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土木工程係指處理與土、水有關的基礎建設之設計、建造和維護之工程，工程範圍由大至小包含基礎建設、公共工程、房屋的建造……等等，內容甚廣且與民生、經濟息息相關，除了建設方面外也包括對空氣、水、土、建築等等之處理，本研究將在諸多土木工程遭遇之實際問題中選擇兩個問題，以理論解析的方式提供解決之初步想法。
本研究第一部分旨在對於公路彎道設計提供概念，採用與傳統交通工程之彎道設計之不同角度，利用流體力學中自由流線理論的線形作為彎道設計之依據，考量過彎時車速過快之因素，以具力學基礎之理論設計，希望能依此設計以增加用路人之行車安全，而求解過程利用施瓦茨克里斯托費爾轉換(Schwarz-Christoffel transformation)、繪製速端曲線(velocity hodograph)等方法以簡化複雜的計算過程，並建立複速度圖、複數勢能圖、物理平面圖之間之關係。
而結論顯示，利用自由流線理論之平面彎道設計線形與入彎之速度與出彎之速度之比值有關，而若考量三維之彎道設計，需加入考量向心力及超高對速度造成之影響，並進一步修正設計；另外考量車體與流體之連體概念並非完全一致，因此也提供未來採用此法進行研究之方向及建議。
第二部分則針對深層抽水及淺層抽水對於地層下陷之影響進行分析，本研究應用簡單的數學方法解析抽水之地層下陷反應，依據曾鈞敏
(2009)推導之三維非耦合抽水引致地層下陷之控制方程式簡化而成一維非耦合方程式，分別為土體與流體之質量守恆方程式與動量守恆方程式，對於多層之非拘限含水層進行分析，本研究採用三層同厚度之土層做為模型，透過不同之案例分析深、淺層抽水引致地層下陷之反應。求解過程分析點源及線段抽水，並利用脈衝函數模擬抽水之點源，透過滿足層與層之間之壓力、位移、流體通量及有效應力連續條件以進行解析。
最後在解析過程對於深層抽水及淺層抽水進行案例分析，結果顯示深層抽水之土體位移量受到中層之阻水層影響較劇，因而對地層下陷之影響較淺層抽水來的大，並分析一維非耦合抽水引致地層下陷之控制方程式之限制，及未來相關研究之建議。

Civil engineering is an engineering discipline that deals with the project of designing, constructing and maintaining physical and naturally built environment. The scope of the project ranges from infrastructure, public construction etc.. It is very extensive and lives with people''s livelihood. In addition to the construction aspect, it also includes the treatment of air, water, solid, architecture, etc. This study will select two cases in the practical problems encountered in many civil engineering projects, and provide preliminary ideas for solving the problem in a theoretical analysis.
The first part of this study aims to provide a concept for 2D highway cornering design. It adopts different perspectives from the traditional design, and uses the free-streamline theory of fluid mechanics as the basis for cornering design. Considering the factors of excessive speed when cornering, the design hopes to increase the safety of road users. The solution process uses velocity and Schwarz-Christoffel transformation to simplify the calculation and establish complex velocity, complex potential energy hodograph and physical plane. The result of curve design using the free streamline theory is related to the ratio of the in-speed and out-speed. To consider the design of the curve of the three-dimensional, we need to consider the speed effect caused by the centripetal force and the superelevation. In addition, the concept of the vehicles and continuums is not completely consistent, so it also provides directions and recommendations for future research using this method.
The second part analyzes the influence of deep pumping and shallow pumping on the subsidence. In this study, a simple mathematical method is used to analyze the subsidence due to pumping. The simplified one dimensional uncoupling equation basing on the uncoupled governing equation of the subsidence caused by the three-dimensional pumping of Tseng’s(2009), which is the mass conservation equation and the momentum conservation
equation of soil and fluid respectively. It is used to analyze the multi-layered aquifer. In this study, three layers of soil with the same thickness were used as
models to analyze the reaction of subsidence caused by deep and shallow pumping through different cases. The process contains the analysis of the point source and the line segment pumping, and uses the Dirac delta function to simulate the point source of pumping, and analyzes the pressure, displacement, fluid flux and stress continuous conditions between the layers.
At last, the case analyses of deep pumping and shallow pumping is carried out. The results show that the displacement of the soil in deep pumping is more
affected by the aquitard in the middle layer, so the impact on the subsidence of the deep pumping is larger than that the shallow pumping. The cases discuss
the limitation of the governing equations of the one-dimensional uncoupled pumping induced subsidence, and the suggestions for future research.

誌謝................................................... i
摘要.................................................. ii
Abstract............................................. iv
目錄 ................................................. vi
表目錄.............................................. viii
圖目錄.............................................. viii
第１章 章節介紹 ............................................................................................... 1
第２章 利用自由流線理論於彎道定線........................................................... 2
２.１ 導論 .................................................................................................. 2
２.１.１ 研究動機與目的 .................................................................. 2
２.１.２ 文獻回顧 .............................................................................. 3
２.２ 研究方法 .......................................................................................... 5
２.２.１ 自由流線理論 ...................................................................... 5
２.２.２ Schwarz-Christoffel 轉換 .................................................... 6
２.３ 道路彎道設計 .................................................................................. 9
２.３.１ 平面彎道定線 ...................................................................... 9
２.４ 結果分析 ........................................................................................ 16
２.５ 額外考量因素 ................................................................................ 18
２.５.１ 加入考量向心力之影響 .................................................... 18
２.５.２ 加入考量高程差之影響 .................................................... 19
２.６ 結論與建議 .................................................................................... 19
２.６.１ 結論 .................................................................................... 20
vii

２.６.２ 建議 .................................................................................... 20
第３章 深、淺層抽水導致之地層下陷......................................................... 21
３.１ 導論 ................................................................................................ 21
３.１.１ 研究動機與目的 ................................................................ 21
３.１.２ 文獻回顧 ............................................................................ 22
３.２ 三維地層下陷模式之建立 ............................................................ 25
３.２.１ 以多孔彈性介質理論建立地層下陷基本方程式 ............ 26
３.２.２ 三維耦合地層下陷控制方程式 ........................................ 28
３.３ 三維非耦合簡化之抽水引致之地層下陷之模式 ........................ 31
３.３.１ 三維非耦合地層下陷控制方程式 .................................... 31
３.３.２ 多孔彈性介質之充分邊界條件 ........................................ 32
３.３.３ 簡化之一維非耦合抽水引致地層下陷之控制方程式 .... 35
３.４ 具深、淺含水層抽水引致之地層下陷之模型案例解析 ............ 37
３.４.１ 模型案例土層建置 ............................................................ 38
３.４.２ 非拘限含水層 .................................................................... 39
３.５ 結果分析 ........................................................................................ 48
３.６ 結論與建議 .................................................................................... 61
３.６.１ 結論 .................................................................................... 61
３.６.２ 建議 .................................................................................... 62
參考文獻 ........................................................................................................... 63
附錄 A 地層下陷質量守恆方程式之推導 .................................................... 68
附錄 B 地層下陷動量守恆方程式之推導 .................................................... 74
附錄 C 無邊界一維點源抽水方程式之解 .................................................... 79

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