Journal of Mining Science, Vol. 44, No. 4, 2008

ROCK FAILURE PARAMETERS FOR IMPACT FRACTURE OF BRITTLE MATERIALS BY PLASTIC SUBSTANCES

A. P. Tapsiev and D. A. Tsygankov

UDC 622.234.4:622.236.4

The paper describes the theoretical and experimental data on fracturing brittle materials with the use of plastic substances. The authors substantiate a method of calculating a fracture dimension depending on the characteristics of the plastic substance applied and the fractured material. It is recommended on the selection of impact fracturing equipment. Hole, plastic substance, rod, impact device, injection, fracture, crack

Rock fracture with the use of plastics is a new field of geomechanics and has not yet been well studied. This results in wrong determination of sizes of cracks and improper choice of fracturing devices. The incipient theoretical investigations into the impact fracture of brittle materials by using plastic substances can not provide the basis for calculating mining technology parameters. In this connection we think it is useful for practical purposes to judge from theoretical findings gained in the static fracture of brittle materials by plastics subject to a small difference between the calculated and experimental results. One of related approaches is based upon studying the quasi-static injection of a ductile substance into a crack. It is supposed that this plastic moves in the crack as an organic whole except for a thin plastic layer that touches the crack walls. The sliding friction arises in this layer and promotes its heat and movement. Currently it is only known that under limit equilibrium of a plastic substance, when it stops moving in the crack due to suspension of the injection and the pressure differential loss, the immobile ductile material may conventionally be taken as a solid medium. Under impact injection, a plastic will always have a resistance higher than under the static injection, as per the law of inertia. Therefore, amount of a plastic substance for the impact injection is always less than for the static. In this context we calculate theoretically the maximum capacity size of a plastic so that to form a crack of the pre-set dimension. Since there are no equations describing the equilibrium condition of a plastic in a crack, we use the equation of a plastic in a pipe or a slot with a planar front [2]: dP T =− , (1) dX W where P is pressure in a plastic in the radial X-direction; Τ is shear stress on the walls of a pipe (slot with a planar front) on exceeding which the plastic transfers to fluidity; W is crack half-opening. Institute of Mining, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 4, pp. 43-59, July-August, 2008. Original article submitted April 10, 2008. 1062-7391/08/4404-0363 ©2008 Springer Science + Business Media, Inc. 363

The plastic front with coordinate X = R is slower than the crack front. There is no pressure behind the plastic substance front: P( X ) = 0 , X > R . The crack half-opening is found with the help of [1]:

2 ⎡ 2 2 −1 / 2 W (X ) = ( X 22 − X 22 ) −1 / 2 dX 2 + ⎢ ∫ X 1P( X1 ) dX1 ∫ ( X 2 − X ) π D ⎣⎢ 0 X X

(2)

⎤ + ∫ X 1P( X 1 ) dX 1 ∫ ( X 22 − X 2 ) −1 / 2 ( X 22 − X 12 ) −1 / 2 dX 2 ⎥ ; ⎥⎦ X X1 L

here, L is crack radius;

L

L

D=

E , 2(1 −ν 2 )

(3)

where E is Young’s modulus and ν is Poisson’s ratio. The needed plastic capacity size Ω [1]: R

Ω = 4π ∫ XWdX .

(4)

0

To simplify (1) – (4) we may introduce dimensionless parameters and avoid some intermediate calculations. To do this, we introduce scale multipliers for the main parameters of fracturing a brittle material by a plastic substance and furnish them with lower case characters [1]:

Ω* = 4πL2 W* , W* =

LT π , P* = DT . 2 P*

(5)

We change to the dimensional capacity size Ω via the scale multiplier Ω* by the formula [1]: Ω = Ω*ω ,

(6)

where ω is dimensionless capacity size of the plastic and it depends on the volume filling γ of the crack [1]. The formula for the crack radius L ensues from (5) and (6): L=3

Ω . 4ω (2π T / D) 0.5

The parameter ω can be found with the help of the relationship in Fig. 1 [1].

Fig. 1. Theoretical relationship between the dimensionless capacity size ω of injected plastic and the volume filling γ of the crack 364

(7)

Fig. 2. Experimental crossplot for longitudinal crack radius L and its volume filling γ 0 with plasticine

To use the relationship in Fig. 1 in practical fracture of brittle materials where the crack can not be seen, we should pre-set the crack volume filling γ . As a reference, for a crack, it is possible to use the data of finding γ 0 in the experimental fracture of organic glass (RF State Standard 15809-70) with the use of plasticine (RF State Standard 6 15-1525-86) as is shown in Fig. 2. To compare the theoretical approach (1) – (7) and practical data, we carried out laboratory impact fracture of organic glass with the use of plasticine. First we determined a shear stress on the pipe walls, T0 , after exceeding which plasticine transfers to fluidity. With this object in mind, we measured pressure p0 on plasticine in the pipe, after going beyond this pressure the plasticine changes to the fluidity. Figure 3 demonstrates the pressure measurement device. In the center of organic glass cylinder 1 with a diameter of 134 mm and a height of 100 mm, we drilled 16 mm-diameter through vertical hole 2 and inserted a metal adapting pipe 3 on the upper side of the cylinder. The pipe contained machine oil retained by a fitted cylindrical piston for attachment of manometer 4. On the bottom side of the cylinder, we inserted injector 5 into the hole. The injector contained plasticine 6. Using handwheel 7, rod 8 and cylindrical piston, we displaced plasticine outward through a side hole 9 with a diameter of 9 mm. The pressure p0 was indicated by manometer 4 at the moment when plasticine displacement through the side hole was visible.

Fig. 3. Pressure measurement device 365

Fig. 4. Impact fracturing of organic glass block by injection of plasticine with a steady and unsteady flow

Using experimentally obtained p( p0 ) , we calculate stresses T (T0 ) :

p ( p0 ) ρ , (8) 2λ where ρ and λ are, respectively, cross-sectional radius and length of horizontal side hole 9 (refer to Fig. 3). The laboratory impact fracturing of organic glass with the use of plasticine injected as a steady and unsteady flow was carried out on a block with dimension 600×580×210 mm (Fig. 4). Block 1 was fractured with the use of cylindrical metal rod 2 inserted into vertical hole 3. We impacted the rod head 4 with metal load 5 falling vertically down on rod 6. The end of rod 2 had two tungsten-carbide inserts to generate stress concentrator on the walls of hole 3. The stress concentrator had the form of two 1 mm deep diametral cuts. The rod end angle was 2 – 25º. By varying blow energies and frequencies of metal load 5, we obtained different flows of plasticine injection. We determined a total capacity size of injected plasticine, that corresponded to the current crack radius 7 depending on the plasticine fill zone radius 8. Plasticine was injected through hole 9 in rod 2 intruded in vertical hole 3. The experimental results are displayed in Fig. 5. T (T0 ) =

Fig. 5. Comparison of the theoretical and experimental data of impact fracturing of organic glass by plasticine injection: 1 — theory; 2 — experiment 366

TABLE 1. Data for Plotting Theoretical Curve 1 in Fig. 5 Point number

L, mm (experiment, Fig. 2)

γ = γ0 , % (experiment, Figs. 1 and 2)

ω (Fig. 1)

Ω, mm3 (9)

1

18

95

1

152

2

46

90

1

2531

3

74

85

1

10536

4

102

80

1

27591

5

120

75

1

44928

6

153

70

1

93121

7

186

65

1.01

168979

8

219

60

1.02

278551

9

247

55

1.04

407472

10

280

50

1.08

616412

11

293

45

1.15

752097

12

300

40

1.29

905580

Theoretical curve 1 in Fig. 5 was plotted based on formula (9) derived from (7): Ω = 4ω

2π T 3 L. D

(9)

We calculated using the data compiled in Table 1 with the following characteristics of organic glass and plasticine: E = 3.3 GPa, ν = 0.33 , D = 1852 MPa, p0 = 378.2 KPa; T0 = 12.7 KPa. The analysis of the curves in Fig. 5 shows that under constant plasticine flow (dark points in the curves), the difference between the theoretical and experimental results is minimal, less than 12 %. Under unsteady plasticine flow (the rest points in the curves), this difference is maximal and ranges from 13 to 45 %). In practical studies into formation of a cross crack in an opaque brittle material when its propagation is invisible, it is possible to refer to the values of volume filling γ 0 experimentally obtained on fracturing organic glass with plasticine (Fig. 6).

Fig. 6. Experimental crossplot of the cross crack radius L and its volume filling γ 0 with plasticine 367

Fig. 7. Impact cross fracturing of organic glass by plasticine injection as a steady and unsteady flow

We carried out the experimental cross fracturing of an organic glass block with a diameter of 134 mm and a height of 10 mm as is shown in Fig. 7. In block 1 we intruded cylindrical metal rod 2 abut on a fitted piston inside injector 3 inserted into vertical hole 4. Plasticine was injected into the formed crack through hole 5. Rod 2 was impacted with a falling load. Varying the blow energies and frequencies resulted in the steady and unsteady flows of plasticine. We determined a total plasticine capacity size corresponding to the current crack radius 6 depending on the crack filling zone radius 7 (Fig. 8). We plotted theoretical curve 1 in Fig. 8 with the help of formula (9). The data used for the calculation agree with those in Table 1. The analysis of the data in Fig. 8 shows the minimal difference between the theoretical and experimental curves, less than 12 % under the constant flow injection of plasticine (dark points in the curves) and the maximal difference in a range of 67 – 26 % under the unsteady flow injection (the rest points in the curves).

Fig. 8. Theoretical (1) and experimental (2) curves for impact cross fracturing of organic glass by plasticine injection 368

TABLE 2. Data for Plotting Theoretical Curve 1 in Fig. 8 Point number

L, mm (experiment, Fig. 2)

1 2 3 4 5 6 7 8 9 10 11 12

11 20 27 29 31 33 40 58 62 63 65 66

γ = γ0 , % (experiment, Figs. 1 and 2) 90 85 80 75 70 65 69 55 50 45 40 35

ω (Fig. 1)

Ω, mm3 (9)

1 1 1 1 1 1.01 1.01 1.04 1.08 1.15 1.29 1.6

35 208 512 634 774 944 1680 5276 6692 7476 9210 11960

We studied the effect of the impact fracturing with a varied energy in the course of impact injection of a plastic substance into a space between two parallel flat surfaces. Two organic glass cylinders 1 with diameters of 134 mm and heights of 50 mm were connected by bolts 2 and screws 3. Four metal spacers 4 with heights of 0.5 mm provide clearance 5. One of the blocks 1 has a 16 mm diameter vertical through hole 6 with installed injector 7 filled with a plastic substance, Litol 24 (RF State Standard 21150-87) as is illustrated in Fig. 9. By using a falling metal load 1.29 kg in weight, we impacted rod 8 with an energy of 18.98 J transferred to the piston inside injector 7. This introduced Litol 24 into clearance 5 via hole 9. The spread zone of the injected Litol 24 had a diameter of 72 mm and a capacity size of 1232 mm3. To obtain the same diameter of the Litol 24 spread zone by a series of impacts with a lower energy, we carried out three experiments with the use of the device in Fig. 9. The first experiment energies ranged from 0.13 to 0.88 J. Litol 24 had spread zone 10 with a diameter of 68 mm and capacity size of 1062 mm3, this required 7 impacts with a total energy of 3.54 J (Fig. 10).

Fig. 9. Experimental device for injection of Litol 24 into the clearance between two parallel flat surfaces 369

Fig. 10. First experiment on Litol 24 injection by 7 impacts with an energy ranging from 0.13 to 0.88 J

Fig. 11. Second experiment on Litol 24 injection by 4 impacts with an energy from 0.13 to 1.52 J

Analyzing the first experiment showed that when we generated identical spread zones of injected Litol 24 by impacting with a lower energy, the total energy reduced by a factor of 5.4. The second experiment impacts had energies from 0.13 to 1.52 J. The Litol 24 spread zone in clearance 5 was 68 mm in diameter, the plastic capacity size was 1062 mm3, we carried out 4 impacts with the total energy of 3.17 J (Fig. 11). Hence, the same spread zone of the plastic material was reached by impacting with the lower energy, and the total energy decreased by a factor of 6. We checked the tendency revealed by carrying out a series of impacts within even lower energy range from 0.13 to 1.01 J. In this case, the spread zone of Litol 24 in the clearance was 70 mm in diameter, the plastic capacity size was 1145 mm3, we made five impacts with the total energy of 3.41 J. The total energy reduced by a factor of 5.6, the experimental results are in Fig. 12. The analysis of data in Fig. 12 implies that a series of impacts with a lower energy for the formation of a plastic spread zone in the clearance between two flat surfaces results in that the total energy consumption is multifold cut down.

Fig. 12. Total energy versus unit impact energy for the case of formation of the Litol 24 spread zone in the clearance between two flat surfaces such that the spread zones have the same dimension: 1 — unit impact with 18.98 J; 2 — series of impacts with 0.13 to 1.52 J; 3 — series of impacts within 0.13 to 1.01 J; 4 — series of impacts within energy range from 0.13 to 0.88 J 370

The commercially applied method of fracturing a stone with the use of plastic substances is impact rather than static. In this case, there is no need to use expensive and large-dimension injection systems, blasthole sealing, adapt different-purpose equipment, as well as less efforts and time is spent. Lightweight percussive devices for the impact fracturing are advantageous for keeping up the other production processes, operation in a cramped environment, economical efficiency due to small dimension and operating front, lower operating costs and high safety [3, 4]. An impact device for the operation is chosen based on the calculation and experimental justification of the impact energy. An approximate impact energy for injecting a plastic substance into a crack may be calculated from the relation: ( P − P1 )V W = , (10) k1 where P is total pressure in the plastic at the impact point and this pressure is sufficient for crack growth at this point; P1 is component of P, generated by joint impact device and man action on the plastic; V is plastic substance capacity size injected into the crack per one impact; k1 is energy loss in the impact system. The total pressure P in the longitudinal crack (refer to Fig. 13a) is found as: P = P0

(11)

P = P0 + k 2 f ( x, t ) ,

(12)

and in the cross crack (refer to Fig. 13b) as: here, P0 is pressure required at the plastic injection point in order to make crack 1 grow; k 2 factor of Τ to T0 ratio; f is function of pressure distribution in plasticine, depending on distance x from the contact point 2 of rod 3 of impact device 4 and plasticine 5 to the plasticine injection point in crack 1 and on the impact-to-impact time t (Fig. 13).

Fig. 13. Framework of the formation of (a) longitudinal and (b) cross crack in a brittle material by impact with the use of plastic substances and light impact devices: 1 — plastic injection point in the crack; 2 — contact of rod 3 of impact device 4 and plastic substance 5 in hole 6; 7 — generated crack; 8 — tungsten carbide insertions; 9 — stress concentrators on the hole walls under the impact device rod intrusion; 10 — crack radius; 11 — plastic filling zone radius in the crack 371

In case when the operation procedure includes stress concentrators on the walls of a hole: P0 < σ t ,

(13)

where σ t is tensile strength of brittle material. In case that the concentrators are unnecessary: P0 = σ t .

(14)

k 2 = T / T0 .

(15)

Factor k 2 is calculated by the formula:

The component of the total pressure arising in the plastic substance due to the joint action of an impact device and a man is: P1 =

4( P2 + P3 )

, (16) πd 2 where P2 is force (weight) generated by impact system; P3 is force generated by man pressing on impact device; d is hole diameter (refer to Fig. 13). As per the vibration safety standards, the force P3 = 200 N. The plastic capacity size V injected in the crack per one impact is calculated from the formula: π d 2h , (17) V = 4 where h is intrusion of rod 3 into hole 6 per one impact (Fig. 13). A laboratory experimental method to determine h is to carry a unit impact (a series of impacts and then re-calculation of an average intrusion of rod 2 into hole 3 per one impact) by a falling load 5 on the rod end 4 (according to Fig. 4). The rod shape and the fractured material characteristics should be maximum compatible to the pre-planned in situ conditions. Here, we take into account hole diameter d; availability (absence) of the impact rod end angle and its actual value; availability (absence) of tungsten carbide insertions on the rod; desired spatial orientation of the crack (as is in Fig. 13); elastic properties of the material (E and ν); as well as parameters of inexplicit importance for the fracture process and their characteristics are impossible to calculate with a desired accuracy. The factor of energy loss in the impact system: k1 = e −2(α l +α n ) , (18) 1

2

where α1 is energy loss in the rod structure per 1 m of its length(for round drill steel, α1 = 0.4 m–1); α 2 is energy loss in one joint of the rod structure (for round drill steel, α 2 = 2 ); l is rod structure length; n is number of joints in the rod structure [5]. Considering the experimentally found function of pressure distribution in plasticine [6], formula (12) acquires the following form: P = P0 + k 2 (5.26 + 0.96 x + 1.46 log t ) . (19) It is practically expedient to express the impact-to-impact time in terms of the impact device rating characteristic f as: 1 (20) t= , f where f is impact frequency. 372

TABLE 3. Experimental Results of Fracturing Marmorized Limestone with the Use of Plastics Plastic capacity size

Impact energy

Specimen

Experiment, × 10-5, mm3

Calculation, × 10-5, mm3

Experiment and calculation difference, %

Experiment, J

Calculation, J

Experiment and calculation difference, %

1 2 3

2.21 1.18 1.41

2.29 1.16 1.42

3.5 1.7 0.7

41.2 41.2 41.2

41.26 44.4 38.1

– 0.14 – 7.2 7.5

In order to explain the results of commercial experiments carried out in mining and construction, we test-calculated dimensions of cracks depending on the injected plastic capacity size and found the unit impact energies of impact devices. Comparison of the obtained data was made with (1) – (8) and (10) – (20). In the capacity of plastic substance for the in situ conditions, we used a powdered clay and water mixture and made an analogous sample of the mixture for the laboratory experiment as shown in Fig. 3. In situ we determined the capacity size of the plastic into the crack by intrusion h (17) of rod 3 (Fig. 13) into the fractured material and then refined this value after the fracturing completion. The experimental impact longitudinal fracturing was carried out on three monolithic marmorized limestone blocks with dimensions 900×580×240 mm, 800×470×250 mm and 850×500×240 mm, respectively, characterized with high natural jointing. We used a coal hammer 4 (MO-7, 41.2 J, 18.3 Hz) with a specially adapted rod 3 having two tungsten carbide insertions 8. The hole 6 was 16 mm in diameter and 400 mm deep. The crack orientation was under control of stress concentrators 9 formed in the walls of hole 3 by intruding rod 3. As a result, we formed 3 cracks with radii 10 of 290 mm, 235 mm and 250 mm (as in Fig. 13). The calculated capacity size of the injected plastic material was higher than the experimental value (radius 11 in Fig. 13) by 0.7 – 3.5 %. In two cases, the unit impact energy in practice was lower than the calculated unit impact energy by 0.14 and 7.2 %, while in the third cаse, it was higher by 7.5 %. Table 3 presents the data on the experiments in mining industry. The plastic capacity size (Table 3) was calculated with the use of (9) and the data from Table 4. The marmorized limestone and plastic substance had the following characteristics: E = 22 GPa; ν = 0.23; D = 11.6 GPa; p = 253.1 KPa; Τ = 8.5 KPa. The volume filling γ (Table 4) was found experimentally as a ratio of volumes characterizing the ellipsoids of revolution, one of the ellipsoids described the crack and the other — the zone of the crack filling with plastic substance, by using the formula: ab (21) γ = 100 1 1 , %, a 2 b2 where a1 and b1 are, respectively, semimonor and semimajor axes of the ellipsoids for the filling zone in the crack; a 2 and b2 are the same for the crack. The measurements were taken after the fracturing completion. TABLE 4. Data for Calculation of Plastic Capacity Size in Table 3 Specimen

L, mm (experiment)

γ = γ0 , % (experiment, (21), Fig. 1)

ω (Fig. 1)

Ω, × 10-5, mm3, (9)

1 2 3

290 235 250

49 55 54

1.09 1.04 1.05

2.29 1.16 1.42 373

TABLE 5. Data for Calculation of Impact Energy in Table 3 Specimen

h, mm, (experiment)

V, mm3, (17)

t, s, (20)

P0, MPa, (13)

P, MPa, (11)

P1, MPa, (16)

k1, (18)

W, J, (10)

1 2 3

0.13 0.14 0.12

26.1 28.1 24.1

0.055 0.055 0.055

20 20 20

20 20 20

1.53 1.53 1.53

0.012 0.012 0.012

41.3 44.4 38.1

The impact energies in Table 3 were calculated with the use of data compiled in Table 5. For the parameter k1 (18), we assumed that l = 0.5 m and n = 1. The cross crack formation in a brick wall 300 mm thick was experimentally studied on the construction practice. We carried out three experiments with coal hammer 4 (MO-10, 44.1 J, 20 Hz), special metal pipe having an internal diameter of 20 mm and a length of 400 mm, lubricated inside with machine oil and filled with a plastic substance. As a result, we formed three cracks with a radius of 150 mm each (by the scheme in Fig. 13). The calculated capacity size of the plastic substance exceeded the experimentally obtained size by 3.6 – 3.9 %. In two cases the actual unit impact energy was higher by the calculated value by 8.4 and 12.5 %, while in the third case it was lower by 3.9 %. The experimental results gained in the construction are given in Table 6. The capacity sizes of plastic substance in Table 6 were calculated with the use of (9) and data from Table 7. The common brick and plastic substance had the following characteristics: averaged E = 12 GPa (common brick has E1 = 2 – 4 GPa, cement-based concrete E 2 = 16 – 26 GPa; ν = 0.19 ; D = 6.2 GPa; p = 253.1 KPa; Τ = 8.5 KPa. The unit impact energies in Table 6 were calculated with the data from Table 8, and for the parameter k1 (18), we used l = 0.5 m and n = 1. TABLE 6. Experimental Results of Fracturing a Brick Wall with the Use of a Plastic Substance Plastic capacity size Specimen

Experiment, × 10-5, mm3

Calculation, × 10-5, mm3

1 2 3

3.29 3.28 3.28

3.16 3.16 3.16

Unit impact energy Experiment and calculation difference, % 3.9 3.6 3.6

Experiment, J

Calculation, J

44.1 44.1 44.1

40.4 38.6 45.9

Experiment and calculation difference, % 8.4 12.5 – 3.9

TABLE 7. Data for Calculation of Plastic Capacity Size in Table 6 Specimen

L, mm (experiment)

γ = γ0 , % (experiment, (21), Fig. 1)

ω (Fig. 1)

Ω × 10-5, mm3, (9)

1 2 3

150 150 150

23 23 23

7.8 7.8 7.8

3.16 3.16 3.16

TABLE 8. Data for Calculation of Unit Impact Energy in Table 6 Specimen

1 2 3 374

h, mm (experiment)

V, mm3, (17)

t, s, (20)

P0, MPa, (14)

k2, (15)

P, MPa, (19)

P1, MPa, (16)

k1, (18)

0.22 0.21 0.25

69.1 65.9 78.5

0.05 0.05 0.05

8 8 8

0.067 0.067 0.067

8 8 8

0.98 0.98 0.98

0.012 0.012 0.012

W, J, (10)

40.4 38.6 45.9

CONCLUSIONS

1. It is possible to calculate the dimension of a crack formed under impact fracturing with the use of a plastic substance on the basis of principles of quasi-static plastic material injection. The thus calculated crack dimensions and plastic capacity sizes will correspond to the maximum values. 2. The low calculation errors may be reached by using an injection mode of the small and constant flow of a plastic substance, which will release from the processes contributing to the plastic transfer from the plastic stage to fluidity. 3. The total energy spent to form a fracture with the use of a plastic substance increases with the growing impact energy of an impact device, given the unit impact energy is sufficient to initiate the cracking process. 4. Formation of a cross crack at the level of hole bottom requires an impact device having the larger unit impact energy as compared with a longitudinal crack formation lengthwise the hole, the other conditions being equal. 5. The authors have put forward and experimentally tested an empirical relationship between a unit impact energy and an average capacity size of a plastic material injected into the crack per one impact. This relationship allows assessment of the impact fracturing efficiency in a brittle material with the use of a plastic substance. 6. The development of the impact fracturing technologies for brittle materials and plastic substances should be based on the advantages of the light impact devices having the unit impact energy no higher than 100 J. REFERENCES

1. O. P. Alekseenko and A. M. Vaisman, “Propagation of a round hydrofracture in an elastic space under plastic material injection,” Prikl. Matem. Mekh., 57, No. 6 (1993). 2. V. V. Sokolovsky, The Plasticity Theory [in Russian], Vyssh. Shk., Moscow (1969). 3. D. A. Tsygankov, “New rock breaking method,” Russian Mining, No. 3 (2005). 4. D. A. Tsygankov, “New technologies of the directional fracturing in construction,” Izv. Vuzov, Stroit., No. 9 (2004). 5. K. I. Ivanov, Drilling Method for Mineral Mining [in Russian], Nedra, Moscow (1975). 6. N. G. Kyu and D. A. Tsygankov, “Method for directional failure of rocks by plastic substances,” Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 6 (2003).

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