Determination of abutment pressure and assessment of stability of seam edges and pillars with postlimiting deformations

Abstract

The theory of postlimiting deformations, developed as a result of progress in rock testing methods, enables us to refine the formulation of problems concerning the calculation of abutment pressure and assessment of the stability of workings and the danger of shock bumps. In this article, we develop previous general results on the one hand, we include postlimiting characteristics in the scheme of solution of the abutment pressure problem; on the other, we derive exact values of the critical combinations of parameters corresponding to loss of stability in certain particular problems. This is not only of practical utility, but also permits us to draw inferences on the error of simple approximate estimates of stability. The asymptotic expressions which we obtain and the results of our calculations will also be of interest for the theory of cracks. We use the same formulation and notation as in reference (1). The difference is that the law governing the increase of normal stresses in the zone of irreversible deformations is not specified in advance, but is found in the process of solving the equations by means of rheological relations for the material of the seam when it is deformed in the postlimiting parts of themore » stress-strain diagrams. In a number of cases of practical importance, problems of determining abutment pressure can be reduced to a consideration of cuts, the flanks of which are subjected to loads sigma yy which are equal in magnitude and opposite in direction (1). The cut includes not only the surfaces of the workings but also sections corresponding to the zones of irreversible deformations in the edge parts of the seams.« less