprint obtained from the indentation of the cone. On examination it turned out that the end surface of the specimen was a surface of very great unevenness. Cracks, projections, etc., were clearly visible. Among these cracks and projections the conical imprint obtained was lost. For this reason all specimens were carefully ground with crocus and oil on the end surface. This ensured the obtaining of a satisfactory surface. Observation of the imprints showed good visibility of the conical indentation, with a clearly expressed cone apex.

Fig. 17

(In the figure: “curve of elastic deformation of the apparatus”; scale: \(P\)—1 cm = 200 g; \(S\)—1 cm = 4 mm.)

Table 29 gives the data of experiments on coal specimens.

Table 29

Specimen	\(P_r\)	Loading, mm	Unloading, mm	Specimen	\(P_r\)	Loading, mm	Unloading, mm
Cheremkhovskii coal	0	0	160	Leninskii coal	0	30	330
Cheremkhovskii coal	40	22	241	Leninskii coal	100	50	385
Cheremkhovskii coal	80	74	255	Leninskii coal	200	86	414
Cheremkhovskii coal	120	116	267	Leninskii coal	300	137	432
Cheremkhovskii coal	160	151	277	Leninskii coal	400	206	447
Cheremkhovskii coal	200	187	286	Leninskii coal	500	266	457
Cheremkhovskii coal	240	226	293	Leninskii coal	600	305	467
Cheremkhovskii coal	280	254	298	Leninskii coal	700	340	472
Cheremkhovskii coal	320	278	304	Leninskii coal	800	384	484
Cheremkhovskii coal	360	310	310	Leninskii coal	900	430	492
Prokopyevskii coal	0	0	268	Leninskii coal	1000	495	—
Prokopyevskii coal	100	3	308
Prokopyevskii coal	200	10	321
Prokopyevskii coal	300	56	330
Prokopyevskii coal	400	112	336
Prokopyevskii coal	500	160	341
Prokopyevskii coal	600	198	344
Prokopyevskii coal	700	235	345
Prokopyevskii coal	800	270	347
Prokopyevskii coal	900	310	350
Prokopyevskii coal	1000	356	356

The readings given in this table were taken after a 10-sec hold, since we observed a considerable phenomenon of coal creep after application of the load. On the basis of the data in this table, graphs of the dependence of deformation on load can be constructed. Fig. 18 shows one of such graphs.

The presence of a clearly expressed conical impression allowed us to measure its diameter. From six measurements made at different positions of the specimen, we established that the mean diameter of the impression was

Fig. 18. Curve for Cheremkhovo bituminous coal. Scale: \(P\)—\(1\text{ cm}=40\text{ g}\); \(\delta\)—\(1\text{ cm}=0.0025\text{ mm}\). The curve indicates loading and unloading.

\[ d = 0.251\ \text{mm}. \]

Since the cone has an angle at the vertex of \(90^\circ\), it follows from Fig. 19 that:

\[ t = r, \]

where \(t\) is the depth of the impression after removal of the load.

Fig. 19.

Fig. 18 shows the straight unloading line, which cuts off on the abscissa axis a deformation equal to \(240\ \text{mm}\) on the scale. Knowing the magnification scale \(\lambda = 2000\),

Fig. 20. Processing of the curve \(P\)-\(\delta\) for Cheremkhovo bituminous coal.

Fig. 21. Curve \(\delta_1\) for Cheremkhovo coal. Scale: \(P\)—\(1\text{ cm}=40\text{ g}\); \(\delta_1\)—\(1\text{ cm}=25\cdot10^{-?}\) [[unclear: exponent and units]]. The figure shows \(P = 6.5\,\delta^{\text{mm}}\).

it is easy to obtain the actual depth of the conical impression after removal of the load:

\[ t = \frac{240}{\lambda} = \frac{240}{2000} = 0.12\ \text{mm}. \]

Thus the diameter of the impression should be equal to \(d=2t=0.24\) mm.
The actual value, as is seen from the experimental results, is \(d=0.251\) mm.
The deviation is insignificant.

The presence in diagrams of the type of Fig. 18 of a sharply curved portion of the unloading curve confirms the known proposition that coal, within certain limits, does not obey Hooke’s law, and only after a certain load is reached is a direct proportionality between load and deformation observed.

The processing of the curves in order to obtain an analytical relation between \(P\) and \(\delta_s\) was carried out by the method of least squares, as shown in our work [16] for metals. The results of this processing are presented in Table 30. The graphs themselves are shown in Figs. 20 and 21.

Table 30

\(x\)	\(x_1\)	\(x_2\)	\(x_3\)	\(x_4\)	\(x_5\)	\(x_6\)	\(x_7\)	\(x_8\)	\(x_9\)
\(125\cdot 10^{-5}\)	7	23,5	37	49,5	60	74	83,5	92	99
\(\xi = Lg\,x\)	0,845	1,371	1,568	1,694	1,778	1,869	1,921	1,964	1,995

\[ \bar{\xi}=\frac{\Sigma Lg\,x}{n}=1,667 \]

\(\xi-\bar{\xi}\)	0,822	0,296	0,099	−0,027	−0,111	−0,202	−0,254	−0,297	−0,328
\((\xi-\bar{\xi})^2\)	0,675	0,088	0,009	0,0001	0,012	0,041	0,065	0,088	0,108

\[ \Sigma(\xi-\bar{\xi})^2 \]

\[ \Sigma(\xi-\bar{\xi})^2=1,138 \]

	\(y_1\)	\(y_2\)	\(y_3\)	\(y_4\)	\(y_5\)	\(y_6\)	\(y_7\)	\(y_8\)	\(y_9\)
\(y\)	40	80	120	160	200	240	280	320	360
\(\eta = Lg\,y\)	1,602	1,903	2,079	2,204	2,301	2,380	2,447	2,505	2,556

\[ \bar{\eta}=\frac{\Sigma Lg\,y}{n}=2,219 \]

\(\eta-\bar{\eta}\)	0,617	0,316	0,140	0,015	−0,082	−0,161	−0,228	−0,286	−0,337
\((\eta-\bar{\eta})(\xi-\bar{\xi})\)	0,506	0,094	0,138	−0,0004	0,009	0,032	0,058	0,025	0,110

\[ \Sigma(\eta-\bar{\eta})(\xi-\bar{\xi}) \]

\[ \Sigma(\eta-\bar{\eta})(\xi-\bar{\xi})=1,032 \]

The equation of the relation between the load \(P\) and the plastic deformation of coal has the form:

\[ P=6{,}6\,\delta_s^{0{,}84} \tag{6} \]

(Cheremkhovo bituminous coal).

\[ p=\frac{\sum(\eta-\bar{\eta})(\xi-\bar{\xi})}{\sum(\xi-\bar{\xi})^2}=0.84 \]

\[ q=\bar{\eta}-p\bar{\xi}=2.219-0.84\cdot1.667=0.819 \]

\[ \lg k=q=0.819;\quad k=6.6 \]

\[ P=6.6\,\delta_s^{0.84} \]

Check: \(P=240\) g.

\[ \lg \delta_s=\frac{\lg P-\lg 6.6}{0.84}=\frac{2.380-0.819}{0.84}=1.875 \]

\[ \delta_s=74.99,\quad \text{percentage deviation } \sim 1\%. \]

Coefficient of restitution when steel strikes bituminous coal

In our work [16] a formula was derived for determining the coefficient of restitution upon impact

\[ \varepsilon_i= \sqrt{ \frac{(n+1)S^{1/n}} {S^{1/n}(n+1)+(k+1)a_0^{1/n}\delta_e^{\frac{k-n}{n}}} }, \]

where \(n\), \(S\), \(a_0\), and \(k\) are the coefficients of the equations of plastic and elastic deformations, namely:

\[ P=S\delta_s^n \tag{8} \]

\[ P=a_0\delta_e^k. \tag{9} \]

Below, in the present work, we obtained

\[ P=6.6\,\delta_s^{0.84} \tag{10} \]

The values of the elastic deformations are shown in Table 31.

Table 31

\[ \delta_e\cdot125\cdot10^{-5}\ \text{mm} \]

\(P_r\)	0	40	80	120	160	200	240	280	320	360
\(\delta_e\)	0	1.5	4.0	7.0	9.5	12.0	14.0	16.0	18.0	20.0

By the method of least squares we processed the curve expressing this dependence of \(P\) and \(\delta_e\), and obtained an equation of the form

\[ P=25.78\,\delta_e^{0.846}, \]

where

\[ k=0.846,\qquad a_0=25.78. \]

To solve equation 7 it is necessary to carry out preliminary calculations, which we have shown for the mean value of the load \(P = 200\) g in Table 32.

Table 32

Material	\(P_r\)	\(n+1\)	\(S\)	\(S^{1/n}\)	\(k+1\)	\(a_0\)	\(a_0^{1/n}\)	\(\delta_e\)	\(\delta_e^{\frac{k-n}{n}}\)
Bituminous coal	200	1,840	6,6	9,44	1,846	25,78	47,87	12,0	1,018

\[ \varepsilon_i = \sqrt{ \frac{1,840 \cdot 9,44} {1,840 \cdot 9,44 + 1,846 \cdot 47,87 \cdot 1,018} } \]

\[ \varepsilon_i = 0,403. \]

We were unable to compare the impact restitution coefficient for steel on bituminous coal obtained by us, because of the absence of works, or even experimental data, in this area.

Coefficient of Friction of Steel on Bituminous Coal and of Coal on Coal

To determine the coefficient of friction of steel on coal and the coefficient of friction of coal on coal, we used the apparatus of engineer I. R. Konyakhin. For carrying out the experiments, specimens were made from bituminous coal of the Cheremkhovo deposit and from bituminous coal of the Leninsk deposit in the form shown in Fig. 22 (a and b).

To investigate the coefficient of friction of steel on coal, the specimen of form a in Fig. 22 was made of steel. The experiment was conducted with a gradual increase of the load up to the moment of failure, which corresponded to the greatest value of the coefficient of friction.

Fig. 22

Fig. 23

We observed that the “instantaneous” coefficient of friction reached a value greater than the reading, but it existed for a very short time, approximately \(0,1 \div 0,5\) sec, and then fell and became established at the values indicated in the tables given below. The experiments were carried out at a magnification, on the scale of the optical setup, equal to 10000. The normal pressure on the specimen was \(N = 24,4\) kg; the force magnification \(\lambda = 15\), where \(P\) is the force read from the spring dynamometer of the apparatus, and 15 is the magnification scale.

The principal scheme of the experiment is shown in Fig. 23, where \(A\) is the lever transmitting the normal load \(N\); \(B\) is the lever setting the specimen in motion; \(C\) is the upper specimen, steel or bituminous-coal; \(D\)—

lower specimen of hard coal, \(E\)—a support with a conical slot for clamping specimen \(D\).

Table 33

Coefficient of friction of steel on Cheremkhovo hard coal

\(P_r\)	0	100	160	170	270	320	370	420	470	500
\(S_{\mathrm{load}}\)	0	5	10	15	20	25	30	35	40	45
\(S_{\mathrm{unload}}\)	—	—	—	—	—	—	—	—	—	0
\(P_r\)	540	580	615	640	670	695	720	738	730	738
\(S_{\mathrm{load}}\)	50	55	60	65	70	75	80	85	90	95
\(S_{\mathrm{unload}}\)	60	140	210	290	365	440	510	585	600	—

Unloading was carried out to the scale reading preceding the given value, and the magnitude of the force at that moment was noted.

Table 34

Coefficient of friction of Cheremkhovo hard coal on coal

\(P_r\)	0	110	180	240	310	360	420	470	520
\(S_{\mathrm{load}}\)	0	10	20	30	40	50	60	70	80
\(S_{\mathrm{unload}}\)	—	—	—	—	—	—	—	0	80
\(P_r\)	550	580	600	620	635	635	—	—	—
\(S_{\mathrm{load}}\)	90	100	110	120	130	140	—	—	—
\(S_{\mathrm{unload}}\)	170	260	350	440	530	—	—	—	—

Table 35

Coefficient of friction of Leninsk hard coal on hard coal

\(P_r\)	70	110	140	170	195	225	245	275	295	315	335	350
\(S_{\mathrm{load}}\)	10	20	30	40	50	60	70	80	90	100	110	120
\(S_{\mathrm{unload}}\)	—	—	—	—	—	—	—	—	—	—	0	10
\(P_r\)	370	385	405	420	435	445	460	465	475	480	490	490
\(S_{\mathrm{load}}\)	120	140	150	160	170	180	190	200	210	220	230	240
\(S_{\mathrm{unload}}\)	50	95	130	170	220	265	300	325	365	400	440	—

Table 36

Steel on Leninsk hard coal

\(P_r\)	0	110	210	300	365	425	470	515	540
\(S_{\mathrm{load}}\)	0	10	20	30	40	50	60	70	80
\(S_{\mathrm{unload}}\)	—	—	—	—	—	—	0	30	100
\(P_r\)	565	575	580	585	585	—	—	—	—
\(S_{\mathrm{load}}\)	90	100	110	120	130	—	—	—	—
\(S_{\mathrm{unload}}\)	180	280	370	470	—	—	—	—	—

From the data of Tables 33–36, the curves in Figs. 24 and 25 were constructed. The value of the coefficient of friction corresponding to the failure moment was determined by the formula

\[ f=\frac{T}{N} \tag{11} \]

Steel on Cheremkhovo bituminous coal

\[ f=\frac{T}{N}=\frac{0.738\cdot 15}{24.4}=0.454 \]

Fig. 24

Cheremkhovo bituminous coal on coal

\[ f=\frac{T}{N}=\frac{0.635\cdot 15}{24.4}=0.391 \]

Steel on Leninsk bituminous coal

\[ f=\frac{T}{N}=\frac{0.585\cdot 15}{24.4}=0.359 \]

Leninsk bituminous coal on coal

\[ f=\frac{T}{N}=\frac{0.490\cdot 15}{24.4}=0.328 \]

Fig. 25

We introduce a new concept, the “coefficient of elasticity,” representing the ratio of force to elastic displacement,

\[ k=\frac{T}{S_{\mathrm{el}}} \tag{12} \]

By elastic displacement we mean the displacement of the specimen upon unloading from \(P_{\max}\) to 0. Taking into account the magnification scale, equal to 10000, we shall obtain, for steel on Cheremkhovo bituminous coal,

\[ k=\frac{0.785\cdot 15\cdot 10000}{4.9}=24000\ \text{kg/cm}. \]

Cheremkhovo bituminous coal, along the angle

\[ k=\frac{0.635\cdot 15\cdot 10000}{6.8}=14000\ \text{kg/cm} \]

Leninsk bituminous coal, along the angle

\[ k=\frac{0.49\cdot 15\cdot 10000}{6.6}=11120\ \text{kg/cm} \]

Steel, according to Leninsk bituminous coal

\[ k=\frac{0.585\cdot 15\cdot 10000}{3.65}=24100\ \text{kg/cm} \]

Hardness of Bituminous Coal

(Static and impact)

The successful solution of the question of studying the behavior of bituminous coal under loading and unloading, the presence of a clearly expressed conical impression, and the possibility of measuring the diameter of the impression made it possible for us to pose the question of determining the hardness of bituminous coal by the method of indentation of a cone under comparatively small loads of \(0 \div 360\) g. The procedure for carrying out the test is set forth by us below. The force acting on the specimen during indentation of the cone was determined by formula 5

\[ Q=2.89P, \tag{5} \]

The load \(P=360\) g was determined by the travel of the micrometric tension screw (see Fig. 14). The diameter of the cone impression was measured in 2 directions (mutually perpendicular), and the mean value of the diameter was used in the calculation. Five experiments were carried out on specimens from each grade of coal.

Table 37

Bituminous coal	Average value of impression diameter I	Average value of impression diameter II	Average value of impression diameter III	Average value of impression diameter IV	Average value of impression diameter V	Adopted diameter
Cheremkhovo . . . . .	0.25	0.26	0.25	0.25	0.26	0.254
Prokopyevsk . . . . .	0.24	0.25	0.24	0.23	0.24	0.24
Leninsk . . . . .	0.27	0.28	0.27	0.26	0.28	0.272

The value of the static hardness was determined by the formula

\[ H_k=\frac{Q}{F_k}, \tag{13} \]

where \(Q\) is the greatest load on the specimen,
\(F_k\) is the area of the conical impression after removal of the load.

Cheremkhovo coal

\[ H_k=\frac{2.89\cdot 360\cdot 4}{3.14\cdot 0.254^2}=20.5\ \text{kg/mm}^2 \]

Prokopyevsk coal

\[ H_k=\frac{2.89\cdot 360\cdot 4}{3.14\cdot 0.24^2}=22.9\ \text{kg/mm}^2 \]

Leninsk coal

\[ H_k=\frac{2.89\cdot 360\cdot 4}{3.14\cdot 0.272^2}=17.8\ \text{kg/mm}^2. \]

At the same time, we introduce a new characteristic determining the static hardness of bituminous coal, which we propose to call the hardness modulus \(H_T\). By this term we mean the quantity

Fig. 26

of the ratio of the ordinate of the load to the abscissa of the elastic shear deformation after removal of the load.

Cheremkhovo coal

\[ H_T=\frac{0{,}36\cdot 2{,}89\cdot 2000}{125}=1600\ \text{kg}/\text{cm}^2 \]

Prokopyevsk coal

\[ H_T=\frac{0{,}36\cdot 2{,}89\cdot 2000}{55}=3770\ \text{kg}/\text{cm}^2 \]

Leninsk coal

\[ H_T=\frac{0{,}36\cdot 2{,}89\cdot 2000}{120}=1725\ \text{kg}/\text{cm}^2 \]

Here 2000 is the magnification scale (see Figs. 26–28).

We now turn to the question of determining the impact hardness of bituminous coal.

Fig. 27

Fig. 28

Impact Hardness

Numerous experiments carried out by a number of investigators—Goldschmidt, Kuznetsov, Levenson-Lessing [17], Schreiner [18], Epstein [19], and others—showed that the method of pressing in a ball on a Brinell press, or a cone and ball on a Rockwell durometer, is completely inapplicable for testing most rocks and, in particular, hard coals. The prism-indentation method was applied to certain rocks by E. F. Epstein [19]. The method of damping of the Herbert pendulum was used in the research work of P. A. Rebinder [20]. E. F. Epstein gave a formula for determining hardness by indentation of a prism:

\[ R_z=\frac{P}{S}, \tag{14} \]

where \(P\) is the pressure, \(R_z\) is the hardness.

\[ S=2h\,\operatorname{tg}\frac{\alpha}{2}\,b, \tag{15} \]

where \(h\) is the depth of penetration of the prism,
\(\alpha\) is the angle of sharpening,
\(b\) is the width of the prism.

L. A. Schreiner [18] came to the conclusion that, usually, because of the absence of simple and convenient methods, the hardness of rocks is not determined, although it is of exceptionally great importance for the mining industry, since in essence it is the sole criterion of the strength of rocks. He also showed that it is impossible to measure the hardness of brittle bodies, especially hard coal, by pressing in cones, prisms, or balls.

We set ourselves the task of determining the hardness of hard coal not by pressing in a cone, but by testing coal with a cone under the action of a live force.

For determining the impact hardness of hard coal we made an apparatus, shown in Fig. 29. The main part of this apparatus is a cone of hardened steel with a cone angle of \(90^\circ\). The impressions obtained from the blow of the cone were clearly visible and showed no signs of destruction (the presence of a conical pit was clearly seen under the microscope).

Fig. 29

As the measure of dynamic hardness we adopted the ratio

\[ H_z=\frac{A}{V}=\frac{Qh}{V}, \tag{16} \]

where \(H\) is the hardness under impact,
\(h\) is the height of rise of the striker in m,
\(Q\) is the weight of the striker in kg,
\(V\) is the volume of the pit in cm\(^3\).

In dimensionality \(H_z\) corresponds to impact toughness. In our case \(Q=0.842\) kg; the height of rise \(h\) varied within the limits from \(0.2\) cm to \(4.22\) cm. The volume of the pit was calculated by the formula:

\[ V=\frac{1}{3}F\cdot t, \tag{17} \]

where \(t\) is the depth and is equal to one-half the diameter of the indentation. The diameter of the indentation was measured with a Brinell measuring microscope with an accuracy of up to 0.005 mm. The following coals were tested: Leninsky, Anzhero-Sudzhensky, Khakassky, and Cheremkhovsky. For testing, plates measuring \(200 \times 100 \times 50\) mm were made from these coals. These plates were carefully ground until the surface showed no traces of cleavage cracks. The test results are summarized in Table 38.

Table 38

Coal	No. of experiment	\(Q\)	\(h\)	\(A\)	\(d\)	\(V\)	\(H_g\)	Notes / average
Anzhero-Sudzhensky	1	0,842	0,02	0,0168	1,1	\(175 \cdot 10^{-6}\)	96,00	220; Average excluding values marked +: 154
Anzhero-Sudzhensky	2	—	0,02	0,0168	0,9	\(95 \cdot 10^{-6}\)	177,00	220; Average excluding values marked +: 154
Anzhero-Sudzhensky	3	—	0,02	0,0168	0,95	\(112 \cdot 10^{-6}\)	150,00	220; Average excluding values marked +: 154
Anzhero-Sudzhensky	4	—	0,02	0,0168	0,75	\(55 \cdot 10^{-6}\)	325,00+	220; Average excluding values marked +: 154
Anzhero-Sudzhensky	5	—	0,02	0,0168	0,95	\(112 \cdot 10^{-6}\)	150,00	220; Average excluding values marked +: 154
Anzhero-Sudzhensky	6	—	0,02	0,0168	0,95	\(112 \cdot 10^{-6}\)	150,00	220; Average excluding values marked +: 154
Anzhero-Sudzhensky	7	—	0,04	0,0337	0,8	\(67 \cdot 10^{-6}\)	505,00+	220; Average excluding values marked +: 154
Anzhero-Sudzhensky	8	—	0,04	0,0337	0,45	\(112 \cdot 10^{-6}\)	301,00+	220; Average excluding values marked +: 154
Anzhero-Sudzhensky	9	—	0,04	0,0337	1,1	\(175 \cdot 10^{-6}\)	193,00	220; Average excluding values marked +: 154
Anzhero-Sudzhensky	10	—	0,04	0,0337	1,15	\(210 \cdot 10^{-6}\)	161,00	220; Average excluding values marked +: 154
Leninsky	1	0,842	0,02	0,0168	0,6	\(28 \cdot 10^{-6}\)	600,0	881; Average excluding values marked +: 715
Leninsky	2	—	0,02	0,0168	0,6	\(28 \cdot 10^{-6}\)	600,0	881; Average excluding values marked +: 715
Leninsky	3	—	0,04	0,0337	0,6	\(36 \cdot 10^{-6}\)	1210,0	881; Average excluding values marked +: 715
Leninsky	4	—	0,04	0,0337	0,65	\(36 \cdot 10^{-6}\)	938,0	881; Average excluding values marked +: 715
Leninsky	5	—	0,04	0,0337	0,70	\(45 \cdot 10^{-6}\)	748,0	881; Average excluding values marked +: 715
Leninsky	6	—	0,044	0,0372	0,85	\(81 \cdot 10^{-6}\)	460,0	881; Average excluding values marked +: 715
Leninsky	7	—	0,076	0,0640	0,7	\(45 \cdot 10^{-6}\)	1420,0+	881; Average excluding values marked +: 715
Leninsky	8	—	0,076	0,0640	0,8	\(67 \cdot 10^{-6}\)	956,0	881; Average excluding values marked +: 715
Leninsky	9	—	0,076	0,0640	0,8	\(67 \cdot 10^{-6}\)	956,0	881; Average excluding values marked +: 715
Leninsky	10	—	0,076	0,0640	0,9	\(95 \cdot 10^{-6}\)	675,0	881; Average excluding values marked +: 715
Leninsky	11	—	0,105	0,0881	1,1	\(175 \cdot 10^{-6}\)	505,0	881; Average excluding values marked +: 715
Khakassky	1	0,842	0,02	0,0168	0,9	\(95 \cdot 10^{-6}\)	177,0	201; Average excluding values marked +: 137
Khakassky	2	—	0,02	0,0168	0,9	\(95 \cdot 10^{-6}\)	177,0	201; Average excluding values marked +: 137
Khakassky	3	—	0,02	0,0168	1,1	\(175 \cdot 10^{-6}\)	96,0	201; Average excluding values marked +: 137
Khakassky	4	—	0,02	0,0168	0,95	\(112 \cdot 10^{-6}\)	150,0	201; Average excluding values marked +: 137
Khakassky	5	—	0,02	0,0168	1,1	\(175 \cdot 10^{-6}\)	96,0	201; Average excluding values marked +: 137
Khakassky	6	—	0,02	0,0168	0,7	\(45 \cdot 10^{-6}\)	374,0	201; Average excluding values marked +: 137
Khakassky	7	—	0,05	0,0422	1,35	\(322 \cdot 10^{-6}\)	131,0	201; Average excluding values marked +: 137
Khakassky	8	—	0,076	0,0640	1,5	\(520 \cdot 10^{-6}\)	119,0	201; Average excluding values marked +: 137
Khakassky	9	—	0,132	0,111	1,3	\(288 \cdot 10^{-6}\)	386,0+	201; Average excluding values marked +: 137
Khakassky	10	—	0,257	0,217	1,75	\(700 \cdot 10^{-6}\)	310,0+	201; Average excluding values marked +: 137
Cheremkhovsky	1	0,842	0,02	0,0168	0,5	\(16 \cdot 10^{-6}\)	1050	1550; Average excluding values marked +: 1610
Cheremkhovsky	2	—	0,04	0,0337	0,5	\(16 \cdot 10^{-6}\)	2201	1550; Average excluding values marked +: 1610
Cheremkhovsky	3	—	0,076	0,0640	0,5	\(16 \cdot 10^{-6}\)	4000+	1550; Average excluding values marked +: 1610
Cheremkhovsky	4	—	0,105	0,0884	0,75	\(55 \cdot 10^{-6}\)	1610	1550; Average excluding values marked +: 1610
Cheremkhovsky	5	—	0,114	0,0961	0,8	\(67 \cdot 10^{-6}\)	1460	1550; Average excluding values marked +: 1610
Cheremkhovsky	6	—	0,164	0,1380	1,0	\(131 \cdot 10^{-6}\)	1050	1550; Average excluding values marked +: 1610
Cheremkhovsky	7	—	0,204	0,1720	0,9	\(95 \cdot 10^{-6}\)	1815	1550; Average excluding values marked +: 1610
Cheremkhovsky	8	—	0,204	0,172	1,5	\(520 \cdot 10^{-6}\)	331+	1550; Average excluding values marked +: 1610
Cheremkhovsky	9	—	0,204	0,172	1,3	\(288 \cdot 10^{-6}\)	598+	1550; Average excluding values marked +: 1610
Cheremkhovsky	10	—	0,280	0,236	0,95	\(112 \cdot 10^{-6}\)	2110	1550; Average excluding values marked +: 1610
Cheremkhovsky	11	—	0,280	0,236	1,3	\(288 \cdot 10^{-6}\)	822	1550; Average excluding values marked +: 1610
Cheremkhovsky	12	—	0,280	0,236	0,9	\(95 \cdot 10^{-6}\)	2480	1550; Average excluding values marked +: 1610
Cheremkhovsky	13	—	0,422	0,355	1,65	\(588 \cdot 10^{-6}\)	604+	1550; Average excluding values marked +: 1610

The conclusion that can be drawn from these data is as follows. The impact hardness of coal as a function of the work \(A_{\mathrm{ud}}\) is expressed by the graphs shown in Fig. 30.

Fig. 30. Dynamic-hardness curve of coal.
Visible labels in the figure include: \(H_{\mathrm{ud}}\); \(N\) of the experiment; Anzhero-Sudzhensk; Leninsk; Khakass; Cheremkhovo; \(H_{\mathrm{ud}} = 1610\); \(H_{\mathrm{ud}} = 164\); \(H_{\mathrm{ud}} = 137\).

As average values of the hardness of coal under impact, one may take

\[ \begin{aligned} \text{Anzhero-Sudzhensk coal} \qquad & H_g = 154,\\ \text{Leninsk coal} \qquad & H_g = 715,\\ \text{Khakass coal} \qquad & H_g = 137,\\ \text{Cheremkhovo coal} \qquad & H_g = 1610. \end{aligned} \]

General Conclusions

The work we have carried out is the first attempt to study certain physico-mechanical properties of the coals of the Kuzbass mines and the Cheremkhovo deposits. In our work we touched upon a number of questions of exceptional practical importance, such as, for example, the question of the moduli of normal and tangential elasticity; the question of the ultimate resistance of coals to failure; the question of the plastic properties of coals; the question of the coefficient of friction of coal on steel and coal on coal; and the question of the static and dynamic hardness of coals. We have shown a number of methods of investigation. Especially broad possibilities for the study of coals are opened up by the use of the apparatus of engineer I. R. Konyakhin. The work does not claim that it has already solved the question, but proceeds from the basic premise that only the first attempt at solving the problem has been made.

In conclusion, I consider it my duty to express gratitude to the senior lecturer of the Department of Strength of Materials of the Tomsk Polytechnic Institute, Comrade I. R. Konyakhin, for kindly placing at our disposal an apparatus of his design, and also to docents A. I. Aleksandrov and A. A. Belitsky for consultations in the course of carrying out this work on questions connected with the geology of coal deposits.

References

1. Adams and Gibson—see the reference in A. I. Medvedko’s work “The Mechanism of Rock Failure.”

2. Phillips—see the reference in A. I. Medvedko’s work.

3. M. V. Klassen-Neklyudova. Plastic Properties and Strength of Crystals, 1934.

4. P. K. Murzin. On the question of calculating coal-cutting machines. Coal, No. 106–107, pp. 123–126, 1934.

5. Prof. L. V. Levenson. Machines for Beneficiation.

6. A. A. Peskovatskii. The normal modulus of elasticity of hard coal. Coal, No. 90–91, p. 144, 1933.

7. M. M. Protodyakonov. Theory of Cutting Coal with Chain Coal-Cutting Machines. ONTI, NKTP, USSR, pp. 56–69, 1936.

8. Prof. P. S. Kuzmin. Elevators, Transmissions, Conveyors, 1929.

9. Prof. A. S. Il’ichev. Theory and Calculation of Mine Oscillating Conveyors, p. 7, 1932.

10. Eng. V. A. Mirov. On the dynamic operating regime of coal-cutting machines. Mining Journal, No. 8, p. 10, 1934.

11. Prof. V. I. Belov. Analytical study of the efficiency of the operation of the bits of coal-cutting machines. Proceedings of the Donetsk Mining Institute, Vol. II, p. 6, 1926.

12. V. M. Ogievskii. Thermal parameters of rocks and stowing materials. Mining Journal, No. 10, 1949.

13. N. I. Gvozdeva. Coals of the Moscow Region Basin and Their Classification According to Physicomechanical Properties. Ugletekhizdat, 1948.

14. A. V. Yatsenko. A lever device for determining the strength of rocks. Mining Journal, No. 9, pp. 7–11, 1934.

15. I. R. Konakhin. Investigation of the Plastic Properties of Materials under Contact Action of Surfaces, 1950.

16. V. P. Shubin. Elucidation of the Regularities of Elastic-Plastic Local Deformations and Their Relation to the Coefficient of Restitution under Impact, 1950.

17. Levenson-Lessing. Petrography, 1935.

18. L. A. Schreiner. The Hardness of Rocks and Its Significance in the Drilling Process, 1943.

19. E. F. Epstein. Theory of Drilling and Cutting Rocks with Hard Alloys, 1939.

20. L. A. Rebinder. Report at the VI Congress of Physicists, 1928.