Stress in ah Infinite Medium around a Spheroidal Cavity Applied with Hydrostatic Pressure

Abstract

Some of Japanese seismologists have been considering the effect of magma lying under the Earth's crust as the real origin of an earthquake, though there are some disagreements among them concerning what the effect of magma is: explosion or simple pressure. The authors have the opinion that the pressure of magma is to rise to break rocks surrounding its cavity and cause an earthquake, and theoretically investigate the relation between the shape of cavity and the breaking point around it. The two shapes, prolate and oblate spheroids, are dealt with, and it is assumed that one of these cavities is lying in an infinite elastic body, in which magma presses hydrostatically its boundary surface. The stress and then the deformation energy in medium around the cavity were calculated, and it is found that the points where the latter takes the maximum value were both poles for the prolate, and those on the equatorial circle for the oblate spheroid. These are considered to be the places to break at first according to von Mieses' theory. These considerations indicate that the points on a cavity with the smallest radius of curvature are liable to break first.