• transversely isotropic linear elasticity;
  • bimaterials;
  • classical Fourier transform;
  • distributed loading;
  • closed-form solutions;
  • rocks


This paper presents the closed-form solutions for the elastic fields in two bonded rocks induced by rectangular loadings. Each of the two bonded rocks behaves as a transversely isotropic linear elastic solid of semi-infinite extent. They are completely bonded together at a horizontal surface. The rectangular loadings are body forces along either vertical or horizontal directions and are uniformly applied on a rectangular area. The rectangular area is embedded in the two bonded rocks and is parallel to the horizontal interface. The classical integral transforms are used in the solution formulation, and the elastic solutions are expressed in the forms of elementary harmonic functions for the rectangular loadings. The stresses and displacements in the rocks induced by both the horizontal and vertical body forces are also presented. The numerical results illustrate the important effect of the anisotropic bimaterial properties on the stress and displacement fields. The solutions can be easily implemented for numerical calculations and applied to problems encountered in rock mechanics and engineering. Copyright © 2011 John Wiley & Sons, Ltd.