Boussinesq-Papkovich Functions for Creep Around a Spherical Cavity or a Rigid Inclusion in a Gravity-Loaded Half Space

Abstract

Boussinesq-Papkovich stress functions are used to determine three-dimensional closed form solutions for steady creep around a spherical cavity or rigid inclusion in a half space under gravity loading. The ratio of cavity depth to radius is assumed to be greater than 5, and the flow law of the half space is linear, which allows for solution in terms of a finite number of spherical harmonics. Numerical results are given to show the influence of the lateral stress component at infinity, the stabilizing effect of internal cavity pressure, and buoyancy forces associated with the motion of a rigid inclusion.