Elastodynamic Solutions of a Finite Soil Layer under Interior Distributed Actions

Shiping Zhang,Zhan Xu,Changjie Zheng

doi:10.1155/2021/5538319

Abstract

Through a method of displacement potentials, Fourier series, and Hankel integral transformation, the generalized solutions of an elastic layer resting on a rigid base under arbitrary, distributed, buried, and time-harmonic loads are developed in this study. With the proposed solution, the specific results for two kinds of uniform distributions as a kind of fundamental solutions in the interaction analysis of media and inclusions by the method of boundary integral equations are included as illustrations. Finally, numerical examples involving surface and buried patch loads are presented to validate the solutions and examine the effects of the thickness of the elastic layer. The results show that the proposed solution can cover the classical half-space solution by taking enough large thickness of the elastic layer (e.g., the ratio of the layer thickness beneath the load to the load radius ≥ 50 ) and the surface load solution by setting the load depth to zero; the underlying rigid base has significant and complex influence on the dynamic response of the thin layer due to wave reflections, which needs to be considered in the design and practice of related engineering.

Highlights

Mechanical behaviors of soils under dynamic loads, such as traffic loads, construction operations, machinery vibrations, and earthquakes, are of fundamental importance in pavement engineering, geotechnical, and seismic engineering [1,2,3]
An analytical investigation for time-harmonic response analysis of an elastic layer resting on rigid base under arbitrary, distributed, and interior excitations is initiated to enhance the current framework for this class of problems. e remainder of this study is structured as follows: In Section 2, displacement potentials are introduced to fully decouple the field equations into three independent wave equations, followed by a finite Fourier transformation and a Hankel transformation, which reduce the dimension of wave equations to one. en, general solutions to arbitrary, distributed, and buried loads are obtained by imposing the boundary condition and the conditions at the load level
Three-dimensional general solutions of an elastic layer resting on rigid base to arbitrary, distributed, and buried loads are presented by a method of displacement potentials and integral transforms

Summary

Introduction

Mechanical behaviors of soils under dynamic loads, such as traffic loads, construction operations, machinery vibrations, and earthquakes, are of fundamental importance in pavement engineering, geotechnical, and seismic engineering [1,2,3]. Together with the fundamental importance of buried load solutions in the soil-structure interaction analysis, the expected generality significance that buried load solutions can be reduced to surface load solutions, and finite-layered solutions to half-space solutions. To this end, an analytical investigation for time-harmonic response analysis of an elastic layer resting on rigid base under arbitrary, distributed, and interior excitations is initiated to enhance the current framework for this class of problems. The effect of the thickness of the elastic layer on its response of displacements is investigated with numerical examples

Statement of Problem and Its Solutions

Green’s Functions of the Elastic Layer under Specific Loads

Reduction of the Solutions and Numerical Examples

Conclusions