臺灣博碩士論文加值系統

未飽和層位於地表與地下水交換之界面，因降雨經地表入滲進而補注地下水時，水流傳輸過程必定先流經未飽和層，故地下水水流於未飽和層中的運動機制為相當重要之課題。
本研究以未飽和層地下水理論為依循基礎，探討土壤水分特性曲線模式以完整描述未飽和層土壤物理行為，並採Gardner提出之指數函數型態經驗公式，以簡化土壤非線性參數項進而線性化理查方程式，後續利用DJIFM建置未飽和層地下水水流數值模式。考量實際工程環境條件下，未飽和層土壤大多屬於非均質材料，本研究將模式應用於求解未飽和層互層土壤地下水水流問題，並針對高度非均質之未飽和層土壤材料進行探討，結果顯示，本研究所發展之模式能有效克服傳統數值方法所面臨數值收斂及運算效率之問題。
相較於前人之研究，本研究以土壤水分特性曲線作為主要思維，掌握線性化理查方程式之優勢，期望本研究所發展之數值模式提供後續應用於更複雜之未飽和層地下水水流問題。

Groundwater resources has been one of the most important water resources in Taiwan. Globally, the amount of water in the unsaturated zone located between the water table and the ground surface represents only a small portion of the total water. However, because the unsaturated zone forms the necessary transition between the atmosphere and large groundwater aquifers at depth, the movement of water within the unsaturated zone of hydrological cycle is significant and plays a critical role in the geotechnical engineering. In this study, the numerical solution of groundwater flow in unsaturated layered soil using the Richards equation is presented. All the studies showed that the unsaturated flow is a highly non-linear process due to the high nonlinearity of soil water characteristics and soil permeability and various boundary and initial conditions. To solve one-dimensional flow in the unsaturated zone of layered soil profiles, the flux conservation and continuity of pressure potential at the interface between two consecutive layers are considered in the numerical model. A linearization process based on the Gardner's exponential model for the nonlinear Richards equation to deal with groundwater flow in unsaturated layered soil is derived. In addition, a novel method, named the Dynamical Jacobian-Inverse Free Method (DJIFM), with the incorporation of a two-side equilibrium algorithm for solving ill-conditioned systems with extreme contrasts in the hydraulic conductivity is proposed. The validity of the model is established for a number of test problems by comparing numerical results with the analytical solutions. The results show that the proposed method can improve the convergence and can increase the numerical stability for solving groundwater flow in unsaturated layered soil with extreme contrasts in the hydraulic conductivity. It is expected that the proposed model can be used to apply for more sophisticated groundwater flow problems in unsaturated layered soil in the near future.

摘要 ............. I
Abstract ............. II
目次 ............. III
圖目次 ............. V
第一章 緒論 ............. 1
1.1 前言 ............. 1
1.2 研究動機與目的 ............. 1
1.3 研究內容 ............. 2
第二章 文獻回顧 ............. 5
2.1 未飽和層地下水水流問題 ............. 5
2.1.1 數值解 ............. 5
2.1.2 解析解 ............. 8
2.2 未飽和層互層土壤之研究 ............. 10
2.3 小結 ............. 10
第三章 未飽和層土壤地下水理論 ............. 11
3.1 未飽和層土壤物理特性 ............. 11
3.1.1 未飽和層土壤定義 ............. 11
3.1.2 未飽和層土壤吸力理論 ............. 14
3.2 土壤水分特性曲線 ............. 17
3.2.1 土壤水分特性曲線參數 ............. 19
3.2.2 特性說明 ............. 19
3.2.3 土壤水分特性曲線模式 ............. 22
3.3 未飽和層透水係數 ............. 34
第四章 未飽和層地下水水流數值模式之建立 ............. 37
4.1 控制方程式 ............. 37
4.1.1 廣義理查方程式 ............. 37
4.1.2 線性化理查方程式 ............. 42
4.2 解析解 ............. 47
4.3 有限差分理論 ............. 50
4.4 數值方法 ............. 54
4.4.1 The Dynamical Jacobian-Inverse Free Method ............. 54
4.4.2 Two-sided equilibrium algorithm ............. 59
第五章 數值案例與參數敏感度分析 ............. 61
5.1.1 未飽和層地下水水流問題 ............. 61
5.1.2 未飽和層土壤入滲分析模式之比較 ............. 68
5.2 應用案例 ............. 79
5.2.1 未飽和層土壤材料之探討 ............. 79
5.2.2 未飽和層互層土壤地下水水流問題 ............. 82
5.3 參數敏感度分析 ............. 99
5.3.1 飽和透水係數 ............. 101
5.3.2 飽和含水量 ............. 103
5.3.3 殘餘含水量 ............. 105
5.3.4 土壤孔隙分布參數 ............. 107
第六章 結論與建議 ............. 109
6.1 結論 ............. 109
6.2 建議 ............. 110
參考文獻 ............. 111

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