Transient response of a transversely isotropic multilayered half-space due to a vertical loading

Abstract

• Governing equations are transformed into the fourth-order ordinary differential equations. • Solutions for displacements are obtained by using the analytical layer-element method. • The analytical layer-element excludes the positive exponential terms. • Effect of loading type, anisotropy and layering of media on the transient response is investigated. This paper investigates the transient response of a transversely isotropic multilayered half-space under vertical loadings. With the aid of a Laplace–Hankel transform, the global stiffness matrix for a multilayered half-space is acquired by assembling the analytical layer-element of each layer medium. The solutions for the displacements in the time domain are obtained by using the global stiffness matrix equations and a numerical inversion procedure. The accuracy of the proposed method is verified through comparisons with existing solutions for displacements induced by a step and rectangular pulse loading. In addition, selected numerical results for displacements induced by the buried loading are presented to illustrate the effect of transient loading type and material anisotropy on the transient response.