不均勻外力作用於層狀半空間內之解析解

Abstract

本研究將延伸主持人過去10年來所發展之方法，求得在層狀半空間中任意分佈外力所造成之地盤反應。其持點與過去不同的地方是外力不限定加在層狀半空間的表面(自由面)。目前能夠將外力加在層狀半空間內部的解，一般是Green Function，但Green Function為一集中載重之解，因此會有奇異點(singularity)之現象。而本文是以任意分佈載重模擬外力，因此不會有奇異點的現象。這對目前利用邊界元素法(BEM)求地盤振動與基礎阻抗矩陣將會有大幅度之改進。 本研究之求解過程中，將假設外力在徑向(r-方向)之分佈為片段線性(piecewise linear)，在θ-方向可分解成傅立葉級數(Fourier Series)。此分佈外力可作用在任何深度。然後可利用主持人過去所發展之方法直接求圓柱座標系統中之波動方程式之解，其最後之解將為一Bessel Function之積分式。本文法最大之持點為外力作用位置之位移沒有奇異的現象。

The proposal is going to deal with the problem of the response of stratified half-space subjected to arbitrary distributed force on an axial symmetric area buried in stratified half-space. Except boundary element method ,the response to a force buried in a stratified half-space is rarely dealt with. However, Green function employed in boundary element method will produce singularity problem in the integration. The ongoing method can avoid the singularity situation, since the external force is arbitrary distributed over an axial symmetric area buried in stratified half-space. In the process of this research, the arbitrarily distributed load can be decomposed into a Fourier Series in Θ-direction and piecewise linear distribution in r-direction is assumed for each Fourier component. Then the wave equations in cylindrical coordinates are directly solved using the technique developed by the applicant. The solution will be an integral with Bessel function. The advantage of the method will be that singularity problem has been avoided.