Elastic solutions for stresses in a transversely isotropic half-space subjected to three-dimensional buried parabolic rectangular loads

Abstract

In many areas of engineering practice, applied loads are not uniformly distributed but often concentrated towards the centre of a foundation. Thus, loads are more realistically depicted as distributed as linearly varying or as parabola of revolution. Solutions for stresses in a transversely isotropic half-space caused by concave and convex parabolic loads that act on a rectangle have not been derived. This work proposes analytical solutions for stresses in a transversely isotropic half-space, induced by three-dimensional, buried, linearly varying/uniform/parabolic rectangular loads. Load types include an upwardly and a downwardly linearly varying load, a uniform load, a concave and a convex parabolic load, all distributed over a rectangular area. These solutions are obtained by integrating the point load solutions in a Cartesian coordinate system for a transversely isotropic half-space. The buried depth, the dimensions of the loaded area, the type and degree of material anisotropy and the loading type for transversely isotropic half-spaces influence the proposed solutions. An illustrative example is presented to elucidate the effect of the dimensions of the loaded area, the type and degree of rock anisotropy, and the type of loading on the vertical stress in the isotropic/transversely isotropic rocks subjected to a linearly varying/uniform/parabolic rectangular load. © 2002 John Wiley and Sons, Ltd.