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研究生： 張志瑋
Chang, Chih-Wei
論文名稱： 以MQ無網格數值法分析孔彈性理論之研究
The Numerical Analysis of Poroelastic Theory by Multiquardrics Meshless Method
指導教授： 徐國錦
Hsu, Kuo-Chin
共同指導教授: 楊德良
Young, Der-Liang
學位類別： 碩士
Master
系所名稱： 工學院 - 資源工程學系
Department of Resources Engineering
論文出版年： 2012
畢業學年度： 100
語文別： 中文
論文頁數： 79
中文關鍵詞： 孔彈性理論 、無網格法數值方法 、MQ(multiquardrics) 、土體變形 、水壓變化 、地層下陷 、應變效應
外文關鍵詞： Poroelastic theory, Meshless method, (MQ)Multiquardrics, Soil deformation, Change in water pressure, Subsidence, Strain effect
相關次數： 點閱：157  下載：8 
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    • 本研究發展孔彈性模式之MQ (Multiquardrics)無網格數值方法。研發耦合及非耦合模式無網格法，探討地層之孔隙水壓與位移行為。數值方法應用於(1)均質地層(2)異質地層(3)考慮水文地質參數受到應變效應之非線性問題。研究中推導孔彈性理論解析解，作為數值方法驗證之用。探討水文地質參數對模式之敏感度，並研究應變效應對水力傳導係數、孔隙水壓與位移之影響。結果顯示在一維案例中，無網格模式與解析解比較結果良好，誤差百分比均低於0.07%。MQ無網格方法不但數學推導容易且可達到極小的模擬誤差。耦合模式與非耦合模式，兩者比較結果良好，誤差百分比均於3%以內。水文地質參數中，水力傳導係數對模擬結果影響最顯著，直接影響壓力梯度分佈，同時影響水流速率。楊氏模數則影響土體力學性質，對穩態孔隙水壓並無影響，但影響土體之變形。在考慮應變效應之非線性模式中，越靠近出水邊界，水力傳導係數變化越大，孔隙水壓變化較無應變效應下少2%，而位移量改變僅有0.8%。應變效應敏感度分析顯示，初始水力傳導係數越小，應變效應越顯著。研究結論得到MQ無網格數值方法可充分描述孔隙力學之行為，提供土水交互作用模擬之用。

    In this study, multiquardrics(MQ) meshless method is proposed to solve poroelastic problem . Couple and decople models were developed to explore the pore pressure and solid deformation in porous media. The model was applied to cause of (1)homogeneous (2) heterogeneous (3) nonlinear parameters due to strain effect. Analytical solution was derived, for the use of model validation. Sensitivity was performed for hydraulic conductivity, Young’s modulus and effective porosity. The strain effects on hydraulic conductivity, pore pressure and displacement change were also investigated. In 1D case, results of meshless method and analytical solution were compared well, relative error smaller than 0.07%. The results of couple and decouple models were compared. The difference is with a the relative error less than 3%. Sensitivity analysis shows that hydraulic conductivity significantly affects the water pressure gradient distribution and the flow rate; Young’s modulus affects the solid mechanism and deformation but not significantly affects the pore pressure at steady state. In the nonlinear model, the locations more close to Neumann boundary condition, the greater change in hydraulic conductivity. And the change in pore pressure is less 2% than that in no strain effect and the change in displacement is only 0.8%. Sensitivity analysis under strain effect shows that the smaller the initial hydraulic conductivity, the more significant the strain effect is. The multiquardric meshless method is shown to be adequately describe the behavior of the pore mechanics and provides the use for the simulation of soil and water interaction.

    目錄 頁次 摘要……………………………………………………………… I ABTRACT………………………………………………………… II 目錄……………………………………………………………… IV 表目錄…………………………………………………………… VII 圖目錄…………………………………………………………… VIII 第一章 緒論…………………………………………………… 1 1.1研究動機與目的………………………………………… 1 1.2文獻回顧………………………………………………… 3 1.2.1 無網格數值方法………………………………… 3 1.2.2 孔彈性理論……………………………………… 5 1.3 研究流程及步驟………………………………………… 8 第二章 理論介紹……………………………………………… 10 2.1孔彈性理論……………………………………………… 10 2.1.1孔彈性理論之推導……………………………… 10 2.1.2一維孔彈性理論………………………………… 14 2.1.3頂端載重底端不排水邊界之解析解…………… 15 2.1.4頂端載重底端排水邊界之解析解……………… 17 2.2無網格數值方法………………………………………… 20 第三章 無網格模式建構……………………………………… 23 3.1 一維非耦合模式………………………………………… 23 3.1.1 均質地層………………………………………… 23 3.1.2異質地層………………………………………… 26 3.2 一維耦合模式建構……………………………………… 28 第四章 一維孔彈性理論應用………………………………… 32 4.1地層下陷模式建構……………………………………… 32 4.2模擬結果-一維孔彈性理論解析解與無網格法比較…… 35 4.3非耦合模式-異質性地層探討………………………… 41 第五章 耦合模式分析………………………………………… 47 5.1非耦合模式與耦合模式………………………………… 47 5.2地層參數敏感度分析…………………………………… 53 5.3 非線性模式分析……………………………………… 60 5.3.1應變效應對孔隙力學之影響…………………… 60 5.3.2非線性模式模擬結果…………………………… 62 5.3.3應變效應敏感度分析…………………………… 65 第六章 結論與建議…………………………………………… 68 6.1結論……………………………………………………… 68 6.1.1地層下陷模擬與模式驗證……………………… 68 6.1.2耦合模式與非耦合模式比較…………………… 69 6.1.3地層參數敏感度分析…………………………… 69 6.1.4非線性模式分析………………………………… 70 6.2建議……………………………………………………… 71 參考文獻………………………………………………………… 72 表目錄 頁次 表4-1模式驗證中使用之參數設定……………………………… 34 表4-2解析解與數值解於不同深度下的誤差百分比…………… 36 表4-3解析解與數值解於不同時間下之誤差百分比…………… 37 表4-4解析解與數值解於不同時間下的誤差百分比(位移量) … 39 表4-5解析解與數值解於不同深度下的誤差百分比(位移量) … 40 表4-6階變型異質模擬情境表…………………………………… 45 表5-1模式比較中使用之參數設定……………………………… 48 表5-2敏感性分析中使用之參數設定…………………………… 54 圖目錄 頁次 圖1.1研究流程圖………………………………………………… 9 圖2-1 單元體在各方向的應力………………………………… 10 圖2-2 一維度土體與邊界條件設定示意圖，其中F＝0(王,2009) 16 圖2-3為rij表示圖………………………………………………… 21 圖3-1 MQ佈點方式……………………………………………… 23 圖3-2於MQ法中，時間步驟間之關係…………………………… 25 圖4-1排水與載重引起地層下陷之水文地質概念模式(王,2009) 32 圖4-2 一維度土體與邊界條件設定示意圖，其中F＝0(王,2009) 33 圖4-3 MQ之c值敏感度分析…………………………………… 35 圖4-4頂端載重底端排水狀況下，水壓變化與時間之關係圖… 36 圖4-5頂端載重底端排水狀況下，水壓變化與深度之關係圖… 37 圖4-6頂端載重底端排水狀況下，位移量與深度之關係圖…… 38 圖4-7頂端載重底端排水狀況下，時間與累積位移量關係圖… 39 圖4-8頂端載重底端排水狀況下，時間與絕對位移量關係圖… 40 圖4-9異質性地層模擬邊界及初始條件示意圖………………… 41 圖4-10異質性地層模擬情境一，水力傳導係數變化圖………… 42 圖4-11異質性地層模擬情境一，水壓變化與深度關係………… 42 圖4-12異質性地層模擬情境二，水力傳導係數變化圖………… 43 圖4-13異質性地層模擬情境二，水壓變化與深度關係………… 44 圖4-14 K值階變型異質地層模擬，初始與邊界條件設定……… 45 圖4-15 K值階變型異質地層模擬，穩態下壓力之分布圖……… 46 圖5-1 一維度土體與邊界條件設定示意圖，其中F＝0(王,2009) 48 圖5-2頂端載重底端排水狀況下，耦合與非耦合模式比較， 時間與孔隙壓力變化關係圖…………………………………… 49 圖5-3頂端載重底端排水狀況下，耦合與非耦合模式比較， 深度與孔隙壓力變化關係圖…………………………………… 50 圖5-4頂端載重底端排水狀況下，耦合與非耦合模式比較， 時間與位移量變化關係圖……………………………………… 51 圖5-5頂端載重底端排水狀況下，耦合與非耦合模式比較， 深度與位移量變化關係圖……………………………………… 52 圖5-6 一維度頂端排水模擬示意圖與邊界條件設定(王, 2009) 53 圖5-7不同楊氏模數下，壓力變化量與時間關係……………… 55 圖5-8不同楊氏模數下，位移量與時間關係圖………………… 56 圖5-9不同水力傳係數下，孔隙壓力變化與時間關係圖……… 56 圖5-10不同水力傳係數下，位移量與時間關係圖……………… 57 圖5-11不同孔隙率下，孔隙壓力與時間關係圖………………… 58 圖5-12不同孔隙率下，位移量與時間關係圖…………………… 58 圖5-11 二階段耦合示意圖……………………………………… 60 圖5-12 應變效應下，水力傳導係數變化圖……………………… 62 圖5-13 應變效應與無應變效應，孔隙壓力變化與時間關係比較圖……………………………………………………………… 63 圖5-14 應變效應與無應變效應，絕對位移量變化與時間關係比較圖…………………………………………………………… 64 圖5-15為不同初始水力傳導係數，水力傳導係數變化率圖…… 65 圖5-16應變效應下，不同初始水力傳導係數，孔隙壓力變化與時間關係圖……………………………………………………… 66 圖5-17應變效應下，不同初始水力傳導係數，位移量與時間關係圖……………………………………………………………… 67

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