This work presents analytical solutions for displacements caused by three-dimensional point loads in a transversely isotropic full space, in which transversely isotropic planes are inclined with respect to the horizontal loading surface. In the derivation, the triple Fourier transforms are employed to yield integral expressions of Green's displacement; then, the triple inverse Fourier transforms and residue calculus are performed to integrate the contours. The solutions herein indicate that the displacements are governed by (1) the rotation of the transversely isotropic planes (φ), (2) the type and degree of material anisotropy (E/E′, v/v′, G/G′), (3) the geometric position (r, φ, ξ) and (4) the types of loading (Px, Py, Pz). The solutions are identical to those of Liao and Wang (Int. J. Numer Anal. Methods Geomechanics 1998; 22(6):425-447) if the full space is homogeneous and linearly elastic and the transversely isotropic planes are parallel to the horizontal surface. Additionally, a series of parametric study is conducted to demonstrate the presented solutions, and to elucidate the effect of the aforementioned factors on the displacements. The results demonstrate that the displacements in the infinite isotropic/ transversely isotropic rocks, subjected to three-dimensional point loads could be easily determined using the proposed solutions. Also, these solutions could realistically imitate the actual stratum of loading situations in numerous areas of engineering.
|Number of pages||42|
|Journal||International Journal for Numerical and Analytical Methods in Geomechanics|
|State||Published - 1 Oct 2007|
- Material anisotropy
- Residue calculus
- Transversely isotropic full space
- Triple Fourier transforms