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研究生:黃漢誠
研究生(外文):Han-Chen Huang
論文名稱:未飽和層土壤水分遲滯效應之研究
論文名稱(外文):A Study of Soil Moisture Hysteresis Effect in Unsaturated Soil
指導教授:譚義績譚義績引用關係
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:生物環境系統工程學研究所
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:133
中文關鍵詞:汲取效應遲滯效應數值模式
外文關鍵詞:Pumping effectHysteresis effectNumerical schemes
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研究依據van Genuchten(1980)之土壤保水曲線關係式發展一可適用於遲滯現象之土壤水分遲滯模式,在已知土壤主要乾燥曲線及主要濕潤曲線之參數下,推衍出任一乾燥或濕潤狀態之土壤水分遲滯曲線;模式係以前人研究之實驗數據及本研究進行之實驗數據進行準確性分析,並與Scott model及KP model進行比較,結果顯示本研究所發展之土壤水分遲滯模式具備簡易、準確及方便等優點,並且能避免相關模式未能處理之汲取效應(Pumping effect)。
研究並將所發展之土壤水分遲滯模式納入土壤水分滲流數值模式中,進行土壤水分與張力混合型控制方程式、張力型控制方程式之數值解析質量平衡分析,結果顯示土壤水分與張力混合型控制方程式之數值模式具備較佳之質量平衡;另數值模式與Gillham(1979)之實驗結果進行比較,結果顯示數值模擬結果與實驗結果相近,代表遲滯效應是土壤水分滲流研究中應予考量之重要因子;最後研究並進行三種不同土壤之水分滲流模擬以進一步探討遲滯現象之特性。

This study present a novel hysteresis model based on van Genuchten’s soil-moisture relationships. The proposed model yields series closed form relationships in which two shape factors and are determined from the main drying and wetting curves. Experiments and literature-cited data were used to assess model accuracy. The proposed model was also compared with the Scott and KP models. Analytical results indicate that the present model is simple, accurate and effective in constructing the series wetting and drying scanning curves. Notably, the proposed model outperforms the Scott and KP models in terms of model accuracy. Moreover, the novel model eliminates the pumping effect and has perfect closure at scanning curve reversal points.
There are two numerical schemes adopted to this research: finite difference method and finite element method. These models combined present hysteresis model to estimate scanning curves. In the research, there are two different forms of Richards equation: h-based and mix form. The results showed that the mix-form of Richards equation has had better mass balance; therefore, the simulation is based on the mix-form of Richards equation. Importance of hysteresis is based on that the numerical scheme is verified by the Gillham’s (1979) experimental data. Finally, three numerical schemes are adopted to three case studies to analyze hysteretic phenomena. The results of numerical analysis are helpful to understand the insight physical behavior of hysteresis.

謝誌 I
摘要 III
英文摘要 IV
目錄 V
圖錄 VIII
表錄 XIII
第一章 前言 1
1.1 研究動機與目的 1
1.2 研究方法與步驟 3
1.3 研究架構 5
第二章 相關理論與文獻回顧 7
2.1 基本概念 7
2.1.1 孔隙率(Porosity) 7
2.1.2 土壤含水量(Soil moisture) 8
2.1.3 毛細力(Capillarity) 8
2.2 土壤水力特性曲線、遲滯現象及相關文獻 9
2.2.1 土壤水力特性曲線模式及相關文獻 9
2.2.2 土壤水分遲滯現象與相關文獻 16
2.3 未飽和土壤水分傳輸 21
2.3.1 Darcy-Buckingham方程式 21
2.3.2 控制方程式(Richards equation) 23
第三章 土壤水分遲滯模式之建立 25
3.1 土壤水分遲滯曲線模式 26
3.2 未飽和水力傳導係數及比水容積遲滯曲線模式 32
3.2.1 未飽和水力傳導係數遲滯曲線模式 32
3.2.2 未飽和比水容積遲滯曲線模式 32
第四章 土壤水分遲滯模式之驗證 34
4.1 前人研究之第1乾燥曲線及第1濕潤曲線實驗與模式驗證 34
4.1.1 第1乾燥曲線及第1濕潤曲線之預測與討論 34
4.1.2 模式修正與討論 40
4.2 高階乾燥曲線及濕潤曲線實驗與模式驗證 43
4.2.1 實驗設置 43
4.2.2 實驗結果與模式驗證 50
4.3 土壤水分遲滯模式應用於數值模擬之原則 55
第五章 數值模式之建立 59
5.1 數值模式 59
5.1.1 一維有限差分法數值模式 60
5.1.2 一維有限元素法數值模式 63
5.1.3 多維有限元素法數值模式 67
5.2 數值模式之迭代求解及流程 69
5.2.1 一維數值模式之迭代求解 69
5.2.2 多維數值模式之迭代求解及流程 72
5.3土壤水分遲滯曲線模式之判斷與質量平衡 74
5.3.1 土壤水分遲滯曲線模式之解析 74
5.3.2 質量平衡 76
第六章 數值模式驗證與分析 77
6.1 土壤水分、張力混合型控制方程式與張力型控制方程式之比較 77
6.2 實驗結果之驗證 83
6.3 模式應用 88
6.3.1 模擬情形一 88
6.3.2 模擬情形二 101
6.3.3 模擬情形三 111
第七章 結論與建議 119
7.1 結論 119
7.2 建議 120
參考文獻 121
符號說明 127
簡歷 130

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