RI 7645 A Method For The Prediction Of Stresses In An Isotropic Inclusion Or Orebody Of Irregular Shape

This report describes the results of a Bureau of Mines investigation in which the stress concentrations and distributions caused by inclusions in a strained elastic plate were determined, Finite element analyses were made for 168 models containing single inclusions of elliptical, ovaloidal, and rectangular shape. The variables studied included: horizontal-to-vertical loading ratios, (Sh/Sv) of 0,0.33,0.5, and 1.0; width-to-height ratios (w/h), of 0.25, 0.5, 2, and 4; and Young's modulus of inclusion to Young?s modulus of plate ratios (K ratios) of 0.33, 0.5, 2.0, and 5.0. The results show that the theory for elliptical inclusions can accurately predict the average stress along the x and y axes of symmetry for circular, ovaloidal, and rectangular inclusions from the width-to-height and K ratios. The actual inclusion shape was insignificant, suggesting that the average stresses in other inclusions of irregular shape (orebodies) can be estimated with the theory for an elliptical inclusion. An application of this technique to mining problems is presented. The stresses in the elliptical inclusions were uniform throughout the inclusion for all the models studied.