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系統識別號 U0026-0312201906010500
論文名稱(中文) 利用位移函數分析多層含水層點載重與點抽水引起之三維壓密問題
論文名稱(英文) Analyzing Three-dimensional Consolidation Problems of Multi-aquifers due to Point Force and Point Sink by Displacement Function
校院名稱 成功大學
系所名稱(中) 土木工程學系
系所名稱(英) Department of Civil Engineering
學年度 108
學期 1
出版年 108
研究生(中文) 楊承桓
研究生(英文) Cheng-Huan Yang
學號 N66061317
學位類別 碩士
語文別 中文
論文頁數 65頁
口試委員 指導教授-林育芸
口試委員-黃忠信
口試委員-黃銘智
口試委員-劉鈞耀
中文關鍵字 壓密問題  點載重  點抽水  多層含水層  位移函數方法 
英文關鍵字 Consolidation problems  Point force  Point sink  Multi-aquifer  Displacement function method 
學科別分類
中文摘要   本研究應用位移函數方法(Displacement function method)來分析單層與多層含水層系統因點載重與點抽水作用引起之三維壓密問題。此方法結合位移函數與拉普拉斯-傅立葉轉換求解Biot的孔隙彈性理論中的方程式。但在(1)時間極短、(2)土層厚度大或(3)土層間的滲透係數差異大的情形下,通解中的自然對數函數會超出MATLAB程式可計算範圍,而出現數值上的困難;本研究提出相關數值技巧以改進此方法在上述極端情況的使用,並減少計算的時間成本。本文先討論單層土層在不同深度位置受點載重或點抽水下的壓密問題;再考慮土層中含阻水層的情形下,滲透係數改變對於壓密行為的影響。此外,也建立有限元素軸對稱模型來驗證位移函數方法之數值結果的準確度;藉由比較(1)結合本研究數值技巧之位移函數方法與(2)有限元素法,本研究提出之數值技巧能不僅有效地解決數值計算上的困難,也顯出位移函數方法在效率上的優勢。
  由本研究結果可知,(1)當點載重或點抽水作用位置越靠近表面時,其導致之最大沉陷量越大,但影響範圍較小;而點抽水影響範圍又較點載重作用下的範圍更廣。(2)無論何種作用力或有無阻水層存在,單一觀測點的水壓皆無法判定該點位移是否達到穩態。因此本文建議在實務應用上,除了針對不同作用的影響調整監測範圍外,同時以有限的水壓觀測值搭配數值分析以完整的評估該區域的沉陷情形。
英文摘要 This thesis used the displacement function method to solve three-dimensional consolidation problems caused by point force or point sink. The displacement functions are the fundamental solutions of Biot’s poroelastic equations in the Laplace-Fourier transformed domain, and are represented by exponential functions. However, at extremely short time, or when soil layer is very thick or when the permeability between soil layers differs significantly, the components in the exponential functions exceed the limit of calculation in MATLAB. Hence, numerical difficulty occurs in these extreme cases. To improve this method and to reduce computational time, we developed several numerical techniques. We solved the consolidation of multi-aquifers cause by point force or point sink applied at different depths. We also discussed the effect of aquitard on the consolidation. Finite element axisymmetric models were carried out to compare with the numerical results calculated by the displacement function method. The comparison show very good agreement between two methods. According to the results, (1) when the location of point force or the point sink is closer to the surface, the maximum settlement is larger, but the range of influence is smaller. Also, the range of influence due to point sink is wider than that due to point force. (2) In general, the pore pressure observed at a single point cannot be used to determine whether the displacement at the same point has reached a steady state.
論文目次 摘要 I
ABSTRACT II
誌謝 XII
目錄 XIII
表目錄 XV
圖目錄 XVI
符號表 XX
第一章 緒論 1
1.1 研究動機與目的 1
1.2 本文架構與內容 2
第二章 文獻回顧 3
2.1 非耦合理論 3
2.2 耦合理論 3
2.3 位移函數方法 4
第三章 相關理論與數值方法 6
3.1 Biot三維多孔彈性理論 6
3.2多孔彈性問題之位移函數方法 8
3.2.1 平面應變壓密 8
3.2.2 三維壓密 9
3.2.3 轉換域中的位移函數解 10
3.3 邊界條件與連續條件 11
3.4 點載重與點抽水條件 12
3.5 數值方法 13
3.5.1 系統矩陣 13
3.5.2 數值反轉換 14
3.5.3 其他數值技巧 15
第四章 數值模擬與結果 20
4.1點載重引致的壓密 20
4.1.1單層非侷限含水層點載重問題 20
4.1.2三層非侷限含水層點載重問題 23
4.2點抽水引致的壓密 25
4.2.1單層非侷限含水層點抽水問題 25
4.2.2三層非侷限含水層點抽水問題 26
4.3計算時間比較 28
第五章 結論 56
參考文獻 58
附錄A 61
附錄B 62
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