Pillar failure by axial splitting in brittle rocks

An analytical approximate elastic model is presented of the pillar failure mechanism in the case of multiple underground openings in brittle rocks by parallel equidistant vertical splitting cracks forming slabs, which are assumed to buckle. The failure region is considered to be elliptical in shape with the major axis growing as failure proceeds parallel to the minimum applied principal stress. A modified solution for the potential energy loss due to the presence of an elliptical hole in an infinite elastic space was derived in order to account for multiple openings. This solution, which yields the failure initiation stress and the crack spacing, was achieved by inserting configuration correction factors estimated by considering certain limiting conditions. In order to obtain simple approximate formulae and after considering the blast damage effect, equivalent effective circular holes are assumed for the case of square openings and elliptical holes for the case of rectangular openings. Next, the stable mode of pillar failure was formulated based on the observation that the weak inclusion of the axially split rock mass reduces the stresses for some distance inside the pillar. The stable model was obtained first by computing the elastic stresses outside the failure zone using a circular approximation and then applying a stability criterion based on Huber's classical fracture hypothesis. Comparison of the theoretical results with field data concerning a bauxite mine using room and pillar have indicated reasonable agreement. Furthermore, the scale effect exhibited by the strength and the axial splitting crack spacing was predicted sufficiently well by the above model.