Many sedimentary rocks are transversely isotropic bodies, the deformation properties of which are characterized by independent constants: E z and E z) the Young's modulus for extension -compression in the plane of isotropy and normal to it; g z3) the Poisson ratio which characterizes contraction in the plane of iso=opy during compression in it; g12) the Poisson ratio characterizing contraction in the direction of the y axis, perpendicular to the plane of isotropy, during compression in the direction of the x or z axis; andGt2) the shear modulus for planes normal to the plane of isotropy.In this system of coordinates, the generalized Hooke's law is written as [1]: 1 e~ = ~ (~ --~2~y --~t~%);

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The solution of the problem concerning the character of the distribution of stresses in a rock mass is extremely important for the proper interpretation of the results of observations of the development of rock pressure, calculation of underground structures, etc.Observations by the stress-relieving method can give some idea of the distribution of stresses outside the zone and in the zone of the effect of mine workings. A more reliable method of experimental investigations of the stressed state of rocks does not exist at present, although, as will be shown below, in this respect it has quite substantial shortcomings.The basis of the stress-relieving method is the use of the characteristics of the elastic recovery of the rock specimen upon artificial disruption of its bond with the mass. The method is widely used for those rocks whosespecimens retain their shape after removal from the mass.The investigations by the stress-relieving method were carried out in horizontal boreholes. The BA-100 machine was the drilling tool. A diamond bit 76 mm in diameter was used for drilling out the core. To record the elastic deformations of the core end released from loading we used strain gauges with a resistance of 100 ohms and a measurement base of 15 ram, a highly accurate galvanometer, and a special attachment. The boreholes were sunk from a horizontal working.The vertical o z and horizontal o x stresses were calculated in conformity with the manual [1] by the formulas of the elasticity theory applicable to the solution of the plane problem:where E is the modulus of elasticity of the rock specimen being relieved; e x, Sz are the relative deformations of the end of the core being relieved.The results of determining the stresses are shown in the table.It is apparent from the table that in all cases the horizontal stresses were on the average two times greater than the vertical stresses. If the vertical stresses were approximately equal to ~H, then the horizontal stresses were (1.5to 2.0)?,H. It was assumed that this character of the distribution of stresses could be explained by tectonic disturbances; by the effect of second and development workings; by the effect on the stressed state of the rocks in the ore zone of two hills at a distance of 500-1000 m away, whose absolute elevation was more than + 800 m, at an absolute elevation of the earth's surface above the mine workings of + 500 m and depth of the mine workings of 350 m. The presence of these hills can apparently have a definite effect on the distribution of stresses in the rock mass. However, a check by the formulas of the elasticity theory showed that the load from the hills cannot exceed 1.2 for the vertical stresses and 11.3 kg/cm ~ for the horizontal. 100

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When a working is cut in the solid rock, stress redistribution takes place. The new state of stress is governed by the initial stress state of the rock, the shape and position of the working, the mechanical properties of the rock, and the mechanical characteristics of the supports used [1]. If we are considering a long working deeper than five times its radius, we can base our calculations on a weightless plane weakened by a hole with the same shape as the cross section of the working, the stresses at infinity being equal to those in the undisturbed rock before the working is cut, at the center of the space which it will occupy.There are three hypotheses concerning the state of stress in the undisturbed rock: 1) a horizontal stress o x = k ill, where k < 1; 2) o x = ~,H, the hydrostatic case; and 3) o x = kyH, where k > 1. At the points of greatest concentration the stresses exceed the strength of the rock, and then plastic zones arise and may encompass the whole periphery of the working or part of it, according to the mechanical properties of the rock and the size, shape, and depth of the working. The methods of calculation of the stress field for regions of elastic deformation differ from those for inelastic deformation, and therefore we must justify their use in any particular case.Let us consider the instantaneous stress distribution at the periphery of the working (for example, during formation of a cavity by drilling and blasting) in relation to the depth of the working, for three values of k, namely 0.5, 1.0, and 2.0, and for circular, elliptical, and square workings.For a working of given cross section, in rock with given mechanical properties, the stresses on the periphery of the hole, other conditions being constant, will depend on the depth of the working below the surface. At some depth H I the greatest s=ess existing at some part of the periphex'y wiU reach the limiting value for the given rock, Oli m, and plastic deformation will begin to develop at this point. At a depth H z >> H l the srnallest stress on the periphery will also be Oli m, and then the whele periphery will be plastically deformed. To find the values of H 1 and H z we need to know the greatest and least stresses on the periphery of the working.For a biaxial state of stress in which the stress at infinity is a tension (compression) with values k),H and yH in directions making angles a and a + Ir/2 to the x axis, respectively, the stress on the periphery was determined in [2]. Then for an eUiptical cross section,