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

This paper presents the closed-form solutions for estimating the displacements in a transversely isotropic half-space subjected to three-dimensional buried linearly varying, uniform, and parabolic rectangular loads. The loading types include an upward linearly varying load, a downward linearly varying load, a uniform load, a concave parabolic load, and a convex parabolic load on a rectangle. The planes of transverse isotropy are assumed to be parallel to the horizontal surface of the half-space. The presented solutions are obtained from integrating of the point load solutions in a Cartesian co-ordinate system for the transversely isotropic half-space. The solutions for a transversely isotropic medium subjected to parabolic rectangular loads are never mentioned in the literature. The parabolic loads might be more realistic than linear variable or uniform loads acting on foundations. The buried depth, the dimensions of loaded area, the type and degree of material anisotropy, and the loading type for transversely isotropic half-spaces influence these solutions. An illustrative example is presented to investigate the effect of the type and degree of rock anisotropy, and the loading types on the displacement. The proposed solutions can provide reasonably results to estimate the induced displacements in the isotropic/transversely isotropic geomaterials subjected to three-dimensional buried parabolic rectangular loads for practical purposes