622.235Various problems in mine construction are solved by driving workings in cohesive compressible rocks which are consolidated by blasting. As a rule, the sides of the cavities made by the blast are intersected by radial cracks, and extra work is required to eliminate them. In drawing up the plan of operations, it is therefore necessary to know the widths of the cracks and their depths of penetration into the ground.Problems of crack formation in brittle ledge rocks can be solved on the basis of theoretical work by V. P. Koryavov [1, 2], For compressible, inelastic rocks, a method is suggested, based on deformation theory and the theory of limiting equilibrium.Let us consider the deformation of an elementary volume of ground at some distance from the charge. When the front of the shock wave passes, this element will deform in conditions comparatively close to uniaxial compression with lateral expansion prevented. Intense bulk deformation is accompanied by relatively slight change of shape. Owing to the high triaxial pressure, deformation occurs by plastic flow, and fissures are not formed.After the wave front has passed into the depths of the rock, the pressure o r falls, but movement of the ground, including the element under consideration, continues. There is intensive change of shape. After the pressure has fallen below a value corresponding to the plasticity conditions of the ground, as the element moves, tensile forces arise in the lateral direction; they exceed the negligibly small tensile strength of the ground, and fissures appear.Thus determination of the crack parameters reduces to determining the displacements and deformations of the layer of rock acted on by the explosion. The displacement of any layer of ground is determined by the bulk compressibility of the rock further into the depth of the mass, while the ratio between the increase inthe perimeter of the layer due to displacement and its deformation by change of shape determines the widths and depths of the fissures.Take spherical coordinates r, ~0, and ~, with origin at the center of the charge (Fig. 1). By symmetry, for [sotropic rock, = 4=0; %4:0: s =% ,~0.(1) ~r 4= 0; % % , Neglecting the tensile strength of the rocks (in view of its smallness in comparison with the pressures arising during blasting), we can write % = %(r); %:%=t~%,where g is a coefficient equal to the ratio between the resultant lateral pressure and the radial pressure.In attacking the problem of the opening of fissures in the side of the cavity, we note that, for the rock layer adjoining the cavity, the main type of deformation is change of shape, bulk compression being small [3]. To simplify the calculations, in solving this problem we can therefore neglect the influence of bulk compressive deformation on the change of shape, and for the latter we can write ~'= e, (*-~); %=% (~_~). <3)
2E'The stresses o r for a completely contained (camouflet) explosion can be calculated from the Jones-Miller adiabatic [4]; the initial pressure of" the detonation products can be found a...