An efficient numerical algorithm for solving the dynamic impedance function of arbitrary-shaped foundations in layered soil

Abstract

In soil–structure interaction analysis, the dynamic impedance solution can be obtained using Green's function based on frequency dependence. To satisfy the mixed boundary conditions of the ground–ground interface, the interface should be frequently divided into several evenly spaced sub-elements instead of finite elements. Generally, the accuracy increases and the computational efficiency decreases with an increase in the number of sub-elements. To obtain reliable solutions and improve efficiency, a numerical algorithm for solving the dynamic impedance function of arbitrary-shaped foundations in layered soil was investigated. Based on the wave propagation equation of a horizontally layered half space, the relationship between the number and radius of sub-disk elements and their dynamic impedance matrix was derived using the high-precision method of solving Green's function for the individual sub-disk elements. The derived equation provides an efficient and accurate method to calculate the dynamic impedance of rigid layered foundations and was verified based on numerical examples. The numerical examples revealed that the proposed method reproduced the results in the literature. With the given accuracy, this method reduces the calculation time and improves the calculation efficiency. This proposed high-precision method for solving the foundation dynamic response is well suited to practical engineering applications.