Elastic solutions for a transversely isotropic half-space subjected to buried asymmetric-loads

Abstract

Elastic closed-form solutions for the displacements and stresses in a transversely isotropic half-space subjected to various buried loading types are presented. The loading types include finite line loads and asymmetric loads (such as uniform and linearly varying rectangular loads, or trapezoidal loads). The planes of transverse isotropy are assumed to be parallel to its horizontal surface. These solutions are directly obtained from integrating the point load solutions in a transversely isotropic half-space, which were derived using the principle of superposition, Fourier and Hankel transformation techniques. The solutions for the displacements and stresses in transversely isotropic half-spaces subjected to linearly variable loads on a rectangular region are never mentioned in literature. These exact solutions indicate that the displacements and stresses are influenced by several factors, such as the buried depth, the loading types, and the degree and type of rock anisotropy. Two illustrative examples, a vertical uniform and a vertical linearly varying rectangular load acting on the surface of transversely isotropic rock masses, are presented to show the effect of various parameters on the vertical surface displacement and vertical stress. The results indicate that the displacement and stress distributions accounted for rock anisotropy are quite different for those calculated from isotropic solutions. Copyright © 1999 John Wiley & Sons, Ltd.