The study of industrial explosions is made difficult by the high pressure and temperatures arising from the detonation of large charges, and by side factors which are difficult to allow for. Simulation by models enables us to cut down the number of costly industrial experiments while maintaining identical conditions so that laboratory resuits can be applied to the full-scale prototypes. The breakup of a medium is governed by its physical and mechanical properties, the characteristics of the explosion, and the conditions of blasting. These factors must be taken into account when designing a model of the process.Breakup is a complex nonstationary process, which can arbitrarily be divided into three main stages: propagation of the stress field, fracture formation, and separation of the fragments formed. In previous work on models of breakup by blasting, the similitude criteria do not allow for the fracture-formation stage, which is critical for the fragmentation process, or the time characteristics of the breakup process. The aim of our present work is to establish similitude criteria which will take account of one phase of the breakup process, namely, fracture formation.The theoretical analysis of the breakup process is based on the hypothesis of A. A. Griffiths and M. V. Machinskii, who postulate that in any body there are defects (microfractures) from which macrofractures originate when a stress field passes. In the propagation of the stress field due to the explosion of a charge, in some volume dv of the medium, dn fractures will open up. The density of sites of origination of individual fractures n o is governed by the maximum applied stress and by the strength properties of the real and model materials, no= ,(s) ds, Ser O)where S is the surface area of a crack, ~(S) is the differential distribution function of the dimensions of the cracks, o is the applied stress, and Scr(O) is the surface area of the smallest crack opened by the stress.As the stress wave spreads, the maximum stresses in it will decrease owing to geometrical expansion and dissipative energy losses in real media: The density of crack initiation sites will be some complicated function of the distance from the charge center, ,r%= (r)]where n o is the number of initiation centers in unit volume, o 0max is the maximum stress at the wail of the blast hole (charge cavity), lob] is the breaking stress under static load, r0 is the radius of the charge, and r is the distance from the charge center.If the body is cylindrical, the total number of crack initiation sites will be R It~ (r)]rc, r n : 2~H, f[-[-~cO 7~o0 where H is the length of the body and R its radius.

In rock blasting, inhomogeneity and fracture have a marked influence on the resulting fragment-size composition.Various authors [1][2][3][4][5] have investigated fragment-size composition taking account of the original jointing of the rock.They make an a priori assumption on the statistical distribution of the fragment sizes, then choose experimental data confirming the assumed distribution law. However, the experimental data on fragment-size composition of blasted rock can be equally well represented by most two-parameter positively asymmetrical distributions [6]. Experimental verification of these laws is very difficult. It is hard to check the agreement between the theoretical and empirical distributions with the aid of some criterion of agreement, because even from the value of the calculated criterion we can often conclude that the experimental data are equally consistent with several distribution laws.The choice of distribution should be based either on the physical essence of the process of cruching rocks by blasting, or on a study of the statistical laws of fracture of inhomogeneous jointed media.This latter basis was used in the investigations made by the present authors.To study the influence of the structure of a broken medium on the resulting fragmentsize composition due to blasting, we performed experiments on inhomogeneous and block models. The inhomogeneous models were made from granite fractions (structural units) measuring 10-20, 20-30, and 30-40 mm (compressive strength 1.2.108 N/m 2) cemented by a 1:6 sand--cement mixture (compressive strength 1.42-107 N/m 2) or by rosin (compressive strength 2.106 N/m2).The granite fractions were placed in a mold measuring 0.2 x 0.2 x 0.2 m which was filled with the cementing material. We prepared six types of models in this way (four types with granite fractions cemented with sand--cement solution and two types cemented with rosin).To study how the structure of the medium and the specific explosives consumption influence the intensity of crushing of the model material, we used PETN charges weighing 50, i00, 200, 400, and i000 mg (charge density 0.9 g/cmS).We performed 4-6 experiments with the same charge weight on each type of model.The averaged results are listed in Table I.The initial dimensions of the units of stronger material (granite) determine the position of the maximum of the fragment-size distribution. If the model contains initial fractions measuring 10-20 and 30-40 mm, then after the blast we observe two maxima on the fragment-size composition distribution (Fig. 2). With a low specific explosives consumption we get fragments with larger dimensions than those of the initial fractions owing to incomplete fracture of the cementing material.This explains the maximum for fractions coarser than those of the original material.The influence of the charge size on the fragmentation results was investigated on models containing the 10-20 mm granite fraction cemented by a sand--cement mixture (Fig. 3) and also on models based on the 20-30 mm fraction cemented...

When rocks are extracted in building-stone and limestone quarries, in addition to the maintenance of highgrade crushing during blasting, one must reduce the yield of overcrushed rock, which depends on the pressure pulse parameters in the charge chamber, characterized by the rate of increase and value of the maximum pressure, and on the duration of the pressure above this level. We will establish the effects of each of these parameters on the stress field characteristic and the crushing intensity of the rocks.The effect of the rate of pressure increase in the shock wave front on the parameters of the stress field created by an explosion in a medium can be established in an elastic approximation. Such an assumption is perfectly acceptable because the fracture time is much greater than the duration of pressure increase in the charge chamber when commercial high explosives are used. Let us assume that the charge cavity of radius r 0 is located in an ideally elastic infinite area. (The condition of limitlessness is automatically satisfied for all laboratory and industrial explosions, because during the period of pressure increase in the charge chamber the stress wave does not reach the free surface.)The one-dimensional stress wave created by the explosion is represented by a single system of generalized equations:Oa r

The mechanism of fragmentation of fissured rocks acted on by blasting has certain features which distinguish it from the mechanism of fragmentation of monolithic media. In rocks with a developed system of fine fissures, the pressure of the explosion products in the cavity falls more rapidly than in monolithic rocks because the compressed gases penetrate tile fissures. The stress field is less intense and the stresses are rapidly attenuated as we go further away from the charge. This is due to absorption of the energy of the stress field as it passes through the fissures and is reflected from their wails. A large part of the stress field energy is converted to kinetic energy of the moving fragments. In this case the percussive effect of the explosion is much reduced and the piston action of the gases becomes more important. In rocks broken up into individual blocks by large sparse fissures, only the block containing the charge chamber is intensely fragmented; the remainder of the rock mass fails apart along the fissures. In rocks with this type of structure, the piston action of the explosion is unimportant, owing to the monolithic structure of the individual blocks and the low density of the fissures (i.e., the small number of cracks per unit volume).The fragment-size distribution of the blasted rubble will be largely determined by the structural elements of the spatial fissure network. A more efficient utilization of the energy stored in the stress field formed by the explosion is possible, in the first place, in conditions which hinder the opening-up of the fissures. The stress field intensity falls off less rapidly if there are only tightly closed fissures or fissures narrower than the absolute deformation of the rock in the region of localization of the fissures. In the second place, the rock must not move as an integral whole, i.e., the velocity field must have a nonzero gradient. In this case there is an additional mechanism for transfer of the stress field energy to the more distant zones in the rock: this is essentially due to collisions between moving rock fragments. A series of such collisions causes a state of stress in the more distant parts of the rock, and thus part of the kinetic energy is re-transformed to energy of the stress field.We used model materials to study the influence of fissuration on the fragmentation of a medium during blasting and the relation to the stress field. The models consisted of rosin cubes, 200 x 200 x 200 mm in size. The fissures were simulated by interlayers of materials which corresponded to the two main types of material which fill cracks in rock. Plastic incompressible fillers such as dense clay or water were simulated by modeling clay; compressible fillers like dust or fine rock fragments were simulated by dense cardboard. Hollow cylinders of modeling clay with wall thicknesses of 0.5, 1.0, and 1.5 cm and equal in height to the models were placed on the bottoms of the molds to coincide with the axis of the blast hole. Cardboard baffles were placed parallel to the cha...