Kinetics of fracture of a projection on the periphery of a working

Abstract

Disturbances to the uniformity of the state of stress of the rock by surface exposures when media in contact have different mechanical properties, or in the case of a sudden change in geometrical outline (e.g., seam--pillar, roughness of the periphery of real working, etc.) under the high pressures in deep horizons or the action of high-amplitude explosion waves, can lead to undesirable fracture on the periphery, which is dangerous to nearby personnel and equipment.A common phenomenon of this type --rock bursts --consists of quasistatic failure of part of the surface of the periphery of a working, accompanied by its separation from the rock, sometimes at high speeds [i].In [2] we discussed some aspects of the nonuniform restriction of the "transverse" deformation, with additional nonuniform concentration of the state of stress near the contacts of different materials, at points of sudden change of the boundary lines, and with fracture of the medium. A similar mechanism is possible for the fracture of projections on the peripheries ofxreal mine workings.Suppose that during mining operations a projection has been formed on the periphery, with amplitude h and transverse dimensions 21 and 6 at its base (Fig. la); the interior of the medium is indicated by shading. The stress field P in the rock may be due to rock pressure in a vertical or horizontal direction depending on the position of the projection on the periphery or to the incidence of seismic blasting waves on the working.In numerical calculations we will model the projection by the region OABCDEO (Fig. ib), with boundary conditionsc) c~=~=OAs usual, h and I are the height and half-width of the bench; the boundary conditions in Fig. la correspond to the plane of symmetry of the middle of the bench; the boundary conditions in Fig. ib-c correspond to the broken surface of the free surface;the conditions in Fig. id* simulate compression at infinity in the form of a given vertical displacement v, constant along the loaded boundary ED, together with rigid restriction along it on the horizontal displacements u. The latter somewhat strengthens the stress concentration and still more emphasizes all the phenomenena as a whole; the conditions (Fig. le*) characterize a uniform undisturbed sta~e of the virgin rock.The whole region is divided into triangular elements, as shown in the upper part of Fig. Ib; the numbers of points on the segments OE, ED, OA are respectively 30, i0, and 15; the maximum dimensions of the region are I x = 25 mm, Iv = 50 mm.In analysis of the influence of the parameters of the projection, an increase in ifs height h or a decrease in its width 2 was given by a corresponding change in the dimensions of the elements while preserving their number; as the elastic properties we chose the values E = 5. i0 ~ kg/cm 2, ~ = 0.15i the method of calculation was similar to that in [2].Under conditions of plane deformation the stress field is characterized by three components Oy, Ox, T x.