The deformation of a mass around a working is one of the most important problems in rock mechanics.It has been investigated in various formulations [1][2][3][4][5]. The situation in which the mass forms an inhomogeneous blocky structure is of particular interest.There are data showing that, at great depths, the blocky structure is clearly expressed in many cases, and plays the basic role in the deformation of the mass [6][7][8].In a strict formulation, the investigation of problems of the deformation of a blocky medium encounters considerable difficulties.However, if from the beginning attention is confined to integral estimates rather than to analysis of the detailed stress distribution within the blocks, such problems can sometimes be considerably simplified.The classical example is the investigation of the earth pressure at a supported wall.One slip line is formed here and if the stress distribution within the block (creep prism) is of no interest the formula for the pressure at the wall is relatively simple.This approach is possible for the fairly general case where the wall roughness, the load acting from above, and other factors are taken into account.It is well known that the value of such solutions is often no less than that of "accurate" solutions obtained using continuum theory.In other words, this "engineering" approach is completely justified and, where possible, its use always makes sense.At the same time, as far as is known from the literature, mine-working problems have only been investigated within the framework of a continuum approach, and this alternative engineering approach has not been used.In the present work, some redress of this imbalance is attempted, i.e., an attempt is made to find a formulation of the problem and calculation scheme similar to the statically determined formulation in the supporting-wall problem.This work was stimulated by analysis of the flow of friable material in a converging channel.Flow conditions with shear localization were observed in [9]. The localization or, equivalently, appearance of a blocky structure permits the formulation of an approximate calculation scheme [i0].In a certain sense, the motion of the rock mass toward the working can be compared to the motion of material in a radial channel with an aperture angle of 360 ~ . On the basis of this interpretation, a kinematic scheme analogous to [10] but for a blocky medium around a working can be constructed.i. Turning to the formulation of the problem, consider an infinite rock mass with a working of radius R 0. The problem is considered in a plane formulation.Isolating the zone in the immediate vicinity of the working with R0 < r < R I in the rock mass and supposing that it has a blocky structure, a simplified approach is adopted, assuming absolute ridigity of the blocks rather than analyzing their internal stress distribution.In other words, all the information on the deformation of the structure is contained in the contact conditions between the blocks.The block boundaries are approximated by straight lin...
