Recent years have seen much discussion [ 1-~] of the development of reliable methods for predicting the behavior of rocks and the selection of the parameters of supports for mining-out faces. The authors of these reports concluded that the rocks above workings usually begin to break up when there is a loss of continuity along various natural weakened points induced by shear or cleavage.The distinguishing feature of sedimentary rocks is the presence of weak links along the beds, which are largely responsible for the onset of the development of disintegration; in igneous and metamorphic rocks the weakened sites are block contacts, cracks, and various other defects.From the practical point of view it is important to know not only the sites of possible break-up of the rocks but also the sequence of the processes of further development of these disturbances. The latter must be used in calculating the support capacity of the roof rocks (delineation of the beds and bands, determination of the stresses induced by the additional load imparted by the superincumbent roof rocks, and determination of the interbed friction forces), in selecting the characteristics of the support and the mining system to be used for underground mining operations.For the case of a single room of rectangular cross section, in [ 5] it was shown analytically for the first time that the loss of continuity of weakened interbed rock contacts by shear begins above the wall of the room. Similar results have been obtained for cases of several contiguous rectangular workings [7, 8]. Nevertheless, there is still no method enabling us to investigate by the use of engineering-geologic data the discrete discontinuity of the solid rock and to predict by calculation the stages of development of bed separation in a stratum at weakened contacts and positions.This article deals with the criterial postulates for such a method.We examine a system of contiguous rectangular workings (rooms) (Fig. 1), for which the geometric dimensions (pillar, room spans), the characteristics of the geological cross section of the layered roof, and the mechanical indices of the contact are known. As a result of the calculation we need to determine the sequence of inception and development of bed separation cracks in the roof rocks.

In the USSR coal industry, zones of elevated mine pressure (IMP) are passed over each year in up to 800 cleaned cuts in coal seams with a dip of up to 35 ~ The effect of IMP on the transition segments is expressed as an increase in the rate at which side walls draw together, and the change in the character and qualitative parameters of rock failure in the roof: an increase in the rate of fracture, a reduction in the size of the blocks into which the rock is fractured, etc. These factors affect the variation in the stability and loading properties of the roof in conformity with which the bracing should be selected and additional measures developed (when necessary) to prevent the collapse of rock into the cleaned cuts under the bracing. Zones in which interseam rock may go into the limiting state, but not be restricted by the analytical description of its stressed state, should therefore be examination with analytical methods of prediction as applies to cleaned cuts. For the sake of brevity, we will hereinafter say that the purpose of the analytical investigations is to calculate the limiting states in interseam rock for different systems of forces actin E on its upper, lower, and lateral boundaries.Let us examine the question concerning force systems that may form on the upper boundary of an interseam.As a rule, a formation of coal seams is worked in descending order: the uppermost coal seam is worked at first, and then other seams of the formation sequentially from upper to lower. Beginning with the second seam, all seams of the formation are, in this case, worked beneath the overworked interseam in which it is also necessary to expose the zone of the limiting state.In predicting zones of limiting state in rock in an overworked interseam, it is extremely critical to assign directly the parameters of the system of forces acting on its upper boundary. These parameters depend on the extent to which the earth's surface is undermined by the upper coal seam, and also on the presence and state of the pillars that remain in working the upper seam.In sections of the upper interseam boundary, above which the earth's surface is completely undermined, it is possible to assign a uniformly distributed specific load equal to the product of the density of the rock and the depth of embedment of the upper boundary of the interseam for the computations. These sections begin to form under conditions when the minimum dimension of the excavated area ~nin of the overworked seam first to exceed the depth H i of its embedment.A general diagram of the layout of remaining coal pillars with a width u and excavated space with a width s on the upper boundary of the interseam after working the upper coal seam in a formation lying at a depth H I is shown in Fig. la. In ananlyzing the diagram, it is necessary to imagine that to the left and right of the pillars, there is a series of pillars between which there are excavated spaces. Different parameters of the force systems in the upper seam, i.e., on the upper boundary of the interseam can be fo...