Stresses in Depth Around Elliptical and Ovaloidal Openings in an Infinite Elastic Medium

CIM Bulletin, 1970

B. B. DHAR, Research Assistant, L. P. GELDART, formerly Professor of Applied Geophysics, J. E. UDD, Assistant Professor, Dept. of Mining Engineering and Ap~lied Geophysics, McGill University, Montreal, Que

Solutions for the stress distributions around simulated underground openings have been limited to calculations of boundary stresses for simple openings in which the boundaries may be expressed in mathematical terms. Studies involving circles, ellipses and ovaloids are reported in the literature. The stresses on the boundary of an opening and those at a distance from it in the medium are of concern to the engineer. The former may be related to the greatest concentrations of stresses encountered; the latter have a bearing on the identification of the "zone of influence" of the opening. Recent advances, in the form of a derivation for the stresses at a distance from an opening of elliptical shape, together with a solution derived previously for stresses in depth around ovaloidal openings, have been combined with computer programming techniques to provide complete solutions for a wide range of cases and variables. Sorne typical results which, it is hoped, may have sorne application to the design of underground openings are given herein.
Keywords: Applications, CIM, Concentration, Loading, McGill University, rock mechanics, sinh, stress concentration, tensile stress, stress, Stress distribution, Stress distributions, Tensile stress, Underground, Value