Analytical formulas and design charts for transversely isotropic half-spaces subject to linearly distributed pressures

Abstract

We provide analytical formulas and design charts for computing displacements, strains and stresses in transversely isotropic half-spaces subject to linearly distributed vertical pressures. The domain integrals extended to the loaded region, resulting from the solution associated with a vertical point load, are first transformed into boundary integrals. For polygonal domains, the boundary integrals are further reduced to algebraic sums depending upon the loading function and the position vertices of the loaded region. A detailed account of this transformation is reported for all integrals in order to highlight the singularities to be coped with and how they can be circumvented. Design charts for the vertical stress are reported in order to validate the proposed formulation. Finally, the values of displacements and stresses underneath a foundation of arbitrary shape comparatively show the influence of modelling half-spaces as isotropic or transversely isotropic media.