Axisymmetric Elastic Fields in Transversely Isotropic Layered Half-Space with Cavity Subjected to Internal Pressure

Abstract

This paper develops an axisymmetric boundary element method (BEM) for analyzing a transversely isotropic (TI) layered half-space with an internal cavity subjected to pressure. The BEM formulation utilizes the fundamental solution of a TI layered solid of infinite extent under body forces uniformly concentrated along a circular ring. Three types of isoparametric elements are used to discretize the core region surrounding the cavity and an infinite element is utilized to discretize the external boundary away from the cavity. A novel numerical quadrature scheme is introduced to calculate the regular and singular integrals in the BEM formulation. Numerical verifications are carried out to confirm the accuracy and computational efficiency of the proposed BEM. The numerical results demonstrate the influence of the heterogeneity and anisotropy of the TI layered solid on the elastic fields in the surrounding rocks around the cavity of either sphere or ellipsoid.