臺灣博碩士論文加值系統

Terzaghi單向度壓密理論被廣泛的應用在工程界，然而Terzaghi單向度壓密理論之優點是解析解易求得﹔缺點則是低估超額孔隙水壓，往後學者如Gibson等人便根據上述的理論缺失來進行修正，於1967年提出飽和黏土的壓密方程式，亦即Gibson-England-Hussey（簡稱GEH）壓密理論，為一非線性的偏微分方程式。其應用範圍不受限於小應變的情況。其優點為假設條件較符合土壤壓密的實際情況﹔缺點則是無法直接求得解析解。但是由最近所發表的文獻中，可知已經能夠將GEH理論的薄黏土層的單向度壓密方程式予以線性化。雖然這是一個新的發現，但所引進新變數的物理意義卻不明確。故本論文研究的目的是探討新變數之間的轉換關係及轉換後的線性化方程的物理意義以及處理移動邊界問題以及求其線性化後的近似解析解和能推導出應用於工程界的速算公式。
本研究所獲得的成果包括：
（１） 找出GEH理論在線性化過程中所導入的變數q所隱含的物理意義，以及各個參數變數之間的相互關係，進而使得人們能夠對Gibson-England-Hussey 壓密理論有更深入的了解。
（２） 利用線性化後所得到的偏微分方程以及衍生出來的移動邊界問題導出Gibson-England-Hussey equation的近似解析解。
（３） 提供人們一個方便計算單向度壓密沉陷量的速算公式。
Terzaghi的單向度壓密理論雖不準，但能求得解析解，解的形式也較簡潔；而Gibson-England-Hussey壓密方程式雖然較準確，以往卻無法求得正確的解析解。本研究的成果便是提供GEH壓密方程式的近似解析解，即是一個簡單而較準確的解，可作為未來應用在工程分析和設計的參考。

Terzaghi's theory of soil consolidation is widely used in engineering practice . Simplicity is its merit . However，the theory will underestimate the excess pore water pressure . Many researchers had tried to propose theorier which match the reality better than Terzaghi's theory does . Among these , the theory proposed by Gibson and his co-workers in 1967 is one of the most propular theories in Literatures .A nonlinear consolidation equation was derived in Gibson's work , which can describe finite strain consolidation . The merit of Gibson's theory is that it describes the behavior of soil better than Terzaghi's theory does .The short come of it is that the consolidation equation is nonlinear，which usually can not be solved analytically . Recently，it was found that the nonlinear consolidation equation is Gibson's theory can be linearized，and thus，could be solved analytically .In this research， we will clarify the physical meaning of the linearization and try to obtain analytical solution of the linearized consolidation equation associated with moving boundaries .A simple formula will be derived for the quick calculation of the settlement of the soil ground in engineering practice .
Our results are summarized as follows .
（1） The physical meaning of the variables used in the linearization is clarified.
（2） A moving boundary value problem of the linearized Gibson's equation is solved analytically and approximately .
（3） A simple formula for quick calculation of settlements is derived.
The formula derived in Terzaghi's theory for calculating settlements is simple but not matches the reality very well . And our formula is simple and matches the reality better than Terzaghi's theory does.

第一章 緒論1
1-1 研究動機與目的1
1-2 研究方法3
1-3 論文內容4
第二章 Gibson-England-Hussey單向度壓密理論簡介5
2-1 前言5
2-2 控制方程式的推導5
2-3 Gibson-England-Hussey 薄土層的控制方程式的推導9
2-4 Gibson-England-Hussey 方程式中材料函數的選取10
第三章 Gibson-England-Hussey 方程式的線性化14
3-1 變數轉換14
3-2 變數角色轉換16
3-3 自變數q的物理意義19
第四章 GEH壓密理論的求解與驗證及速算公式的推導25
4-1 移動邊界問題的介紹25
4-2 GEH 方程式的近似解法28
4-3 GEH 近似解的驗證32
4-4 GEH 壓密理論的速算公式推導35
第五章 問題研究與討論43
5-1 數值解的分析方法43
5-2 實例分析研究43
5-3 問題討論85
第六章 結論與建議87
6-1 結論87
6-2 建議88
參考文獻90

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