| In recent years, the rail transit has developed rapidly in China and abroad. However, the noise and vibrations induced by rail transit are becoming more and more serious, which affects people living and working nearby the railway. In the researches of environmental vibrations, the study of wave propagation in the foundation soil is the bottleneck because the propagation path greatly influents the magnitude of ground vibrations. This thesis explores the dynamic response of the foundation soil by applying the finite element and infinite element coupling method, and the rules and conclusions will consequently make contribution to vibration control by providing theoretical basis and reference.This thesis briefly introduces the basic principles of finite element method, infinite element method, and the coupling method in the first part. The calculation process of the element stiffness matrix and the expression by deriving shape function as well as the infinite element coordinate transformation function of the eight-node unit are presented in detail which makes more convenient for programming. This thesis analyzes the dynamic response characteristics of semi-infinite foundation soil by applying numerical simulation approach. In order to simulate the boundary conditions of semi-infinite soil accurately, the thesis still applies the traditional eight-node hexahedral solid elements to the near region, and three-dimensional unidirectional mapping infinite element, bidirectional mapping infinite element together with three-way mapping infinite element to the remote region, and then they are coupled on the interface. By means of Matlab, the thesis makes use of Newmark-β to solve dynamic equation, calculates the dynamic response of a semi-infinite foundation soil under different loads, and finally sums up the characteristics of wave propagation on the surface of infinite soil. |
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