An Explicit Solution for the Green Functions for Dynamic Loads in Layered Media

摘要

Solutions to elastodynamic problems of continua subjected to static and dynamic loads are reviewed and their value as tools is emphasized in solving involved boundary value problems arising in seismology and geomechanics. Ways to determine the response of a soil deposit to dynamic loads, caused either by a seismic excitation or by prescribed forces at some location in the soil mass, are discussed. That the loads must be resolved in terms of their temporal and spatial Fourier transforms is stressed. The stiffness matrix approach, an alternative method of analysis for layered soils, is explained. Green functions for ring loads, disk loads, point loads, and internal stresses are given. The Green functions for an arbitrarily layered stratum are evaluated by means of a computer program. An explicit, closed-form solution for the Green functions is presented. 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 be readily evaluated.