Point loads on the surface of a transversely isotropic linear elastic half-space

Abstract

General solutions for the displacements, strains and changes in stress in a transversely isotropic linear elastic (TILE) half-space subject to a point load were published in 1998. They represent a massive advance on the nineteenth-century solutions by Boussinesq, Cerruti and others, which were for fully isotropic linear elastic half-spaces. The 1998 solutions were for loads at a general depth below the surface and were criticised for being difficult. The present paper deduces more accessible expressions for the special case of loads that are on the surface. This allows one clarification and one potential error in the original equations to be identified and avoided. With support from existing data of geological materials, agreement is found with a previous claim that a limit proposed in 1970 on one of the shear moduli for a TILE material is invalid. Corrected equations derived herein can be the basis of calculating ground stresses and movements due to linear responses to distributed surface loads, behaviours of flexible foundations and stiffnesses for rigid surface footings.