The qualitative and quantitative indices of the external loading of supports in mining-out workings are determined by the laws of deformation, fracture, and displacement of mul,dlayer sedimentary strata. The external loading indices of supports usually vary as the face advances. The greater their range of variation, the severer the conditions under which the supports must operate. The variation of these indices as the face advances is due to periodic fracture and displacement of the thicker and stronger layers in the immediate and main roofs. In absence of such layers, the changes in rock pressure as the face advances are less marked.It has been assumed that the layers of the immediate and main roofs break up as result of flexure. Investigations by the All-Union Scientific-Research Mine Surveying Institute (VNIMI) in mines [1, 2 J have shown that the ratio of the length of the blocks to the thickness of the layer is often 0.25-0.40, or even less than 0.1; i.e., in mines the disintegration of thick layers into blocks, the length of which is close m the thickness of the layer or less, evidently takes place under stresses different from those on which the basic condition of limiting stress is based in bending calculations. In these cases fracture may be due either to shear deformations (where the layers above the face are compressed) or breaking-away (above the area around the face, under the effect of bending moments). Bearing in mind that rocks are brittle, Kuznetsov [3] suggested that cleavage calculations should be performed for thick cantilever beams. The condition of the limiting state during cleavage has been described only approximately. Fisenko [4] assumes that the bending moment due to external forces and gravity is balanced by the internal forces in the rock which resist cleavage and are distributed over the whole cross section of the beam in accordance with a linear law. This method of calculating cleavage must be regarded as approximate, because the actual stress distribution in short beams has never been experimentally investigated and strict analytical solutions are absent. Hence the conditions of limiting stress, on which calculations of cantilevers of rock layers are based, correspond to two types of stress distribution patterns in unsafe cross sections-bending and shear. When brittle rocks are bent, fracture begins also in the regions of tension, i.e., as a result of cleavage.Calculations on real thick layers of rocks are complicated by the fact that in many cases they consist of a stack of mutually cohesive Iayers of different thicknesses, with different moduli of eIasticity and different coefficients of lateral deformation. The greater the thickness of the layer being calculated, the more likely is it to be nonuniform. Furthermore, in a mine this layer is wedged above supports and interacts in a fairly comrJlicated way with the superincumbent layers. In theoretical investigations, it is difficult to take account of whole range of factors on which the sequence of development of fracture of the r...

The stress distributions near the faces of workings of finite length are of scientific and practical interest, because they are related to the stability of rock walls and the rock pressure phenomena found in driving workings, including shock bumps, which are felt in certain conditions at great depths.In assessing the stabilities of rock walls without supports, we take account of the known [1] stress distribution near an extended part of the shaft; according to [1], the stresses at its surface are:Here o z, op, and a 0 are the vertical, radial, and tangential stresses, Tpz, r0z, and Tp0 are the tangential stresses, is the density of the rock, H is the depth, and X is the coefficient of lateral thrust.The maximum stresses (o z or o0) are compared with the calculated resistance of the rocks. However, notice is not taken of the fact that, during the sinking of a shaft, the walls all the way along it are for some time near the face, and undergo greater stresses than those predicted by (1).Analytical solution of the stress distribution near the face of a shaft [2] is difficult, and therefore to solve this problem we used the optical-polarization method of investigation with three-dimensional models containing "frozen" stresses,The stresses were studied for the four most typical types of face ( Fig. 1): flat (a); slotted (b), formed in core drilling; spherical (c), characteristic of cutter-loader operations; and stepped (d), when the shaft is driven in two phases. These shapes were reproduced in a single cylindrical model, 300 mm in diameter and 230 mm in height, made of epoxy resin. The cavities simulating the shafts were formed with the aid of fusible inserts 20 mm in diameter with ends of the appropriate shapes. We used the method described in [3].The model was subjected to hydrostatic pressure, so that it simulated the stresses in an elastic rock mass with a coefficient of lateral thrust k = 1. After "freezing", the model was sawn into blocks including the "shafts"; from each block we cut plates (slices) 1.6 mm thick -one meridional (Fig. 1), and several lateral-to determine the vertical and tangential stresses at the surfaces of the shafts. The isochromes and isoclines of the plates were measured with a coordinate-synchronous polarimeter with a compensator.The stress measurement results are represented in the form of concentration coefficients, i.e., the ratios Of the stresses to the external hydrostatic pressure P on the model. From the stress distribution diagram it follows that, in the region near the face, the shaft walls undergo a concentration of vertical stresses which attain their greatest value for the fiat face (a). At the corner between the face and the wails, the concentration coefficient is a maximum, and depends on the radius of curvature, which in the experimental conditions was taken as 0.05 b, where b is the diameter of the shaft. In this case the concentration coefficient of the vertical stresses is 4.5. There was a similar concentration of radial stresses at the end of the face where it meets the...

Sinking of vertical shafts and other mine workings by drilling and blasting leads to the development of roughheSS (projections and hollows) in the peripheral rock; with the usual type of drilling and blasting, these reach 50-70 cm in depth (Fig. 1). A number of recent analytical papem [1-3, etc.] show that these roughnesses have a marked influence on the stress distribution in the periphery of a working, especially an unsupported one. We have experimentally attacked the problem of the action of a sprayed-concrete support (lining) and its interaction with the surrounding solid rock weakened by curved apertures.Mathematically, the problem is analogous to that of the stress distribution in a weightless plate with a hole, the periphery of which simulates the roughnesses of the unsupported working, or in a plate supported by a ring which repeats these roughnesses, with uniform compressive stress at "infinity." We used the optical-polarization method of investigation, with plane models with "frozen-in" stresses. The scale of the models was 1:100.The models were disks, 175 mm in diameter and 10 mm thick At the center of each disk was a hole simulating a vertical working with a rough* or smooth periphery. In preparing models with supported contou~ we glued a ring into the hole, so that its external contour matched the internal contour of the hole. The models were made Disks simulating the solid rock were made from SD-10 resin, which has a modulus of elasticity of E = 140 kg/cm z at 'the freezing point. The model supports were made from SD-5 (E = 45 kg/cm~ or epoxy resin (E = 400 kg/cm~.

The optical-polarization method of stress measurement is often used to attack problems in rock geomechanics, especially in research on the stress distributions in rocks around mine workings, based on models made of optically sensitive materials. This method is used to determine a number of complicated stress-strain states in the rocks, due to the driving of workings; it would be difficult to solve these problems analytically.To attack problems with the photoelastictty method, use is made of optically sensitive materials which have various different moduli of elasticity. For example, one can determine the stresses around workings driven in a stratified rock mass, investigate the states of stress of various combined supports, study the interactions between mine supports and the rock, etc.In optical model practice, materials which are commonly used include epoxy and polyester resins [1][2][3]. These materials possess good photoelastic properties, and it is easy to make models of them. They are also readily avMlable. Materials with variable elasticity modulus for work using the "freezing" method, based on these resins, can be made by adding plasticizers [1] to the liquid resin, or by altering the degree of crosslinking of the polymer by varying the ratio of resin-ologomer to hardener [2]. Thus, from epoxy resin, by varying the degree of crosslinking, we can obtain materials with elasticity moduli differing by factors of 10-15.However, when models with low elasticity moduli are made from epoxy or polyester resins, a number of undesirable phenomena arise. Materials based on these resins display reduction in the "freezing" temperature simultaneously with reduction in the elasticity modulus. Therefore, in preparing materials with very low elasticity moduli (of order of tens of kg/cmP), we have to deal with low "freezing" temperatures, sometimes not far above room temperature. This makes it difficult to cut the models, because the "frozen-in" stresses can become annealed out. Furthermore, total or partial annealing of models or sections made of these materials may even occur owing to temperature variations in the room where the model is kept. Low-modulus materials based on epoxy or polyester resins have increased brittleness, which makes it harder to work them mechanically. The preparation of low-modulus plates and blocks of epoxy resin involves a high percentage of wastage due to cracking of the models during polyme r [z at ion.

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