RI 7838 A Geometric Method for the Prediction of Stresses in Inclusions, Orebodies, and Mining Systems

This report describes the results of a Bureau of Mines investigation in which an elastic inclusion, orebody, or mining system is replaced for purposes of analysis with an imaginary effective inclusion of rectangular shape that encloses the region. This effective inclusion has averaged physical properties that are directly related to the average inclusion stresses. The results were in excellent agreement with those predicted by Donnell's theory (2)2 for an isotropic elliptical inclusion in a state of plane strain for all height-to-width ratios and for all degrees of inclusion hardness from very soft to very hard. The results are exact for an isotropic circular inclusion and provide an easy method of evaluating the stresses obtained by cylindrical inclusions in boreholes when the Poisson's ratio for both host and inclusion equals 0.25 for plane strain or 0.333 for plane stress. The theory was also used to predict the average stresses in 48 finite-element models of single transversely isotropic inclusions of ovaloid and rectangular shape. An interesting and useful observation from this work was that the forces on elliptical inclusions in the x and y directions, produced by applied uniaxial stresses in the y and x directions, respectively, were equal in magnitude but opposite in sign when the applied stresses were equal. This occurred when the plane strain condition was used with a Poisson's ratio of 0.25. The practical usefulness of the method is given by treating a variety of mining problems: (1) The average stresses in an orebody of irregular shape; (2) the average stresses in single-level room-and-pillar mining systems; (3) the average stresses in multiple-level room-and-pillar mining systems; (4) the effect of mining sequence on the average stresses produced during mining; (5) the stresses in cylindrical borehole plug related to host rock stresses as a function of plug hardness; and (6) methods for simplifying finite-element analysis of complex structures.