推导沉埋基础振动之土壤形状函数.PDF

稻江學報第三卷第二期 推導沉埋基礎振動之土壤形狀函數 劉俊秀 1 鍾瑜隆 2 1 國立台灣交通大學土木系教授 2 國立台灣交通大學土木系博士生 摘 要 本篇文章發展軸對稱沉埋基礎振動之形狀函數，分析整體的層狀土壤可分成内域與外 域兩部分，而外域部份，其解析解必需滿足三維波傳的邊齊性邊界條件，而內域部份除了 滿足三維波傳的邊齊性邊界條件之外必需滿足特解的邊界條件。在基礎本身的表面力以片 段線性表示，並基礎振動以片段線性表示時可以將其解以貝索函數展開，因此便可求得土 壤內域與外域之形狀函數，在求得形狀函數後，本文將解析求得扭轉振動和垂直振動之形 狀函數，因此土壤形狀函數後便可進而求得土壤之間的阻抗矩陣。 關鍵詞： 形狀函數、阻抗矩陣、三維波傳 1 稻江學報第三卷第二期 A Unified Method Of Constructing The Shape Function For Foundations Embedded In Layered Media 1Gin-Show Liou 2I. L Chung Department of Civil Engineering National Chiao-Tung University, Professor Department of Civil Engineering National Chiao-Tung University, Graduate Student Abstract The shape function of impedance matrices are developed in frequency domain for axial-symmetric foundations embedded in layered media. In the scheme the whole soil domain is divided into interior and exterior domains. For the exterior domain, the analytic solutions are obtained by solving 3D wave equations satisfying homogeneous boundary conditions. For the interior domain, the analytical solutions are obtained by solving 3D wave equations satisfying the homogeneous boundary and the prescribed boundary conditions. The prescribed conditions are the tractions at the interfaces between embedded foundation and surrounding soil. The tractions are assumed to be piecewise-linear. The piecewise linear tractions at the bottom face of foundations can be deco