mining in the field, this process is studied in the laboratory with the aid of models. To get reliable data for calculating the parameters of the discharge figures, the system of mining, and the ore discharge indices, we must maintain geometrical similarity and similarity of the mechanical properties of the loose medium between the model and the prototype. In this case, to convert the parameters of the system of mining, found from the ore discharge indices, to the prototype scale, it is enough to multiply the results by the scale factor. Whereas it is easy to maintain geometrical similarity in a model, it is very difficult to obtain similarity of the mechanical properties of the loose media. Investigators who have studied ore discharge usually recommend that the model should preserve equality or similarity of the natural angles of internal friction and repose, the coefficient of distention of the loose material, the moisture content, the grain-size composition, and other mechanical characteristics which influence the running properties of the broken-down ore [1, 2]. To determine most of these characteristics in industrial conditions is very difficult or impossible, and in the laboratory, as a rule, one cannot obtain the required combination of these indices. Therefore in a model one usually obtains equality or similarity of only a small fraction of the mechanical characteristics of the caved ore, and investigations have not infrequently led to results which differ between the model and prototype. To avoid modeling all the mechanical properties of a loose medium in laboratory experiments we can use some parameters which characterize these properties as a whole. These are the eccentricity of the discharge ellipsoid $, the indexof looseness of the ore {the radius of curvature of the vertex of the discharge diagram) P, the diameter of the caving crater on the surface of the caved ore d, etc.; on this basis G. M. Malakhov, V. V. Kulikov, and V. R. Imenitov [1-3] have developed the best-known conditions of similarity for modeling the discharge of caved ore. These similarity conditions and expressions for ~ and P were developed for platform ore discharge for which the discharge figure is a symmetric solid in the shape of an ellipsoid of revolution. In layerwise end discharge of ore in a system of subpanel caving, the discharge figure is a triaxial ellipsoid or an ellipsoid of revolution truncated by the planes of uncaved rock, and this governs its development and prevents us from using the above parameters to preserve similarity in the model. In this case a model of discharge can be made by preserving geometrical similarity alone, and the test parameters of the system of mining, calculated from the parameters of the discharge figures, can be determined by comparing the absolute values of the latter obtained in the laboratory and in the field. This preserves equality of the absolute values of the discharge indices of the ore in the model and prototype. As a confirmation of this, we will give a method of calculating the parameters of a system of mining, starting from a comparison between the parameters of the discharge figures of the model and prototype, with equality of the ore discharge indices. To simplify the calculations, we assume that the discharge figure is an ellipsoid of revolution, that the major axis of the figure lies alongthe plane of the uncaved reck, and that the caved layer of ore has the form of a parallelepiped with free dimensions in the ratio 1 : 2.
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