Interaction of a system of griffith cracks in an elasto-brittle material

Martynyuk, P. A.

doi:10.1007/bf00912649

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(4 citation statements)

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“…Sytyi [12] gives an empirical equation for the camouflet depth h+ for explosion of a long cylindrical charge in a soil of the loam type; this agrees in sense with the value _ 3iT_I"~" o h+ 2VTVW, m (15) for the given blasting conditions.…”

Section: P~ X) ;mentioning

confidence: 74%

“…We can therefore use the principal relations of the theory of a single equilibrium crack for a plane state of deformation and the condition of existence of a system of equilibrium Griffiths cracks of half-length l, spaced 2h apart in an elastic--brittle medium [13][14][15].…”

Section: H Bx --Ax a + (2ah --C) X 2 2~aoxmentioning

confidence: 99%

“…2) We replace the smooth fall of pressure in the wave front by a stepped one and divide the volume Vo into i zones with approximately constant values of p. 3) For each of these zones, following [13][14][15], we calculate Z, and h, where the section (l,, L), L being the maximum dimension of the initial cavities, is divided into j intervals with respect to I. 4) For the given rock mass we fix the probability distribution of the initial cavity dimensions.…”

Section: H Bx --Ax a + (2ah --C) X 2 2~aoxmentioning

confidence: 99%

“…6) From the given shape of cracks a with equilibrium distribution, using [14,15], we calculate the volume of the cracks themselves, Vo*, contained in V,.…”

Section: H Bx --Ax a + (2ah --C) X 2 2~aoxmentioning

confidence: 99%

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The optimum depth for long cylindrical explosive charges

Stepanov¹,

Demchuk²

1975

Soviet Mining Science

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By the optimum depth for a long vertical cylindrical explosive charge, h,, we mean the length of the monolithic stemming of homogeneous material which, under given explosion conditions (given mechanical properties of the rock and stemming, natural parting of the rock, quantity and properties of the explosives, presence or absence of air gaps between the charge and the borehole walls, and direct or reverse initiation), will give the maximum utilization of the energy of the explosion in terms of newly formed free surface (crushing) and the total crushed volume.We will consider hz from two points of view.First we calculate the optimum maximum depth hz = h+, which we find by means of the phenomenological theory of puncturing of a barrier Of finite thickness, as developed in [I, 2]. Then we will use another criterion for hl --simultaneity of ejection of the stemming and emergence of the explosion products at the free surface through the clefts in the surrounding rock [3]. The two approaches will be compared by means of an illustrative example. Experimental ResultsWe investigated the commonest stemming materials (sand, gravel, clay, and water) with charges of Ammonite 6ZhV weighing Q = 300 g, with diameter do = 4.2 cm, length ~o = 22 cm, in 1 m boreholes in a granite quarry in the region of the "Kuznechnoe" station of the Leningrad region and in the Bugaevskii sandstone quarry in the Voroshilovgrad region.To record the motion of the stemming and its time of flight from the borehole we constructed a special apparatus, based on recording the changes of inductance in a coil 2 m in diameter in which a magnetic field from ferrite rings pressed into the stemming at distances of 60, 40, and 20 cm from the borehole mouth moved.The coil was placed around the borehole. The emf induced in the transducers was recorded with an oscillograph.The velocities of the transducers were equated with the velocity of the corresponding layers of stemming.The time marks were made with an ionization gage at the opposite end of the cartridge from the detonator. The resulting oscillograms were processed in conformity with calibration graphs taken before the explosion after warming up the apparatus and balancing the measurement bridge.The start of motion of the stemming was monitored with an SKS-IM instrument. *Deceased. All-Union Scientific-Research Institue of Natural Gas.

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Section: P~ X) ;mentioning

confidence: 74%

Section: H Bx --Ax a + (2ah --C) X 2 2~aoxmentioning

confidence: 99%

Section: H Bx --Ax a + (2ah --C) X 2 2~aoxmentioning

confidence: 99%

“…6) From the given shape of cracks a with equilibrium distribution, using [14,15], we calculate the volume of the cracks themselves, Vo*, contained in V,.…”

Section: H Bx --Ax a + (2ah --C) X 2 2~aoxmentioning

confidence: 99%

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