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系統識別號 U0026-2011201809345600
論文名稱(中文) 受重力影響下土壤壓密沉陷之孔彈性理論
論文名稱(英文) Poroelastic Theory of Consolidation Incorporating Gravitational Body Forces
校院名稱 成功大學
系所名稱(中) 水利及海洋工程學系
系所名稱(英) Department of Hydraulics & Ocean Engineering
學年度 107
學期 1
出版年 107
研究生(中文) 趙南傑
研究生(英文) Nan-Chieh Chao
電子信箱 chaoxam@gmail.com
學號 N88021113
學位類別 博士
語文別 中文
論文頁數 107頁
口試委員 指導教授-羅偉誠
口試委員-賴建信
口試委員-徐國錦
口試委員-吳建宏
口試委員-謝平城
口試委員-陳主惠
口試委員-李振誥
中文關鍵字 孔彈性理  多孔隙介質  壓密沉陷  重力 
英文關鍵字 Poroelasticity  Porous media  Consolidation  Gravity effect 
學科別分類
中文摘要 土壤壓密沉陷是一種由土壤受外力因素影響(如抽水或外部載重等)導致孔隙介質及內含流體(空氣及水)產生形變進而造成土壤體積減少的現象,過去相關問題常利用Terzaghi (1925)或Biot (1941)的理論為基礎來求解,其中Biot (1941)的理論被稱為孔彈性理論,但在其理論發展過程中重力影響通常被忽略;本研究將以Lo et al. (2005)的所推導出的多孔隙介質中含有兩相非混和、可壓縮且具有黏滯性流體之孔彈性理論方程式為理論基礎,並考慮各相密度及體積分率的微小變化量重新推導出具重力影響之質量守恆方程式及動量守恆方程式,並使兩平衡方程式與應力應變關係式耦合進而推導出三維具重力影響之孔彈性土壤壓密沉陷理論。
本研究僅以一維垂直方向作為理論範例的研究,在土體達穩態最終沉陷時,土體中流體皆已消散情況下推導出最終土體沉陷量解析解,並將其結果與未考慮重力的結果做比較,探討穩態下不同初始飽和度、排水方式、土體厚度及土壤性質下土壤壓密沉陷受重力影響情形;此外本研究利用顯式有限差分法對控制方程式進行離散,並配合四種初始飽和度(0.7、0.8、0.9及1.0)及三種情境(雙邊排水、單邊頂部排水及單邊底部排水)求得數值解,模擬飽和及非飽和土壤受垂直固定載重影響所產生壓密沉陷情形,發展孔彈性土壤在重力作用下壓密沉陷數值模式。
根據穩態結果可發現重力對於質地較軟之土壤(如黏土)影響較大,對質地較硬之土壤(如砂土)無顯著影響,不考慮重力影響時,最終陷量僅由土壤性質、垂直固定載重及土體厚度決定且與初始飽和度無關,當考慮重力影響最終陷量將隨初始飽和度增加而降低;根據數值模擬的結果發現,不考慮重力影響時,雙邊排水的超額孔隙水壓曲線上下對稱,兩種單邊排水的超額孔隙水壓曲線互為上下顛倒,其餘物理現象皆不受邊界改變影響,考慮重力影響後,土體將產生額外的沉陷量及超額孔隙水壓,雙邊排水的超額孔隙水壓曲線將不再上下對稱,而兩種單邊排水的將因邊界不同產生不同物理現象,根據研究結果顯示,在土體高度較厚或質地較軟的土壤,重力的影響將不可被忽視,此研究結果與Mei (1985)對於飽和土壤受重力影響下壓密沉陷的結果相同。
英文摘要 Soil consolidation is a transient process by which soil volume is decreased due to the coupling between deformation of a porous medium and interstitial fluid flows. The effect of body force has been conventionally ignored in the consolidation theory of poroelasticity for either saturated or unsaturated soils. The objective of this study is to develop the consolidation theory of poroelasticity which incorporates gravitational body forces to discuss different situations. In this study, based on the poroelastic theory of consolidation developed by Lo et al. (2005), the gravity effect is well taken into account in the coupled diffusion equations that feature the excess pore water and air pressure as dependent variables, thus leading to additional first-order time-derivative terms for unsaturated soils. Besides, Saturated soil consolidation is a special case for unsaturated soil consolidation. By reducing the governing equations for unsaturated soil, coupled diffusion equations for saturated soil can be derived. Considering a one-dimensional condition with external loads and three types of drained boundary condition, finite difference methods will be used to solve those equations with consolidation problems. The comparisons of the results with body forces and without body forces reveal that variations in the excess pore water pressure due to the existence of body forces increase with soil depth and more total settlement is induced when body forces is considered.
論文目次 摘要 I
ABSTRACT III
誌謝 X
目錄 XII
表目錄 XIV
表目錄(附錄) XV
圖目錄 XVI
圖目錄(附錄) XXI
符號說明 XXIV
1. 第一章 緒論 1
1.1. 研究目的及方法 1
1.2. 文獻回顧 3
1.3. 本文架構 6
2. 第二章 研究理論 7
2.1. 平衡方程式 7
2.1.1. 動量平衡方程式 7
2.1.2. 質量平衡方程式 10
2.2. 應力應變關係式 12
2.3. 控制方程式 15
2.4. 具重力影響之飽和土壤壓密沉陷理論 19
2.5. 初始條件 22
2.6. 邊界條件 25
3. 第三章 數值模式 29
3.1. 數值離散 32
3.2. 模式建構 36
3.3. 模式參數 38
3.4. 模式驗證 41
4. 結果與討論 51
4.1. 重力對不同性質土壤的影響 51
4.2. 模擬結果討論 55
4.2.1. 重力對非飽和土壤壓密沉陷的影響 55
4.2.2. 重力對非飽和土壤及飽和土壤壓密沉陷之比較 65
4.2.3. 考慮重力影響下土壤單邊排水壓密沉陷比較 69
5. 結論與建議 79
5.1. 結論 79
5.2. 建議 81
附錄 82
A-1 不考慮重力影響之非飽和土壤壓密沉陷孔彈性理論(Lo et al., 2014) 82
A-2 不考慮重力影響之飽和土壤壓密沉陷(Biot, 1941) 87
A-3 非飽和土壤情境二及情境三之模擬結果 90
A-4 飽和土壤各情境模擬結果 100
參考文獻 105

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