Analytical layer-element solution for 3D transversely isotropic multilayered foundation

This paper presents a solution for 3D transversely isotropic multilayered foundations under external loading, for which the analytical layer-element method is used because it has good numerical stability due to its symmetry and no existence of positive exponents. Based on the basic equations for transversely isotropic elastic materials, an analytical layer-element, which describes the relationship between the displacements and stresses of 3D transversely isotropic single-layered foundations, is exactly derived in the transformed domain by applying the double Fourier transform technique and the Cayley–Hamilton theorem. Taking account of the continuity conditions between adjacent layers, the global stiffness matrix can be obtained by assembling the interrelated layer elements. The solutions in the physical domain can be obtained by a numerical Fourier inversion. Finally, numerical examples are carried out to verify the presented theory and to elucidate the effect of stratification on the deformation of a foundation.