Displacements and stresses due to vertical subsurface loading for a cross-anisotropic half-space

This paper presents the analytical solutions for estimating the displacements and stresses in a cross-anisotropic half-space due to various loading types of an axially loaded pile. The loading types include an embedded point load for an end-bearing pile, uniform skin friction, linear variation of skin friction, and non-linear variation of skin friction for a friction pile, respectively. The planes of cross-anisotropy are assumed to be parallel to its horizontal surface. The derived solutions have not yet appeared in the literature, and can be obtained by integrating the point load solutions in a Cartesian co-ordinate system for the cross-anisotropic half-space. A part of the solutions are identical with the Mindlin's and Geddes's solutions when the medium is isotropic. The presentation of these proposed solutions is concise and systematized; also, they indicate that the displacements and stresses in a cross-anisotropic half-space are affected by the type and degree of material anisotropy, and the loading types. Furthermore, two illustrative examples are given to investigate the effect of the type and degree of soil anisotropy, and four different loading types on the vertical surface displacement and vertical normal stress, respectively. The results show that the displacement and stress accounted for soil anisotropy are quite different from those estimated by isotropic solutions.