UDCIt is well-known that after explosion of charges in contouring blast holes in the rock beyond the contour, a series of cracks is formed and propagated some way from the surface of the working.Cracks in the walls of workings reduce the subsequent resistance of the rocks to loads, and hence reduce the overall stability of the workings.Furthermore, inexact drilling of the mouths of the blast holes and deviations of the holes during drilling from the plane of the contour of the working usually cause overcutting and roughness of the walls and roofs of the workings.It is usually assumed that the size of the zone of crack formation depends on a number of factors, primarily on the charge weight and type and the mechanical properties of the surrounding rocks. For spherical charges the dimensions of the zone are usually considered to depend on the radius of the charge, i.e., the radius of the cavity occupied by explosives of a certain weight. Therefore it is natural to ask how fracture and crack formation will occur when the charges are of elliptical cross section.Yanovskaya et al.[1] investigated the velocity field arising in an infinite medium on explosion of an elliptical charge using a simplified model of the action of the explosion according to the theory of O. E. Vlasov. According to this theory the action of the explosion is instantaneous, and at the moment at which the energy of the explosion gases is transferred to the medium, the latter is regarded as an ideal incompressible liquid. During the explosion, the velocity field of the particles of the medium has a potential which, at all points within the region, satisfies the well-known equation of Laplace.
References [1][2][3] indicate that oval-sectioned charges are more effective than circular ones. Nonuniformity of stress distribution in the solid rock is a very important factor in rock fracturing under dynamic load [4]. We have therefore tried to study the stress field formed in the rock when oval-sectioned charges are fired.According to the authors of [5][6][7], the most important factor in rock fracture is the pistonlike pressure of the detonation products. The stress distribution is the same and the mode of fracture similar for static and dynamic loads [8,9]. The authors of [4,10,11] say that hard rocks do not display significant plastic deformation during shotfiring (the yield stress increases with the deformation velocity, thereby decreasing the possibility of plastic deformation); in [12][13][14] it is said that, during rapid load application, the deformations in rocks are linear functions of the stresses over a very wide range of loads. Experiments by Filippov [5] have shown that rock fracturing during shotfiring in three-dimensional and plane models has the same character in the laboratory as in the mine. This has enabled us to use solutions based on elasticity theory for studying to a first approximation the qualitative character of stress distribution around an oval charge, and to compare the stress field thus obtained with that aroud a circular charge.If we cut the layer of rock by two planes perpendicular to the charge axis at its center, and take the charge length as greater than its diameter, it may be assumed that we are dealing with a plane problem in elasticity theory, namely the determination of the stress field in an infinite plane with a hole whose edge is subjected to a uniformly distributed normal pressure. To study the stress fields produced by firing oval charges with various semiaxis ratios (with constant area of the "hole"), we used the solution of the plane problem of elasticity theory for stresses in an infinite plane with an elliptical hole whose edge is subjected to a uniform pressure P [16]. The stresses were determined by the equations ~o = --P-b
In the dynamic fracture of material, nonuniformity of the stress distribution is very important [1]. To study the stress concentrations in the rock during the firing of charges of rectangular cross section, we have attempted to investigate the stress fields formed by the explosion of such charges with various proportions of the sides.According to some authors [2], the theory of elasticity can beused to study the stresses during the initial stage of the action of the explosion products on the rock, and to estimate the strength of the rock. To find the stresses round a charge of rectangular cross section, we applied the elasticity theory for stresses in a planar medium weakened by an opening [3] to the case when the external forces are zero at infinity and the periphery of the opening is subjected to a uniformly distributed normal pressure with intensity P. The problem is solved by means of two functions of a complex variable, ~0(I) and ~,(I), which are given by the functional equations of the problem, where y is the contour formed by the edge of the opening, o is a complex number corresponding to a point on the contour, I is a complex number corresponding to any point in the plane, and w(I) is a function which maps the region under study conformally on to the interior of the unit circle. From ~o(I) and ~,(I) as found from (1), we determined the stress components %, a0, ~r0 in a curvilinear orthogonal coordinate system [4] ( X[~ (I) ~" (I) o' (I)--?" (I)~" (I) tI"' (I)1From the values found for :0, :0, ~r0 at each point, we found N t and Nz, the principal stresses, and rma x, the greatest tangential stress. In this way, we investigated the stress fields for a square and for various rectangles.The results for the square (a/b = 1) and rectangles (a/b = 3, 11) are listed in Tables 1-3. These tables give the greatest normal and tangential stresses as fractions of P, the pressure in the charge hole, at various points in the solid rock: the position of each point is given by p, its relative distance from the charge hole, and O, the angle between the radius to the point and the x axis (Fig. 2). The rock-charge boundary corresponds top=l, 692
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