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。這個新的發現所引進新變數的物理意義已經明確討論出來。雖然GEH理論已經可求得解析解，但是應用上卻太過於麻煩。故本論文研究的目的是在於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）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。 （２）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，進而推導出一個簡單而較準確速算式，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 theoriers 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 popular 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 shortcome 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）A moving boundary value problem of the linearized Gibson’s equation is solved analytically and approximately . （2）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.
