Dynamic loads in the interior of a layered stratum: An explicit solution

Abstract

This paper presents an explicit, closed-form solution for the Green functions (displacements due to unit loads) corresponding to dynamic loads acting on (or within) layered strata. These functions embody all the essential mechanical properties of the medium and can be used to derive solutions to problems of elastodynamics, such as scattering of waves by rigid inclusions, soil-structure interaction, seismic sources, etc. The solution is based on a discretization of the medium in the direction of layering, which results in a formulation yielding algebraic expressions whose integral transforms can readily be evaluated. The advantages of the procedure are: (a) the speed and accuracy with which the functions can be evaluated (no numerical integration necessary); (b) the potential application to problems of elastodynamics solved by the boundary integral method; and (c) the possibility of comparing and verifying numerical integral solutions implemented in computer codes.