Abstract
It is a longstanding problem of the coalmining industry that alter a roadway has been driven, the surrounding rock will gradually be forced into the opening. The problem is being studied by the National Coal Board, using experimental and mathematical methods. This study is intended to evolve a mathematical method that is able to take into account the properties of the failed rock, and at the same time be faster in execution time and easier to run than the Finite Element Method, which is most commonly used for this type of work. The method described is based on analytic solutions to the equations for elastic and failed solids, the two regions being treated separately in the analysis. A boundary separating the two regions is defined, and the equations for the stresses are used to derive the shape of the boundary so that the failure criteria are satisfied on the boundary. This calculation of the boundary shape is performed by correcting an estimate of the boundary shape in an iteration procedure. When the shape of the boundary is finally derived the stresses in the whole region can be calculated. These calculations have been used in two computer programs, one being written for roadways which are symmetric, the second for roadways with no symmetry. Three modes of failure have been assumed in the computer programs: plastic, granular and shear failure, and in addition a pattern of failure which assumes a region of granular material surrounded by shear-failed rock has been studied. The results quoted cover a range of roadways, but this study does not attempt to provide comprehensive solutions to all relevant problems.