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Directional fracturing by slotting-blasting-caused stress wave form changes
Accepted Manuscript
Directional Fracturing by Slotting-Blasting-Caused Stress Wave Form Changes Chengwei Liu , Yiyu Lu , Binwei Xia , Peng Yu PII: DOI: Reference:
S0734-743X(18)30576-1 https://doi.org/10.1016/j.ijimpeng.2019.02.002 IE 3236
To appear in:
International Journal of Impact Engineering
Received date: Revised date: Accepted date:
7 June 2018 28 January 2019 11 February 2019
Please cite this article as: Chengwei Liu , Yiyu Lu , Binwei Xia , Peng Yu , Directional Fracturing by Slotting-Blasting-Caused Stress Wave Form Changes, International Journal of Impact Engineering (2019), doi: https://doi.org/10.1016/j.ijimpeng.2019.02.002
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Highlights
Discussed the mechanism of directional stress concentration in material tip caused by Stress Wave Form Changes.
Discussed the mechanism of directional fracture overcome deflection control of the static stress field. Observing stress wave propagation in materials using high-speed cameras.
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Directional Fracturing by Slotting-Blasting-Caused Stress Wave Form Changes Chengwei Liu 1,2, Yiyu Lu 1,2, Binwei Xia 1,2,* and Peng Yu 1,2 State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China 2 College of Resources and Environmental Science, Chongqing University, Chongqing 400030, PR China * Correspondence: [email protected]; Tel.: +86 13508382008 1
Received: date; Accepted: date; Published: date
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Abstract: Slotting blasting is widely used for directional fracture in geotechnical engineering. Due to limited research methods, the basic propagation theory of stress waves has not yet been applied in the literature to explain directional fracturing mechanism. In this work, the stress wave propagation during slotting blasting has been analysed, and through the dynamic caustics blasting experiments, the blastings in circular-holed, square-holed and slotting-holed specimens have been contrast-analysed, the propagation of stress waves and the explosion cracks have been observed. The theoretical and experimental results show that ①As the shock wave reached the slotting tip, based on “Huygens principle”, it separated into two independent waves symmetric to the median axis of the slotting tips and transmitted in different directions, due to directional stress concentration in materials. The directional fracture zone and directional damage zone were formed as the stress wave is attenuated during propagation; ②Observed in the experiment. The stress waves, which propagated outward in concentric circles, in circular-holed specimens did not change in form. Whereas those of square-holed and slotting-holed specimens changed significantly. The presence of the blasting hole tip changed the stress wave propagation form in the specimen, and the tip propagation angle of stress wave measured was in good agreement with the theoretical calculation; ③The explosion cracks of the experiment specimens have been analysed statistically. The blasting holes with tip overcame the static field stress, since the directional damage zone have been formed, leading to directional initiating and propagation of the cracks. In circular-holed specimens, the distribution of crack initiation was random, and in square-holed and slotting-holed specimens, the cracks were initiating at the tip. Crack deflected at twice blasting hole diameter and at six times blasting hole diameter in circular-holed and square-holed specimens, respectively. In contrast, cracks didn’t deflect in slotting-holed specimens. The research results can provide theoretical support for selecting the shape and arrangement of the blasting holes for directional fracturing in geotechnical engineering.
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1. Introduction
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Keywords: Slotting blasting; stress wave; directional fracturing; fracture propagation
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Blasting is a widely applied method of material breakage, and effective control of the blasting energy and associated cracks has been extensively studied. In 1905, Foster CL first proposed that control of the crack propagation direction can be achieved by prefabricating a V-shaped slotting around the rock hole[1]. Because of its convenient construction, the production and development of cracks caused by blasting can be accurately controlled and the fracture surface can be formed in a predetermined direction that protects the material integrity in the remaining directions. An increasing number of scholars have therefore applied slotting directional fracture blasting technology to various engineering practices including tunnel and slope excavation, low-damage mining, directional roof breaking to eliminate ore pressure, and directional coal body breaking to increase permeability and directional dismantling. With the popularization of engineering applications, further studies focused on the mechanism of directional fracture blasting. In 1963, Langfors U et al. first indicated that stress concentration is produced owing to slotting, which contributes to the formation and development of cracks along the channel direction [2]. A two-dimensional model established by Harries suggests that shear strain of the slotting tip due to the blasting gas pressure is the main reason for crack formation [3]. Yang [4] suggests that stress wave diffraction at the slotting leads to non-uniform stress distribution. Nakamura, Yuichi, Yang, C.P. Yi et al. confirmed stress concentration at the slotting edge experimentally [5-7]. Stress concentration at the blasting tip, which is
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2. Directional fracturing mechanism in the stress wave
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considered the main factor leading to crack generation and propagation, has been reported in the literature but the generation of tip stress concentration has not been elaborated in detail. The effect of stress waves on material breaking dynamics is very important [8-10]. Fracture phenomena under the dynamic impact [11], directional blasting guided by the hole [12], and dynamic crack development in the jointed materials [13-16] have been widely recognized based on the theory of stress wave transmission, reflection, and superposition. However, these principles have not yet been applied in the literature to explain stress concentration phenomena during the directional blasting process. In this study, tip stress concentration caused by the form change of incident stress wave is analyzed in detail based on the basic wave propagation theory. The observed static stress field under the dynamic caustics, stress wave propagation due to slotting blasting, and generation and extension of cracks verified theoretical derivation. Results further clarify and improve the theoretical mechanism of directional fracture blasting and theoretical support for engineering application is provided.
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During blasting, a high-temperature and pressure gas is produced owing to a violent chemical reaction within the blasting reaction zone, and a detonation wave forms. The forward propagation of the detonation wave leads to continuation of the blasting reaction, which provides further energy for detonation wave propagation. The detonation wave then rapidly propagates into and strongly compresses the surrounding medium, thus forming a shock wave[17]. The shock wave follows “Huygens principle” during the spreading process. Each point reached by the shock wave is the source of a secondary subwave, which propagates in all directions at the velocity and frequency of the original wave. The new wave front is the envelope of these secondary subwaves, as shown in Figure 1. As the wave encounters an obstacle during the propagation process, reflection, incidence, interference, and other phenomena occur that lead to new forms of propagation.
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Figure 1. Schematic diagram of Huygens principle.
Figure 2. Schematic diagram of slotting blasting.
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During slotting blasting, the hole wall guides the shock wave to the coal-rock body with a non-spherical shape. As a consequence, a stress wave also propagates in the preset direction, which leads to stress concentration on the slotting tip particles. A directional fracture thus occurs along the orientation of the tip extension line, as shown in Figure 2. In this study, microelements of the tip were selected for the analysis. Because of a large distance from the source, the curvature radius of the shock wave in the microelement is very large. The involved wave is considered as a plane wave to facilitate analysis and calculation. 2.1 Shock wave incidence at the coal-rock body interface Once blasting occurs in the slot-shaped hole, the shock wave first propagates in the hole and incidence occurs as the shock wave reaches the hole wall. As shown in Figure 3 where OO′ represents the hole wall, the shock wave front (OA) enters the coal-rock body with an incident angle β and wave velocity v1. At t = t1, the partial wave begins to enter the coal-rock body and the wave refracts at an angle of β′ owing to differences between the average density of both sides of OO′. The wave velocity also changes to v2 while the rest of wave continues to propagate with velocity v1. When t = t3, OA propagates to point O′, and the incident secondary subwave propagates to point O, in addition to point B of the coal-rock body with the wave source of point O at t = t1. When Δt = t3 – t1, all incident subwaves jointly lead to the compression and displacement of the coal-rock
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body, and the stress wave is finally formed. Meanwhile, the stress wave continues to propagate and the envelope is composed of secondary subwaves with wave sources of each point at the interface OO′, namely the stress wave front. During this stage, the angle between the stress wave front and interface of the coal-rock body is β′ and the propagation velocity is v2.
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Figure 3. Schematic diagram of the incident stress wave at the slotting tip.
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As the shock wave reaches the slotting tip, the stress wave of the incident medium can be regarded as independent stress waves (1 and 2) with an axis symmetric to the horizontal centerline of slotting tip. The two waves then intersect at the middle of the slotting tip and a stress wave is eventually formed, which is different from the original shock wave, and propagates along the slotting tip.
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2.2 Directional fracture of the slotting tip due to superposed stress waves
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The shock wave enters from the slotting tip and the formed stress wave can be regarded as two independent waves. Two waves also overlap on the tip extension line. The blasting stress wave is usually composed of a compression phase and a tensile phase. Since the tensile strength of the coal-rock body is much less than the compressive strength, damage of the coal-rock body is mainly due to tensile failure. The tensile phase of the stress wave is treated by the “Mohr circle” diagram method. Additionally, the tensile stress of the normal phase is positive and the normal pressure stress of the normal phase is negative. The shear stress is considered positive for the clockwise moment and negative for the inverse clockwise moment. Figure 4 shows the superposition of stress waves 1 and 2 with stress values of σ1 and σ2, respectively. The oz axis is located on the intersection line of the two wave fronts, the stress direction is perpendicular to the wave fronts (σ1 and σ2), and the ox and oy axes are located on the spatial plane, which evenly divides two wave fronts.
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Figure 4. The oblique reference plane of two stress waves.
Where σz is parallel to the oz axis, as follows:
z (1 2 )v / (1 v)
(1)
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where ν is the Poisson ratio. Principal stresses, σx and σy in the xoy plane, can also be treated by the “Mohr circle” diagram method. The “Mohr circle” of stress state for stress wave 1 is calculated, and σ1x, τ1x, σ1y, and τ1y can be obtained by σ1, as shown in Figure 5. The “Mohr circle” of stress state for the stress wave 1 is given as:
Figure 5. The “Mohr circle” of the stress wave 1.
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The stress state for the stress wave 1 is given as:
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1 1x 2(1 v) 1 (1 2v) cos 2 1 1 y 2(1 v) 1 (1 2v) cos 2 1 (1 2v) sin 2 1x 2(1 v) 1 (1 2v) sin 2 1y 2(1 v)
where α is a half of the angle between wave fronts 1 and 2. Similarly, the stress state for stress wave 2 is given as:
(2)
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(3)
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2 2 x 2(1 v) 1 (1 2v) cos 2 2 2 y 2(1 v) 1 (1 2v) cos 2 2 (1 2v) sin 2 2x 2(1 v) 2 (1 2v) sin 2 2 y 2(1 v) The stress state after the superposition of two waves can be expressed as follows:
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x 1x 2 x 1y 2y y x 1x 2 x y 1 y 2 y
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1 2 x 2(1 v) 1 (1 2v) cos 2 1 2 y 2(1 v) 1 (1 2v) cos 2 ( 1 2 )(1 2v) sin 2 x 2(1 v) ( 2 1 )(1 2v) sin 2 y 2(1 v)
(4)
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Since σ1 = σ2, the above equations can be simplified to:
1 x 1 v 1 (1 2v) cos 2 1 1 (1 2v) cos 2 y 1 v x 0 0 y
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The stress state of slotting tip caused by the stress wave can also be expressed as:
1 x 1 v 1 (1 2v) cos 2 1 1 (1 2v) cos 2 y 1 v 2v 1 z 1 v
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As for the actual blasting engineering, the coal-rock body around the hole is controlled by the original stress field so the particle stress state of the slotting tip can be expressed as:
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1 x 1 v 1 (1 2v) cos 2 H 1 1 (1 2v) cos 2 v y 1 v 2v 1 z 1 v h
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where σH , σh and σv are in-situ stress. However, the shock wave pressure produced by blasting is generally beyond 109 Pa, which is much larger than the original stress. The particle stress state is therefore mainly determined by the stress due to the stress wave. Since the propagation velocity of wave 1 is the same as that of wave 2, the intersection line of two waves is always located in the xoz plane and parallel to the oz axis. As the shock wave enters from the slotting tip to the coal-rock body, the particles of the slotting tip bear the maximum stress in the y direction with a slotting tip angle less than 90, namely 2α > 90. As the stress is larger than the tensile strength, the particles are stretched from the y direction such that the crack propagates into the xoz plane. With the propagation of stress waves, the stress gradually attenuates until it is less than the tensile strength of the particles, which stop the crack owing to the effect of the stress wave. However, the stress value can affect meso-scale material damage, which leads to damage in the xoz plane, formation of a directional damage zone, and will also influence the subsequent directional development of cracks under the resulting quasi-static pressure. 3. Experimental
3.1 Specimen preparation
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Dynamic caustics experiment express stress waves in materials through clearly and distinctly bright caustic curves[16,18].In order to verify the mechanisms of the crack orientation and development under stress wave action, we performed a dynamic caustics experiment of slotting blasting, Three polymethyl methacrylate (PMMA) specimens with circular, square, and horizontal slotting forms were manufactured, and a vertical principal stress was applied. We also studied the influence of hole shape on the propagation form of blasting stress wave and the characteristics of crack development under different principal stress conditions.
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The test specimen is PMMA with mechanical parameters listed in Table 1 and dimensions of 315 mm × 285 mm × 10 mm. Table 1. Dynamic mechanical parameters of PMMA.
315
315
12
6
285
4
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315
6
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285
285
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Parameters vp/(m/s) vs/(m/s) Ed/GPa vd Ct/(m2/N) Values 2125 1090 3.595 0.32 0.08 NOTE: Dynamic mechanical parameters are provided by supplier (Business Department, Lutao Plexiglass, Foshan). A circular hole with a 6-mm diameter, 6-mm square hole edge length, and horizontal slotting hole with a length, height, and angle of 12 mm, 4 mm, and 60, respectively, was installed in the center of the test specimen. The test specimen structure is shown in Figure 6.
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¡ 60
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Figure 6. Test specimen structure. (a) Circular boreholes specimen; (b) Square boreholes specimen; (c) Horizontal slotting
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boreholes specimen.
3.2 Design of experimental groups
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Under static stress conditions, cracks are generated perpendicular to the minimum principal stress. In this experiment, the minimum principal stress plane is used to test hole shape transformation, dynamic loading, and the generation and development of cracks and their orientation under static-dynamic load. For safety considerations, three groups of stress conditions were designed in combination with equipment strength conditions and prefabricated specimens using a single vertical stress of either 0, 2, or 4 MPa. Three hole shapes were employed including circular, square, and horizontal slotting. The experimental group design is listed in Table 2. Table 2. Design of experimental groups with two factors. Boreholes shape Test
Vertical stress /MPa
0 2 4
Circular shape
Square shape
Horizontal slotting shape
1 4 7
2 5 8
3 6 9
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3.3 Experimental apparatus
3.3.1 New digital laser system of dynamic caustics
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The digital laser system of dynamic caustics used in this study is composed of a solid laser, beam expander, field mirror, loading device, synchronous control switch, high-speed camera, and computer, as shown in Figure 7. The core of this system is the combination of a high-speed photography system, using a high-speed camera and solid laser with the caustics method, and dynamic caustics photography during the dynamic fracture process while an explosive load is realized. The experimental system is controlled by computer software and digital images are acquired.
Figure 7. New digital laser system of dynamic caustics.
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3.3.2 Static-dynamic loading system The static-dynamic loading system is composed of a static loading apparatus along the vertical uniaxial direction and a blasting loading apparatus, as shown in Figure 8. The hydraulic jack and pressure sensor are used for static loading and stress collection. A charge of lead azide is used with a 100-mg dosage installed in the hole of each test specimen to achieve dynamic loading.
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Figure 8. Static-dynamic loading system.
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After installing the test specimens and debugging the equipment system, the high-speed camera is switched on. The experimental group is detonated by electronic ignition. Nine groups of test specimens were successfully detonated and the results are discussed below. 4. Results and discussion 4.1 Stress wave morphology
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According to the analysis described in Section 2.1, the shock wave entering from the slotting tip decomposes into two independent stress waves, which propagate in the medium. In the experiment, the designed tip is 60 and 90, and the incident and refraction media are air and PMMA, respectively. The propagation angle of the two stress waves after entering the PMMA is expressed as follows:
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' 2 '
(9)
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where α is the tip angle and β′ is the refraction angle. Additionally,
n
sin sin '
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where n is the refraction ratio of medium and β is the incident angle. Since the stress wave is perpendicular to the central axis, α = β and the incident ratio (n) for air entering PMMA is 1.49. We can then show that
' 2 arcsin
sin 1.49
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The propagation angle of two stress waves is calculated by entering the specimen parameters into the equation (11) while the blasting shock wave enters from the air into PMMA.
'Sl =131
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'Sq =144
(13)
Stress wave propagation analysis was carried out for nine groups of specimens (t = 30 μs), as shown in Figure 9.
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Figure 9. Stress wave propagation of specimen (t = 30 μs).
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Specimen numbers 1, 4, and 7 involve a circular hole. During blasting, the circular shock wave enters the PMMA uniformly from the hole wall, and the blasting hole does not change the propagation direction of the original shock wave. The shock wave formed in the test specimen forms a concentric circle around the hole center. Vertical stresses of 2 and 4 MPa were loaded on specimens 3 and 5, respectively. According to the observed stress wave shape, static stress does not affect the propagation form of the stress wave. Specimen numbers 2, 5, and 8 involve a square hole and have four tips of 90. The shock wave enters the PMMA from these four tips. Stresses with angles in each of the tip directions are clearly formed. The whole stress wave takes an octagonal shape with four shadow spots moving along these four directions. Static stress has no obvious effect on the propagation form of stress wave for these three specimens. Specimen numbers 3, 6, and 9 involve a slotting tip with two 60 tips in the horizontal direction. The shock wave enters the PMMA from the two tips and the stress wave clearly forms from the tip extension line, which also has an obvious tip. The whole stress wave forms an elliptical stress wave that propagates outward with the long axis along the tip extension line and short axis in the vertical direction. The shadow spot also moves along the extension line direction. Different static stresses have no obvious effects on the propagation forms of stress waves for these three specimens.
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Figure 10. Angular distribution of the stress wave tip. (a) Square boreholes specimen; (b) Horizontal slotting boreholes specimen.
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Statistical analysis for the tip angles of stress waves on the left sides-of-view of the square and slotting specimens was conducted, as shown in Figure 10. Results demonstrate that the tip angle of stress waves propagating in the specimen is similar to the theoretical value within error of the measurement. As the shock wave enters the specimen from the hole, the incident stress wave forms at the tip with a certain refractive index, which is divided into two independent stress subwaves. The two stress subwaves and associated angle propagate along the extension line direction. The superimposed stress field also forms in the extension line direction, which leads to a concentration of stress. 4.2 Crack morphology
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Blasting shock wave and detonation gas are two main blasting productions. Crack formation can also be divided into two stages, namely crack generation caused by the blasting shock wave and the detonation gas wedging the slotting tip that leads to continuous crack development.
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4.2.1 Crack generation angle
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In the experiments, lead azide is used as the blasting source and the peak pressure of the shock wave front is expressed as follows[17]:
Pm 53.3(
W 1/3 1.13 Qi 1.13/3 ) ( ) r QT
(14)
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where Qi is the detonating heat of lead azide (367 kc/kg), QT is the detonating heat of TNT (1000 kc/kg), W is the charge quantity (0.1 × 10-3 kg), and r is the distance from the blasting center (0.3 × 10 -3 m). The peak pressure of the shock wave entering the specimens is 1.09 × 109 Pa. As the specimen is subjected to a static stress field of 0–4 MPa, the blasting causes the dynamic load to enter the hole wall on the order of 109 Pa. The stress magnitude is much larger than the static stress, which is practically negligible, and the crack generation angle of the hole wall is mainly controlled by the blasting dynamic load. According to theoretical studies and analyses described in Section 4.1, we find that the using a circular hole does not affect the shape of the blasting shock wave, but rather leads to stress concentration in the specified region. A comparison of crack generation conditions from hole numbers 1, 4, and 7 demonstrates the effect of the static stress field in the direction of crack generation under the blasting dynamic load, as shown in Figure 11. The experimental results show that the crack generation angle of specimens with a circular hole is random and does not follow a specific theoretical law under stress conditions of 0, 2, or 4 MPa. Additionally, the static stress field has no obvious effect on the initiation angle of the blasting crack.
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Figure 11. Cracks details of circular boreholes specimen.
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Analysis of specimens 2, 5, and 8 indicate a stress superposition area while the stress wave propagates into the specimen, and the crack starts from the tip extension line, as shown in Figure 12. Based on the crack generation and development, we find that the deviation angles of four cracks are less than 1, and the deviation angle of six cracks are between 1 and 2. Additionally, only three cracks have deviation angles larger than 2 with a maximum deviation angle of 5.21.
Figure 12. Cracks details of square boreholes specimen.
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Specimens 3, 6, and 9 have tips and the main crack angle rarely deviates from the direction of the tip extension line, as shown in Figure 13. As the tip starts to crack, multiple branch cracks can be observed. The generation angle of branch cracks deviates from the tip extension line with the three largest deviation angles of cracks of 42.51, 46.55, and 48.04. The deviation angles of 42.51 and 48.04 appear in the 0-MPa specimen, and the deviation angle of 46.55 appears in the 2-MPa specimen. The maximum value of the tip initiation angle deviating from the extension line in the specimen of 4 MPa is 33.52. Crack angle deviation is therefore unaffected by the static stress field. Cho S H et al. carried out an experimental study of slotting blasting in PMMA and found that all tip cracks lead to the initiation of a branch crack[19-21]. However,Xia et al. carried out an experimental study of slotting blasting in rock or concrete specimens found that all specimens presented a single directional fracture along the tip extension line[22-24]. It can therefore be concluded that the generation of branch cracks is related to specimen material.
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Figure 13. Cracks details of horizontal slotting boreholes specimen.
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A comparison of the three kinds of hole shapes indicates that crack generation does not occur with a circular hole. However, a branch crack only appears on the tip of the right end of specimen 5 among the square specimens. Moreover, a wide range of branch cracks is not observed. By comparing the generation point of cracks for three specimens, it is found that six, eight, and nine generation points are randomly generated for the three circular specimens. The square specimens have four generation points of cracks, while the slotting specimen have only two. The total statistical length of the produced cracks is shown in Figure 14. Under identical loading conditions, the total energy provided to generate and develop cracks, and the total crack lengths remains essentially constant. During blasting in the slotting specimen, the generated energy is concentrated on the two points for crack generation because these specimens only have two dominant tip points. However, dynamic (high-speed) crack development has unique characteristics compared with quasi-static (low-velocity) crack development and crack bifurcation[25]. There is a speed limit of crack development, and the crack extension energy E is constant. As the blasting energy of G enters the crack tip with the form of a stress wave, the propagation speed is greater than the crack development speed limit, and the energy of G is greater than E. Moreover, elastic-plastic materials can absorb excess energy through plastic deformation at the crack tip, while brittle materials undergo little or no plastic deformation at the crack tip. Therefore, only newly generated cracks can consume the excess energy.
Figure 14. Length of total fracture.
Figure 15. Distribution of fracture initiation angular.
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The blasting shock wave leads to the formation of cracks and prompts crack development to a certain distance in the PMMA. Because of the rapid attenuation of the stress wave, the energy is not sufficient for crack development. The generated detonation gas leads air expansion, which prompts crack development. Since the quasi-static pressure of the detonation gas is much smaller than that of the shock wave front, which belongs to the same order of magnitude as the static stress field, the static stress field has a certain effect on crack development. Crack development in specimens 1, 4, and 7 have been observed, as shown in Figure 16. As specimen 1 did not have the static stress field, cracks continued to develop along the direction of crack generation until stopping and without deflection. The cracks in specimen 4 began deflecting at the circular range at distance of about 12 mm from the hole center. Additionally, the cracks turn towards the direction of the maximum principal stress. With an increase of the static stress field, the effect of the static stress field on crack propagation in specimen 7 is more apparent. There are two obvious deflections of cracks; the first and second deflection radii are 8 and 13 mm, respectively.
Figure 16. Crack deflection of circular boreholes specimen.
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Crack development phenomena in specimens 2, 5, and 8 demonstrate that the effect of the static stress field on crack deflection of specimens with a square hole is not clear, as shown in Figure 17. In specimen 5, a small deflection occurs at the end of crack and the deflection radius is 36 mm, which is much larger than the circular hole. As the stress increases to 4 MPa, the first crack deflection for specimen 7 appears at a distance of 18 mm away from the hole. Additionally, the deflection amplitude is small and the second deflection occurs 35 mm away from the hole center.
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Figure 17. Crack deflection of square boreholes specimen.
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Cracks in specimens 3, 6, and 9 do not present an obvious deflection to the maximum principal stress, as shown in Figure 18. After the tip bifurcation fractures, the main crack far from the extension line also deflects to the tip extension line.
Figure 18. Crack deflection of horizontal slotting boreholes specimen.
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The final morphologies of the nine specimens were analyzed and a clear effect of the static stress field on non-guided cracks is observed. There is no effective weak zone in the circular hole medium to guide crack development and most cracks deflect or stop under the control of the static stress field after developing to a certain distance. The static stress field inhibits crack development in the non-principal stress directions but either promotes the development length of protogenetic cracks or the crack deflects to the main stress direction, as shown in Figure 19.
Figure 19. Length of fracture deflection.
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The leading static stress field plays a dominant role for the directional hole with a tip. The static stress field does not appear to change the development of the directional crack and only inhibits the crack development length. The stress wave of the tip does not directly lead to fracture after attenuation, and the stress superposition area will lead to material damage along the tip extension line, which forms a weak zone. Since inertia affects dynamic crack development, the cracks tend to track the weak zone of the tip extension line. As for the deflection control resisting the static stress field, the latter is controlled by crack deflection that exceeds the damage range of the stress wave. When crack development is near completion, crack deflection and development distance are limited.
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5. Conclusions
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1. The directional fracture mechanism of the material tip caused by the blasting shock wave entering from the hole tip has been investigated based on “Huygens principle.” As the shock wave reaches the V shape slotting tip, it separates into two independent waves with a symmetry axis along the horizontal centerline of the slotting. The two waves then propagate in different directions, and the tensile stress zone forms in the normal direction of the extension line. When the stress is larger than the tensile strength of material, the material fractures in the direction of the tip extension line. When the stress is less than the tensile strength and larger than the damaging strength of the material, the damage zone will formed along the tip extension line, which leads to subsequent directional development of the crack. 2. Theoretical analysis have been verified experimentally. The stress waves, which propagated outward in concentric circles, in circular-holed specimens did not change in form. Whereas those of square-holed and slotting-holed specimens changed significantly. As the shock wave enters from the hole tip, the stress wave forms with a certain refractive index. The stress wave is divided into two independent subwaves at the tip, and the two stress subwaves propagate along the direction of the extension line with a certain angle. Moreover, the angle of the stress wave obtained experimentally is in agreement with theoretical calculations. 3. Crack initiating and propagation have been analyzed by the experimental statistics, and the direction of crack development is mainly controlled by the hole shape. The static stress field has no significant influence on the crack initiating angle, while the hole shape does. Explosion cracks are initiated randomly from circular-holed specimens, and in square-holed and slotting-holed specimens, the cracks were initiating at the tip. During subsequent crack propagation, tip guidance remains dominant compared with the static stress field. As the cracks with circular hole develop for some distance, most cracks deflect or stop under the control of the static stress field. As for the directional hole with a tip, cracks tend to track the directional damage zone caused by the stress wave, and overcome deflection control of the static stress field, as well as continuing to develop along the direction of the extension line.
ACCEPTED MANUSCRIPT Acknowledgments: The work is jointly supported by the National Key Basic Research Program of China (NO. 2014CB239206), the National Natural Science Foundation of China (No. 51625401), the Program for Changjiang Scholars and Innovative Research Team in University of China (No. IRT13043).. Author Contributions: Chengwei Liu, Yiyu Lu, Binwei Xia and Peng Yu conceivedand designed the experiments, analysed the data and wrote the paper; Chengwei Liu and Peng Yu performedthe experiments. Conflicts of Interest: The authors declare no conflict of interest.
References
8. 9. 10. 11. 12. 13. 14. 15. 16.
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4.
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2. 3.
Tsoutrelis, C.E.; Gikas, N.; Nomikos, P.; et al. Use of notched boreholes for fracture controlled blasting in the ornamental stone quarries. Fragblast 1997, 1, 445-463. Langefors, U.; Kihlström, B. The modern technique of rock blasting, 2nd ed.; Almquist and Wiksell, Sweden, 1963. Harries, G. Amathematical model of cratering and blast-ing. In National Symposium on Rock Fragmentation, Adelaide; Institution of Engineers, Australia, 1973; pp. 41-45. Yang, Y.K.; Qiu, X.D.; Zhang, Z.C. The directing mechanism of V-notch within V-notching blasting. Journal of Chongqing University 1990, 13, 68-74. Nakamura, Y.; Cho, S.; Yoneoka M.; et al. Model experiments on crack propagation between two charge holes in blasting. Science and Technology of Energetic Materials 2004, 2, 34-39. Yang, R.S.; Song, J.S.; Yang Y.Q. Experimental study of slotting blasting mechanism model. Journal of China Coal Society 1995, 20, 198-200. Yi, C.P.; Daniel J.; Ulf N. Stress wave interaction between two adijacent blast holes. Rock mechanics and rock engineering 2015, 49, 1803-1812. Field, J.E.; Ladegaard-Pedersen A. The importance of the reflected stress wave in rock blasting. International Journal of Rock Mechanics & Mining Sciences & Geomechanics Abstracts 1971, 8, 213-220. Kutter, H.K.; Fairhurst C. On the fracture process in blasting. International Journal of Rock Mechanics & Mining Sciences & Geomechanics Abstracts. 1971, 8, 188-189. Donzé, F.V.; Bouchez J.; Magnier S.A. Modeling fractures in rock blasting. International Journal of Rock Mechanics and Mining Sciences 1997, 34, 1153-1163. Lu, Y.; Huang, F.; Liu, X.; Ao, X. On the failure pattern of sandstone impacted by high-velocity water jet. International Journal of Impact Engineering 2015, 76, 67-74. Wen, Y.Z.; Yang, G.; Peng, X.U.; Qian, W.; Yi, Z.J. Experimental study on the mechanism of blast-induced crack propagation under directional fracture controlled blasting. Engineering Mechanics 2016, 33, 50-58. Rossmanith, H.P. Fracture and damage of concrete and rock, fdcr-2: proceedings of the second intern. conference on fracture and damage of concrete and rock, vienne, nov. 1992. Journal of Clinical Pharmacology 1993, 49, 773-81. Li, J.; Huang, Q.; Ren, X. Dynamic initiation and propagation of multiple cracks in brittle materials. Materials 2013, 6, 3241-3253. Li, J.; Ma, G. Analysis of blast wave interaction with a rock joint. Rock Mechanics & Rock Engineering 2010, 43, 777-787. Yue, Z.; Qiu, P.; Yang, R.S.; Zhang, S.C.; Yuan, K.; Li, Z.F. Stress analysis of the interaction of a running crack and blasting waves by caustics method. Engineering Fracture Mechanics 2017, 184, 339-351. Li Y.Q.; Ma S.Z. Explosion mechanics [in Chinese]; Science Press: Beijing, China, 1992. Yang R.S.; Niu X.C.; Shang H.S.; Jing L.W. Dynamic caustics analysis of crack in samdwich materials under blasting stress wave. Journal of China Coal Society 2005, 30, 36-39. Cho, S.H.; Nakamura, Y.; Mohanty, B. Numerical study of fracture plane control in laboratory-scale blasting. Engineering Fracture Mechanics 2008, 75, 3966-3984. Wang X.C. Study of mechanism of smooth blasting combined with water jets slotting in soft-rock and its experiment. Ph. D. Thesis, Chongqing University, Chongqing, China, 2011. Yang, R.S.; Wang Y.B.; Yang L.Y.; Xu P. Dynamic caustic experimental study of crack propagation in two borehole cut blasting. Journal of China University of Mining & Technology 2012, 41, 868-872. Xia B.W.; Liu C.W.; Lu Y.Y.; et al. Experimental study of Propogation of directional fracture with slotting hydraulic blasting. Journal of China Coal Society 2016, 41, 432-438. Yang L.Y. The experimental study on rock-type materials dynamic fracture and blasting crack propagation under confining pressure. Ph. D. Thesis, China University of Mining and Technology, Jiangsu, China, 2011. Liu J.; Liu Z.G.; Gao K.; et al. Experimental study and application of directional focused energy blasting in deep boreholes. Chinese Journal of Rock Mechanics and Engineering 2014, 12, 2490-2496.
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1.
19. 20. 21. 22. 23. 24.
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Meyers M.A. Dynamic Fracture. In Dynamic Behavior of Materials, John Wiley & Sons, Inc.: New York, United States, 2007; Volume 16, pp. 488-566.
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Directional Fracturing by Slotting-Blasting-Caused Stress Wave Form Changes Chengwei Liu , Yiyu Lu , Binwei Xia , Peng Yu PII: DOI: Reference:
S0734-743X(18)30576-1 https://doi.org/10.1016/j.ijimpeng.2019.02.002 IE 3236
To appear in:
International Journal of Impact Engineering
Received date: Revised date: Accepted date:
7 June 2018 28 January 2019 11 February 2019
Please cite this article as: Chengwei Liu , Yiyu Lu , Binwei Xia , Peng Yu , Directional Fracturing by Slotting-Blasting-Caused Stress Wave Form Changes, International Journal of Impact Engineering (2019), doi: https://doi.org/10.1016/j.ijimpeng.2019.02.002
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Highlights
Discussed the mechanism of directional stress concentration in material tip caused by Stress Wave Form Changes.
Discussed the mechanism of directional fracture overcome deflection control of the static stress field. Observing stress wave propagation in materials using high-speed cameras.
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Directional Fracturing by Slotting-Blasting-Caused Stress Wave Form Changes Chengwei Liu 1,2, Yiyu Lu 1,2, Binwei Xia 1,2,* and Peng Yu 1,2 State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China 2 College of Resources and Environmental Science, Chongqing University, Chongqing 400030, PR China * Correspondence: [email protected]; Tel.: +86 13508382008 1
Received: date; Accepted: date; Published: date
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Abstract: Slotting blasting is widely used for directional fracture in geotechnical engineering. Due to limited research methods, the basic propagation theory of stress waves has not yet been applied in the literature to explain directional fracturing mechanism. In this work, the stress wave propagation during slotting blasting has been analysed, and through the dynamic caustics blasting experiments, the blastings in circular-holed, square-holed and slotting-holed specimens have been contrast-analysed, the propagation of stress waves and the explosion cracks have been observed. The theoretical and experimental results show that ①As the shock wave reached the slotting tip, based on “Huygens principle”, it separated into two independent waves symmetric to the median axis of the slotting tips and transmitted in different directions, due to directional stress concentration in materials. The directional fracture zone and directional damage zone were formed as the stress wave is attenuated during propagation; ②Observed in the experiment. The stress waves, which propagated outward in concentric circles, in circular-holed specimens did not change in form. Whereas those of square-holed and slotting-holed specimens changed significantly. The presence of the blasting hole tip changed the stress wave propagation form in the specimen, and the tip propagation angle of stress wave measured was in good agreement with the theoretical calculation; ③The explosion cracks of the experiment specimens have been analysed statistically. The blasting holes with tip overcame the static field stress, since the directional damage zone have been formed, leading to directional initiating and propagation of the cracks. In circular-holed specimens, the distribution of crack initiation was random, and in square-holed and slotting-holed specimens, the cracks were initiating at the tip. Crack deflected at twice blasting hole diameter and at six times blasting hole diameter in circular-holed and square-holed specimens, respectively. In contrast, cracks didn’t deflect in slotting-holed specimens. The research results can provide theoretical support for selecting the shape and arrangement of the blasting holes for directional fracturing in geotechnical engineering.
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1. Introduction
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Keywords: Slotting blasting; stress wave; directional fracturing; fracture propagation
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Blasting is a widely applied method of material breakage, and effective control of the blasting energy and associated cracks has been extensively studied. In 1905, Foster CL first proposed that control of the crack propagation direction can be achieved by prefabricating a V-shaped slotting around the rock hole[1]. Because of its convenient construction, the production and development of cracks caused by blasting can be accurately controlled and the fracture surface can be formed in a predetermined direction that protects the material integrity in the remaining directions. An increasing number of scholars have therefore applied slotting directional fracture blasting technology to various engineering practices including tunnel and slope excavation, low-damage mining, directional roof breaking to eliminate ore pressure, and directional coal body breaking to increase permeability and directional dismantling. With the popularization of engineering applications, further studies focused on the mechanism of directional fracture blasting. In 1963, Langfors U et al. first indicated that stress concentration is produced owing to slotting, which contributes to the formation and development of cracks along the channel direction [2]. A two-dimensional model established by Harries suggests that shear strain of the slotting tip due to the blasting gas pressure is the main reason for crack formation [3]. Yang [4] suggests that stress wave diffraction at the slotting leads to non-uniform stress distribution. Nakamura, Yuichi, Yang, C.P. Yi et al. confirmed stress concentration at the slotting edge experimentally [5-7]. Stress concentration at the blasting tip, which is
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2. Directional fracturing mechanism in the stress wave
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considered the main factor leading to crack generation and propagation, has been reported in the literature but the generation of tip stress concentration has not been elaborated in detail. The effect of stress waves on material breaking dynamics is very important [8-10]. Fracture phenomena under the dynamic impact [11], directional blasting guided by the hole [12], and dynamic crack development in the jointed materials [13-16] have been widely recognized based on the theory of stress wave transmission, reflection, and superposition. However, these principles have not yet been applied in the literature to explain stress concentration phenomena during the directional blasting process. In this study, tip stress concentration caused by the form change of incident stress wave is analyzed in detail based on the basic wave propagation theory. The observed static stress field under the dynamic caustics, stress wave propagation due to slotting blasting, and generation and extension of cracks verified theoretical derivation. Results further clarify and improve the theoretical mechanism of directional fracture blasting and theoretical support for engineering application is provided.
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During blasting, a high-temperature and pressure gas is produced owing to a violent chemical reaction within the blasting reaction zone, and a detonation wave forms. The forward propagation of the detonation wave leads to continuation of the blasting reaction, which provides further energy for detonation wave propagation. The detonation wave then rapidly propagates into and strongly compresses the surrounding medium, thus forming a shock wave[17]. The shock wave follows “Huygens principle” during the spreading process. Each point reached by the shock wave is the source of a secondary subwave, which propagates in all directions at the velocity and frequency of the original wave. The new wave front is the envelope of these secondary subwaves, as shown in Figure 1. As the wave encounters an obstacle during the propagation process, reflection, incidence, interference, and other phenomena occur that lead to new forms of propagation.
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Figure 1. Schematic diagram of Huygens principle.
Figure 2. Schematic diagram of slotting blasting.
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During slotting blasting, the hole wall guides the shock wave to the coal-rock body with a non-spherical shape. As a consequence, a stress wave also propagates in the preset direction, which leads to stress concentration on the slotting tip particles. A directional fracture thus occurs along the orientation of the tip extension line, as shown in Figure 2. In this study, microelements of the tip were selected for the analysis. Because of a large distance from the source, the curvature radius of the shock wave in the microelement is very large. The involved wave is considered as a plane wave to facilitate analysis and calculation. 2.1 Shock wave incidence at the coal-rock body interface Once blasting occurs in the slot-shaped hole, the shock wave first propagates in the hole and incidence occurs as the shock wave reaches the hole wall. As shown in Figure 3 where OO′ represents the hole wall, the shock wave front (OA) enters the coal-rock body with an incident angle β and wave velocity v1. At t = t1, the partial wave begins to enter the coal-rock body and the wave refracts at an angle of β′ owing to differences between the average density of both sides of OO′. The wave velocity also changes to v2 while the rest of wave continues to propagate with velocity v1. When t = t3, OA propagates to point O′, and the incident secondary subwave propagates to point O, in addition to point B of the coal-rock body with the wave source of point O at t = t1. When Δt = t3 – t1, all incident subwaves jointly lead to the compression and displacement of the coal-rock
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body, and the stress wave is finally formed. Meanwhile, the stress wave continues to propagate and the envelope is composed of secondary subwaves with wave sources of each point at the interface OO′, namely the stress wave front. During this stage, the angle between the stress wave front and interface of the coal-rock body is β′ and the propagation velocity is v2.
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Figure 3. Schematic diagram of the incident stress wave at the slotting tip.
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As the shock wave reaches the slotting tip, the stress wave of the incident medium can be regarded as independent stress waves (1 and 2) with an axis symmetric to the horizontal centerline of slotting tip. The two waves then intersect at the middle of the slotting tip and a stress wave is eventually formed, which is different from the original shock wave, and propagates along the slotting tip.
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2.2 Directional fracture of the slotting tip due to superposed stress waves
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The shock wave enters from the slotting tip and the formed stress wave can be regarded as two independent waves. Two waves also overlap on the tip extension line. The blasting stress wave is usually composed of a compression phase and a tensile phase. Since the tensile strength of the coal-rock body is much less than the compressive strength, damage of the coal-rock body is mainly due to tensile failure. The tensile phase of the stress wave is treated by the “Mohr circle” diagram method. Additionally, the tensile stress of the normal phase is positive and the normal pressure stress of the normal phase is negative. The shear stress is considered positive for the clockwise moment and negative for the inverse clockwise moment. Figure 4 shows the superposition of stress waves 1 and 2 with stress values of σ1 and σ2, respectively. The oz axis is located on the intersection line of the two wave fronts, the stress direction is perpendicular to the wave fronts (σ1 and σ2), and the ox and oy axes are located on the spatial plane, which evenly divides two wave fronts.
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Figure 4. The oblique reference plane of two stress waves.
Where σz is parallel to the oz axis, as follows:
z (1 2 )v / (1 v)
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where ν is the Poisson ratio. Principal stresses, σx and σy in the xoy plane, can also be treated by the “Mohr circle” diagram method. The “Mohr circle” of stress state for stress wave 1 is calculated, and σ1x, τ1x, σ1y, and τ1y can be obtained by σ1, as shown in Figure 5. The “Mohr circle” of stress state for the stress wave 1 is given as:
Figure 5. The “Mohr circle” of the stress wave 1.
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The stress state for the stress wave 1 is given as:
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1 1x 2(1 v) 1 (1 2v) cos 2 1 1 y 2(1 v) 1 (1 2v) cos 2 1 (1 2v) sin 2 1x 2(1 v) 1 (1 2v) sin 2 1y 2(1 v)
where α is a half of the angle between wave fronts 1 and 2. Similarly, the stress state for stress wave 2 is given as:
(2)
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2 2 x 2(1 v) 1 (1 2v) cos 2 2 2 y 2(1 v) 1 (1 2v) cos 2 2 (1 2v) sin 2 2x 2(1 v) 2 (1 2v) sin 2 2 y 2(1 v) The stress state after the superposition of two waves can be expressed as follows:
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1 2 x 2(1 v) 1 (1 2v) cos 2 1 2 y 2(1 v) 1 (1 2v) cos 2 ( 1 2 )(1 2v) sin 2 x 2(1 v) ( 2 1 )(1 2v) sin 2 y 2(1 v)
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Since σ1 = σ2, the above equations can be simplified to:
1 x 1 v 1 (1 2v) cos 2 1 1 (1 2v) cos 2 y 1 v x 0 0 y
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The stress state of slotting tip caused by the stress wave can also be expressed as:
1 x 1 v 1 (1 2v) cos 2 1 1 (1 2v) cos 2 y 1 v 2v 1 z 1 v
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As for the actual blasting engineering, the coal-rock body around the hole is controlled by the original stress field so the particle stress state of the slotting tip can be expressed as:
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1 x 1 v 1 (1 2v) cos 2 H 1 1 (1 2v) cos 2 v y 1 v 2v 1 z 1 v h
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where σH , σh and σv are in-situ stress. However, the shock wave pressure produced by blasting is generally beyond 109 Pa, which is much larger than the original stress. The particle stress state is therefore mainly determined by the stress due to the stress wave. Since the propagation velocity of wave 1 is the same as that of wave 2, the intersection line of two waves is always located in the xoz plane and parallel to the oz axis. As the shock wave enters from the slotting tip to the coal-rock body, the particles of the slotting tip bear the maximum stress in the y direction with a slotting tip angle less than 90, namely 2α > 90. As the stress is larger than the tensile strength, the particles are stretched from the y direction such that the crack propagates into the xoz plane. With the propagation of stress waves, the stress gradually attenuates until it is less than the tensile strength of the particles, which stop the crack owing to the effect of the stress wave. However, the stress value can affect meso-scale material damage, which leads to damage in the xoz plane, formation of a directional damage zone, and will also influence the subsequent directional development of cracks under the resulting quasi-static pressure. 3. Experimental
3.1 Specimen preparation
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Dynamic caustics experiment express stress waves in materials through clearly and distinctly bright caustic curves[16,18].In order to verify the mechanisms of the crack orientation and development under stress wave action, we performed a dynamic caustics experiment of slotting blasting, Three polymethyl methacrylate (PMMA) specimens with circular, square, and horizontal slotting forms were manufactured, and a vertical principal stress was applied. We also studied the influence of hole shape on the propagation form of blasting stress wave and the characteristics of crack development under different principal stress conditions.
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The test specimen is PMMA with mechanical parameters listed in Table 1 and dimensions of 315 mm × 285 mm × 10 mm. Table 1. Dynamic mechanical parameters of PMMA.
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Parameters vp/(m/s) vs/(m/s) Ed/GPa vd Ct/(m2/N) Values 2125 1090 3.595 0.32 0.08 NOTE: Dynamic mechanical parameters are provided by supplier (Business Department, Lutao Plexiglass, Foshan). A circular hole with a 6-mm diameter, 6-mm square hole edge length, and horizontal slotting hole with a length, height, and angle of 12 mm, 4 mm, and 60, respectively, was installed in the center of the test specimen. The test specimen structure is shown in Figure 6.
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Figure 6. Test specimen structure. (a) Circular boreholes specimen; (b) Square boreholes specimen; (c) Horizontal slotting
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boreholes specimen.
3.2 Design of experimental groups
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Under static stress conditions, cracks are generated perpendicular to the minimum principal stress. In this experiment, the minimum principal stress plane is used to test hole shape transformation, dynamic loading, and the generation and development of cracks and their orientation under static-dynamic load. For safety considerations, three groups of stress conditions were designed in combination with equipment strength conditions and prefabricated specimens using a single vertical stress of either 0, 2, or 4 MPa. Three hole shapes were employed including circular, square, and horizontal slotting. The experimental group design is listed in Table 2. Table 2. Design of experimental groups with two factors. Boreholes shape Test
Vertical stress /MPa
0 2 4
Circular shape
Square shape
Horizontal slotting shape
1 4 7
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3 6 9
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3.3 Experimental apparatus
3.3.1 New digital laser system of dynamic caustics
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The digital laser system of dynamic caustics used in this study is composed of a solid laser, beam expander, field mirror, loading device, synchronous control switch, high-speed camera, and computer, as shown in Figure 7. The core of this system is the combination of a high-speed photography system, using a high-speed camera and solid laser with the caustics method, and dynamic caustics photography during the dynamic fracture process while an explosive load is realized. The experimental system is controlled by computer software and digital images are acquired.
Figure 7. New digital laser system of dynamic caustics.
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3.3.2 Static-dynamic loading system The static-dynamic loading system is composed of a static loading apparatus along the vertical uniaxial direction and a blasting loading apparatus, as shown in Figure 8. The hydraulic jack and pressure sensor are used for static loading and stress collection. A charge of lead azide is used with a 100-mg dosage installed in the hole of each test specimen to achieve dynamic loading.
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Figure 8. Static-dynamic loading system.
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After installing the test specimens and debugging the equipment system, the high-speed camera is switched on. The experimental group is detonated by electronic ignition. Nine groups of test specimens were successfully detonated and the results are discussed below. 4. Results and discussion 4.1 Stress wave morphology
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According to the analysis described in Section 2.1, the shock wave entering from the slotting tip decomposes into two independent stress waves, which propagate in the medium. In the experiment, the designed tip is 60 and 90, and the incident and refraction media are air and PMMA, respectively. The propagation angle of the two stress waves after entering the PMMA is expressed as follows:
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where α is the tip angle and β′ is the refraction angle. Additionally,
n
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where n is the refraction ratio of medium and β is the incident angle. Since the stress wave is perpendicular to the central axis, α = β and the incident ratio (n) for air entering PMMA is 1.49. We can then show that
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The propagation angle of two stress waves is calculated by entering the specimen parameters into the equation (11) while the blasting shock wave enters from the air into PMMA.
'Sl =131
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'Sq =144
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Stress wave propagation analysis was carried out for nine groups of specimens (t = 30 μs), as shown in Figure 9.
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Figure 9. Stress wave propagation of specimen (t = 30 μs).
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Specimen numbers 1, 4, and 7 involve a circular hole. During blasting, the circular shock wave enters the PMMA uniformly from the hole wall, and the blasting hole does not change the propagation direction of the original shock wave. The shock wave formed in the test specimen forms a concentric circle around the hole center. Vertical stresses of 2 and 4 MPa were loaded on specimens 3 and 5, respectively. According to the observed stress wave shape, static stress does not affect the propagation form of the stress wave. Specimen numbers 2, 5, and 8 involve a square hole and have four tips of 90. The shock wave enters the PMMA from these four tips. Stresses with angles in each of the tip directions are clearly formed. The whole stress wave takes an octagonal shape with four shadow spots moving along these four directions. Static stress has no obvious effect on the propagation form of stress wave for these three specimens. Specimen numbers 3, 6, and 9 involve a slotting tip with two 60 tips in the horizontal direction. The shock wave enters the PMMA from the two tips and the stress wave clearly forms from the tip extension line, which also has an obvious tip. The whole stress wave forms an elliptical stress wave that propagates outward with the long axis along the tip extension line and short axis in the vertical direction. The shadow spot also moves along the extension line direction. Different static stresses have no obvious effects on the propagation forms of stress waves for these three specimens.
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Figure 10. Angular distribution of the stress wave tip. (a) Square boreholes specimen; (b) Horizontal slotting boreholes specimen.
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Statistical analysis for the tip angles of stress waves on the left sides-of-view of the square and slotting specimens was conducted, as shown in Figure 10. Results demonstrate that the tip angle of stress waves propagating in the specimen is similar to the theoretical value within error of the measurement. As the shock wave enters the specimen from the hole, the incident stress wave forms at the tip with a certain refractive index, which is divided into two independent stress subwaves. The two stress subwaves and associated angle propagate along the extension line direction. The superimposed stress field also forms in the extension line direction, which leads to a concentration of stress. 4.2 Crack morphology
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Blasting shock wave and detonation gas are two main blasting productions. Crack formation can also be divided into two stages, namely crack generation caused by the blasting shock wave and the detonation gas wedging the slotting tip that leads to continuous crack development.
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4.2.1 Crack generation angle
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In the experiments, lead azide is used as the blasting source and the peak pressure of the shock wave front is expressed as follows[17]:
Pm 53.3(
W 1/3 1.13 Qi 1.13/3 ) ( ) r QT
(14)
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where Qi is the detonating heat of lead azide (367 kc/kg), QT is the detonating heat of TNT (1000 kc/kg), W is the charge quantity (0.1 × 10-3 kg), and r is the distance from the blasting center (0.3 × 10 -3 m). The peak pressure of the shock wave entering the specimens is 1.09 × 109 Pa. As the specimen is subjected to a static stress field of 0–4 MPa, the blasting causes the dynamic load to enter the hole wall on the order of 109 Pa. The stress magnitude is much larger than the static stress, which is practically negligible, and the crack generation angle of the hole wall is mainly controlled by the blasting dynamic load. According to theoretical studies and analyses described in Section 4.1, we find that the using a circular hole does not affect the shape of the blasting shock wave, but rather leads to stress concentration in the specified region. A comparison of crack generation conditions from hole numbers 1, 4, and 7 demonstrates the effect of the static stress field in the direction of crack generation under the blasting dynamic load, as shown in Figure 11. The experimental results show that the crack generation angle of specimens with a circular hole is random and does not follow a specific theoretical law under stress conditions of 0, 2, or 4 MPa. Additionally, the static stress field has no obvious effect on the initiation angle of the blasting crack.
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Figure 11. Cracks details of circular boreholes specimen.
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Analysis of specimens 2, 5, and 8 indicate a stress superposition area while the stress wave propagates into the specimen, and the crack starts from the tip extension line, as shown in Figure 12. Based on the crack generation and development, we find that the deviation angles of four cracks are less than 1, and the deviation angle of six cracks are between 1 and 2. Additionally, only three cracks have deviation angles larger than 2 with a maximum deviation angle of 5.21.
Figure 12. Cracks details of square boreholes specimen.
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Specimens 3, 6, and 9 have tips and the main crack angle rarely deviates from the direction of the tip extension line, as shown in Figure 13. As the tip starts to crack, multiple branch cracks can be observed. The generation angle of branch cracks deviates from the tip extension line with the three largest deviation angles of cracks of 42.51, 46.55, and 48.04. The deviation angles of 42.51 and 48.04 appear in the 0-MPa specimen, and the deviation angle of 46.55 appears in the 2-MPa specimen. The maximum value of the tip initiation angle deviating from the extension line in the specimen of 4 MPa is 33.52. Crack angle deviation is therefore unaffected by the static stress field. Cho S H et al. carried out an experimental study of slotting blasting in PMMA and found that all tip cracks lead to the initiation of a branch crack[19-21]. However,Xia et al. carried out an experimental study of slotting blasting in rock or concrete specimens found that all specimens presented a single directional fracture along the tip extension line[22-24]. It can therefore be concluded that the generation of branch cracks is related to specimen material.
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Figure 13. Cracks details of horizontal slotting boreholes specimen.
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A comparison of the three kinds of hole shapes indicates that crack generation does not occur with a circular hole. However, a branch crack only appears on the tip of the right end of specimen 5 among the square specimens. Moreover, a wide range of branch cracks is not observed. By comparing the generation point of cracks for three specimens, it is found that six, eight, and nine generation points are randomly generated for the three circular specimens. The square specimens have four generation points of cracks, while the slotting specimen have only two. The total statistical length of the produced cracks is shown in Figure 14. Under identical loading conditions, the total energy provided to generate and develop cracks, and the total crack lengths remains essentially constant. During blasting in the slotting specimen, the generated energy is concentrated on the two points for crack generation because these specimens only have two dominant tip points. However, dynamic (high-speed) crack development has unique characteristics compared with quasi-static (low-velocity) crack development and crack bifurcation[25]. There is a speed limit of crack development, and the crack extension energy E is constant. As the blasting energy of G enters the crack tip with the form of a stress wave, the propagation speed is greater than the crack development speed limit, and the energy of G is greater than E. Moreover, elastic-plastic materials can absorb excess energy through plastic deformation at the crack tip, while brittle materials undergo little or no plastic deformation at the crack tip. Therefore, only newly generated cracks can consume the excess energy.
Figure 14. Length of total fracture.
Figure 15. Distribution of fracture initiation angular.
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The blasting shock wave leads to the formation of cracks and prompts crack development to a certain distance in the PMMA. Because of the rapid attenuation of the stress wave, the energy is not sufficient for crack development. The generated detonation gas leads air expansion, which prompts crack development. Since the quasi-static pressure of the detonation gas is much smaller than that of the shock wave front, which belongs to the same order of magnitude as the static stress field, the static stress field has a certain effect on crack development. Crack development in specimens 1, 4, and 7 have been observed, as shown in Figure 16. As specimen 1 did not have the static stress field, cracks continued to develop along the direction of crack generation until stopping and without deflection. The cracks in specimen 4 began deflecting at the circular range at distance of about 12 mm from the hole center. Additionally, the cracks turn towards the direction of the maximum principal stress. With an increase of the static stress field, the effect of the static stress field on crack propagation in specimen 7 is more apparent. There are two obvious deflections of cracks; the first and second deflection radii are 8 and 13 mm, respectively.
Figure 16. Crack deflection of circular boreholes specimen.
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Crack development phenomena in specimens 2, 5, and 8 demonstrate that the effect of the static stress field on crack deflection of specimens with a square hole is not clear, as shown in Figure 17. In specimen 5, a small deflection occurs at the end of crack and the deflection radius is 36 mm, which is much larger than the circular hole. As the stress increases to 4 MPa, the first crack deflection for specimen 7 appears at a distance of 18 mm away from the hole. Additionally, the deflection amplitude is small and the second deflection occurs 35 mm away from the hole center.
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Figure 17. Crack deflection of square boreholes specimen.
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Cracks in specimens 3, 6, and 9 do not present an obvious deflection to the maximum principal stress, as shown in Figure 18. After the tip bifurcation fractures, the main crack far from the extension line also deflects to the tip extension line.
Figure 18. Crack deflection of horizontal slotting boreholes specimen.
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The final morphologies of the nine specimens were analyzed and a clear effect of the static stress field on non-guided cracks is observed. There is no effective weak zone in the circular hole medium to guide crack development and most cracks deflect or stop under the control of the static stress field after developing to a certain distance. The static stress field inhibits crack development in the non-principal stress directions but either promotes the development length of protogenetic cracks or the crack deflects to the main stress direction, as shown in Figure 19.
Figure 19. Length of fracture deflection.
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The leading static stress field plays a dominant role for the directional hole with a tip. The static stress field does not appear to change the development of the directional crack and only inhibits the crack development length. The stress wave of the tip does not directly lead to fracture after attenuation, and the stress superposition area will lead to material damage along the tip extension line, which forms a weak zone. Since inertia affects dynamic crack development, the cracks tend to track the weak zone of the tip extension line. As for the deflection control resisting the static stress field, the latter is controlled by crack deflection that exceeds the damage range of the stress wave. When crack development is near completion, crack deflection and development distance are limited.
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5. Conclusions
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1. The directional fracture mechanism of the material tip caused by the blasting shock wave entering from the hole tip has been investigated based on “Huygens principle.” As the shock wave reaches the V shape slotting tip, it separates into two independent waves with a symmetry axis along the horizontal centerline of the slotting. The two waves then propagate in different directions, and the tensile stress zone forms in the normal direction of the extension line. When the stress is larger than the tensile strength of material, the material fractures in the direction of the tip extension line. When the stress is less than the tensile strength and larger than the damaging strength of the material, the damage zone will formed along the tip extension line, which leads to subsequent directional development of the crack. 2. Theoretical analysis have been verified experimentally. The stress waves, which propagated outward in concentric circles, in circular-holed specimens did not change in form. Whereas those of square-holed and slotting-holed specimens changed significantly. As the shock wave enters from the hole tip, the stress wave forms with a certain refractive index. The stress wave is divided into two independent subwaves at the tip, and the two stress subwaves propagate along the direction of the extension line with a certain angle. Moreover, the angle of the stress wave obtained experimentally is in agreement with theoretical calculations. 3. Crack initiating and propagation have been analyzed by the experimental statistics, and the direction of crack development is mainly controlled by the hole shape. The static stress field has no significant influence on the crack initiating angle, while the hole shape does. Explosion cracks are initiated randomly from circular-holed specimens, and in square-holed and slotting-holed specimens, the cracks were initiating at the tip. During subsequent crack propagation, tip guidance remains dominant compared with the static stress field. As the cracks with circular hole develop for some distance, most cracks deflect or stop under the control of the static stress field. As for the directional hole with a tip, cracks tend to track the directional damage zone caused by the stress wave, and overcome deflection control of the static stress field, as well as continuing to develop along the direction of the extension line.
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References
8. 9. 10. 11. 12. 13. 14. 15. 16.
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17. 18.
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2. 3.
Tsoutrelis, C.E.; Gikas, N.; Nomikos, P.; et al. Use of notched boreholes for fracture controlled blasting in the ornamental stone quarries. Fragblast 1997, 1, 445-463. Langefors, U.; Kihlström, B. The modern technique of rock blasting, 2nd ed.; Almquist and Wiksell, Sweden, 1963. Harries, G. Amathematical model of cratering and blast-ing. In National Symposium on Rock Fragmentation, Adelaide; Institution of Engineers, Australia, 1973; pp. 41-45. Yang, Y.K.; Qiu, X.D.; Zhang, Z.C. The directing mechanism of V-notch within V-notching blasting. Journal of Chongqing University 1990, 13, 68-74. Nakamura, Y.; Cho, S.; Yoneoka M.; et al. Model experiments on crack propagation between two charge holes in blasting. Science and Technology of Energetic Materials 2004, 2, 34-39. Yang, R.S.; Song, J.S.; Yang Y.Q. Experimental study of slotting blasting mechanism model. Journal of China Coal Society 1995, 20, 198-200. Yi, C.P.; Daniel J.; Ulf N. Stress wave interaction between two adijacent blast holes. Rock mechanics and rock engineering 2015, 49, 1803-1812. Field, J.E.; Ladegaard-Pedersen A. The importance of the reflected stress wave in rock blasting. International Journal of Rock Mechanics & Mining Sciences & Geomechanics Abstracts 1971, 8, 213-220. Kutter, H.K.; Fairhurst C. On the fracture process in blasting. International Journal of Rock Mechanics & Mining Sciences & Geomechanics Abstracts. 1971, 8, 188-189. Donzé, F.V.; Bouchez J.; Magnier S.A. Modeling fractures in rock blasting. International Journal of Rock Mechanics and Mining Sciences 1997, 34, 1153-1163. Lu, Y.; Huang, F.; Liu, X.; Ao, X. On the failure pattern of sandstone impacted by high-velocity water jet. International Journal of Impact Engineering 2015, 76, 67-74. Wen, Y.Z.; Yang, G.; Peng, X.U.; Qian, W.; Yi, Z.J. Experimental study on the mechanism of blast-induced crack propagation under directional fracture controlled blasting. Engineering Mechanics 2016, 33, 50-58. Rossmanith, H.P. Fracture and damage of concrete and rock, fdcr-2: proceedings of the second intern. conference on fracture and damage of concrete and rock, vienne, nov. 1992. Journal of Clinical Pharmacology 1993, 49, 773-81. Li, J.; Huang, Q.; Ren, X. Dynamic initiation and propagation of multiple cracks in brittle materials. Materials 2013, 6, 3241-3253. Li, J.; Ma, G. Analysis of blast wave interaction with a rock joint. Rock Mechanics & Rock Engineering 2010, 43, 777-787. Yue, Z.; Qiu, P.; Yang, R.S.; Zhang, S.C.; Yuan, K.; Li, Z.F. Stress analysis of the interaction of a running crack and blasting waves by caustics method. Engineering Fracture Mechanics 2017, 184, 339-351. Li Y.Q.; Ma S.Z. Explosion mechanics [in Chinese]; Science Press: Beijing, China, 1992. Yang R.S.; Niu X.C.; Shang H.S.; Jing L.W. Dynamic caustics analysis of crack in samdwich materials under blasting stress wave. Journal of China Coal Society 2005, 30, 36-39. Cho, S.H.; Nakamura, Y.; Mohanty, B. Numerical study of fracture plane control in laboratory-scale blasting. Engineering Fracture Mechanics 2008, 75, 3966-3984. Wang X.C. Study of mechanism of smooth blasting combined with water jets slotting in soft-rock and its experiment. Ph. D. Thesis, Chongqing University, Chongqing, China, 2011. Yang, R.S.; Wang Y.B.; Yang L.Y.; Xu P. Dynamic caustic experimental study of crack propagation in two borehole cut blasting. Journal of China University of Mining & Technology 2012, 41, 868-872. Xia B.W.; Liu C.W.; Lu Y.Y.; et al. Experimental study of Propogation of directional fracture with slotting hydraulic blasting. Journal of China Coal Society 2016, 41, 432-438. Yang L.Y. The experimental study on rock-type materials dynamic fracture and blasting crack propagation under confining pressure. Ph. D. Thesis, China University of Mining and Technology, Jiangsu, China, 2011. Liu J.; Liu Z.G.; Gao K.; et al. Experimental study and application of directional focused energy blasting in deep boreholes. Chinese Journal of Rock Mechanics and Engineering 2014, 12, 2490-2496.
CE
1.
19. 20. 21. 22. 23. 24.
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Meyers M.A. Dynamic Fracture. In Dynamic Behavior of Materials, John Wiley & Sons, Inc.: New York, United States, 2007; Volume 16, pp. 488-566.
AC
CE
PT
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AN US
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25.