Elastic Solutions for a Transversely Isotropic Half‐Space Subjected to Arbitrarily Shaped Loads Using Triangulating Technique

Abstract

Elastic closed‐form solutions for the displacement and stresses in a transversely isotropic half‐space subjected to a buried right triangular loaded region are presented. The loading types include a uniform load, a linearly varied load in the X‐direction, and a linearly varied load in the Y‐direction, respectively. The planes of transverse isotropy are assumed to be parallel to its horizontal surface. These solutions are obtained from integrating the point load solutions in a transversely isotropic half‐space. The exact solutions indicate that the displacements and stresses are influenced by several factors, such as the buried depth, the loading types, the dimensions of loaded region, and the degree and type of material anisotropy. Two illustrative examples are presented to investigate the effect of various parameters on the displacement and stress induced by uniform/linearly varying triangular loads. The results indicate that the displacement and stress distributions accounted for rock anisotropy are quite different for those calculated from isotropic solutions. Besides, an example to demonstrate the extension of triangular loading solutions to calculate the stress due to arbitrarily shaped loads is also illustrated. It is shown that the usage of triangulating technique for calculating the displacements and stresses due to any type of loaded area is simple, efficient, as well as accurate enough. This method can be a practical alternative to the existing numerical and graphical methods.